Attrition Data Analysis

library(RCurl)
library(tidyverse)
library(ggplot2)
library(DataExplorer)
library(Hmisc) #rcorr(), generates a correlation matrix
library(corrplot) #to plot the correlation matrix
library(gridExtra) #to arrange plots in a grid
library(RColorBrewer)
library(caret) #ConfusionMatrix()
library(e1071) #naiveBayes()
library(class) #knn
library(combinat)
library(patchwork)
library(GGally)
library(kableExtra) #kable() tables
library(pander) #pander() tables
library(dplyr) #loading this after Hmisc because of conflict in summarize? can use summarise instead
library(olsrr) #variable selection
library(car) #model evaluation

# import data: CaseStudy2-data.csv from AWS S3 msdsds6306 bucket

cs2 = read.table(textConnection(getURL(
  "https://s3.us-east-2.amazonaws.com/msdsds6306/CaseStudy2-data.csv"
)), sep=",", header=TRUE, stringsAsFactors = TRUE)

# save a copy of the data
# write.csv(cs2, file = "data/CaseStudy2-data.csv", row.names = FALSE)

# get a sense of the data
str(cs2)

'data.frame':   870 obs. of  36 variables:
 $ ID                      : int  1 2 3 4 5 6 7 8 9 10 ...
 $ Age                     : int  32 40 35 32 24 27 41 37 34 34 ...
 $ Attrition               : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ BusinessTravel          : Factor w/ 3 levels "Non-Travel","Travel_Frequently",..: 3 3 2 3 2 2 3 3 3 2 ...
 $ DailyRate               : int  117 1308 200 801 567 294 1283 309 1333 653 ...
 $ Department              : Factor w/ 3 levels "Human Resources",..: 3 2 2 3 2 2 2 3 3 2 ...
 $ DistanceFromHome        : int  13 14 18 1 2 10 5 10 10 10 ...
 $ Education               : int  4 3 2 4 1 2 5 4 4 4 ...
 $ EducationField          : Factor w/ 6 levels "Human Resources",..: 2 4 2 3 6 2 4 2 2 6 ...
 $ EmployeeCount           : int  1 1 1 1 1 1 1 1 1 1 ...
 $ EmployeeNumber          : int  859 1128 1412 2016 1646 733 1448 1105 1055 1597 ...
 $ EnvironmentSatisfaction : int  2 3 3 3 1 4 2 4 3 4 ...
 $ Gender                  : Factor w/ 2 levels "Female","Male": 2 2 2 1 1 2 2 1 1 2 ...
 $ HourlyRate              : int  73 44 60 48 32 32 90 88 87 92 ...
 $ JobInvolvement          : int  3 2 3 3 3 3 4 2 3 2 ...
 $ JobLevel                : int  2 5 3 3 1 3 1 2 1 2 ...
 $ JobRole                 : Factor w/ 9 levels "Healthcare Representative",..: 8 6 5 8 7 5 7 8 9 1 ...
 $ JobSatisfaction         : int  4 3 4 4 4 1 3 4 3 3 ...
 $ MaritalStatus           : Factor w/ 3 levels "Divorced","Married",..: 1 3 3 2 3 1 2 1 2 2 ...
 $ MonthlyIncome           : int  4403 19626 9362 10422 3760 8793 2127 6694 2220 5063 ...
 $ MonthlyRate             : int  9250 17544 19944 24032 17218 4809 5561 24223 18410 15332 ...
 $ NumCompaniesWorked      : int  2 1 2 1 1 1 2 2 1 1 ...
 $ Over18                  : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
 $ OverTime                : Factor w/ 2 levels "No","Yes": 1 1 1 1 2 1 2 2 2 1 ...
 $ PercentSalaryHike       : int  11 14 11 19 13 21 12 14 19 14 ...
 $ PerformanceRating       : int  3 3 3 3 3 4 3 3 3 3 ...
 $ RelationshipSatisfaction: int  3 1 3 3 3 3 1 3 4 2 ...
 $ StandardHours           : int  80 80 80 80 80 80 80 80 80 80 ...
 $ StockOptionLevel        : int  1 0 0 2 0 2 0 3 1 1 ...
 $ TotalWorkingYears       : int  8 21 10 14 6 9 7 8 1 8 ...
 $ TrainingTimesLastYear   : int  3 2 2 3 2 4 5 5 2 3 ...
 $ WorkLifeBalance         : int  2 4 3 3 3 2 2 3 3 2 ...
 $ YearsAtCompany          : int  5 20 2 14 6 9 4 1 1 8 ...
 $ YearsInCurrentRole      : int  2 7 2 10 3 7 2 0 1 2 ...
 $ YearsSinceLastPromotion : int  0 4 2 5 1 1 0 0 0 7 ...
 $ YearsWithCurrManager    : int  3 9 2 7 3 7 3 0 0 7 ...

df_summary = summary(cs2)
df_summary

       ID             Age        Attrition           BusinessTravel   DailyRate                       Department  DistanceFromHome
 Min.   :  1.0   Min.   :18.00   No :730   Non-Travel       : 94    Min.   : 103.0   Human Resources       : 35   Min.   : 1.000  
 1st Qu.:218.2   1st Qu.:30.00   Yes:140   Travel_Frequently:158    1st Qu.: 472.5   Research & Development:562   1st Qu.: 2.000  
 Median :435.5   Median :35.00             Travel_Rarely    :618    Median : 817.5   Sales                 :273   Median : 7.000  
 Mean   :435.5   Mean   :36.83                                      Mean   : 815.2                                Mean   : 9.339  
 3rd Qu.:652.8   3rd Qu.:43.00                                      3rd Qu.:1165.8                                3rd Qu.:14.000  
 Max.   :870.0   Max.   :60.00                                      Max.   :1499.0                                Max.   :29.000  
                                                                                                                                  
   Education              EducationField EmployeeCount EmployeeNumber   EnvironmentSatisfaction    Gender      HourlyRate    
 Min.   :1.000   Human Resources : 15    Min.   :1     Min.   :   1.0   Min.   :1.000           Female:354   Min.   : 30.00  
 1st Qu.:2.000   Life Sciences   :358    1st Qu.:1     1st Qu.: 477.2   1st Qu.:2.000           Male  :516   1st Qu.: 48.00  
 Median :3.000   Marketing       :100    Median :1     Median :1039.0   Median :3.000                        Median : 66.00  
 Mean   :2.901   Medical         :270    Mean   :1     Mean   :1029.8   Mean   :2.701                        Mean   : 65.61  
 3rd Qu.:4.000   Other           : 52    3rd Qu.:1     3rd Qu.:1561.5   3rd Qu.:4.000                        3rd Qu.: 83.00  
 Max.   :5.000   Technical Degree: 75    Max.   :1     Max.   :2064.0   Max.   :4.000                        Max.   :100.00  
                                                                                                                             
 JobInvolvement     JobLevel                          JobRole    JobSatisfaction  MaritalStatus MonthlyIncome    MonthlyRate   
 Min.   :1.000   Min.   :1.000   Sales Executive          :200   Min.   :1.000   Divorced:191   Min.   : 1081   Min.   : 2094  
 1st Qu.:2.000   1st Qu.:1.000   Research Scientist       :172   1st Qu.:2.000   Married :410   1st Qu.: 2840   1st Qu.: 8092  
 Median :3.000   Median :2.000   Laboratory Technician    :153   Median :3.000   Single  :269   Median : 4946   Median :14074  
 Mean   :2.723   Mean   :2.039   Manufacturing Director   : 87   Mean   :2.709                  Mean   : 6390   Mean   :14326  
 3rd Qu.:3.000   3rd Qu.:3.000   Healthcare Representative: 76   3rd Qu.:4.000                  3rd Qu.: 8182   3rd Qu.:20456  
 Max.   :4.000   Max.   :5.000   Sales Representative     : 53   Max.   :4.000                  Max.   :19999   Max.   :26997  
                                 (Other)                  :129                                                                 
 NumCompaniesWorked Over18  OverTime  PercentSalaryHike PerformanceRating RelationshipSatisfaction StandardHours StockOptionLevel
 Min.   :0.000      Y:870   No :618   Min.   :11.0      Min.   :3.000     Min.   :1.000            Min.   :80    Min.   :0.0000  
 1st Qu.:1.000              Yes:252   1st Qu.:12.0      1st Qu.:3.000     1st Qu.:2.000            1st Qu.:80    1st Qu.:0.0000  
 Median :2.000                        Median :14.0      Median :3.000     Median :3.000            Median :80    Median :1.0000  
 Mean   :2.728                        Mean   :15.2      Mean   :3.152     Mean   :2.707            Mean   :80    Mean   :0.7839  
 3rd Qu.:4.000                        3rd Qu.:18.0      3rd Qu.:3.000     3rd Qu.:4.000            3rd Qu.:80    3rd Qu.:1.0000  
 Max.   :9.000                        Max.   :25.0      Max.   :4.000     Max.   :4.000            Max.   :80    Max.   :3.0000  
                                                                                                                                 
 TotalWorkingYears TrainingTimesLastYear WorkLifeBalance YearsAtCompany   YearsInCurrentRole YearsSinceLastPromotion
 Min.   : 0.00     Min.   :0.000         Min.   :1.000   Min.   : 0.000   Min.   : 0.000     Min.   : 0.000         
 1st Qu.: 6.00     1st Qu.:2.000         1st Qu.:2.000   1st Qu.: 3.000   1st Qu.: 2.000     1st Qu.: 0.000         
 Median :10.00     Median :3.000         Median :3.000   Median : 5.000   Median : 3.000     Median : 1.000         
 Mean   :11.05     Mean   :2.832         Mean   :2.782   Mean   : 6.962   Mean   : 4.205     Mean   : 2.169         
 3rd Qu.:15.00     3rd Qu.:3.000         3rd Qu.:3.000   3rd Qu.:10.000   3rd Qu.: 7.000     3rd Qu.: 3.000         
 Max.   :40.00     Max.   :6.000         Max.   :4.000   Max.   :40.000   Max.   :18.000     Max.   :15.000         
                                                                                                                    
 YearsWithCurrManager
 Min.   : 0.00       
 1st Qu.: 2.00       
 Median : 3.00       
 Mean   : 4.14       
 3rd Qu.: 7.00       
 Max.   :17.00       
                     

# convert numerical ranking variables to factors
numVars_to_fact = c("Education", "EnvironmentSatisfaction",
                    "JobInvolvement", "JobLevel", "JobSatisfaction",
                    "PerformanceRating", "RelationshipSatisfaction",
                    "StockOptionLevel", "WorkLifeBalance")
cs2_conv = cs2 %>%
  mutate(across(all_of(numVars_to_fact), as.factor))
# check the conversion
str(cs2_conv)

'data.frame':   870 obs. of  36 variables:
 $ ID                      : int  1 2 3 4 5 6 7 8 9 10 ...
 $ Age                     : int  32 40 35 32 24 27 41 37 34 34 ...
 $ Attrition               : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ BusinessTravel          : Factor w/ 3 levels "Non-Travel","Travel_Frequently",..: 3 3 2 3 2 2 3 3 3 2 ...
 $ DailyRate               : int  117 1308 200 801 567 294 1283 309 1333 653 ...
 $ Department              : Factor w/ 3 levels "Human Resources",..: 3 2 2 3 2 2 2 3 3 2 ...
 $ DistanceFromHome        : int  13 14 18 1 2 10 5 10 10 10 ...
 $ Education               : Factor w/ 5 levels "1","2","3","4",..: 4 3 2 4 1 2 5 4 4 4 ...
 $ EducationField          : Factor w/ 6 levels "Human Resources",..: 2 4 2 3 6 2 4 2 2 6 ...
 $ EmployeeCount           : int  1 1 1 1 1 1 1 1 1 1 ...
 $ EmployeeNumber          : int  859 1128 1412 2016 1646 733 1448 1105 1055 1597 ...
 $ EnvironmentSatisfaction : Factor w/ 4 levels "1","2","3","4": 2 3 3 3 1 4 2 4 3 4 ...
 $ Gender                  : Factor w/ 2 levels "Female","Male": 2 2 2 1 1 2 2 1 1 2 ...
 $ HourlyRate              : int  73 44 60 48 32 32 90 88 87 92 ...
 $ JobInvolvement          : Factor w/ 4 levels "1","2","3","4": 3 2 3 3 3 3 4 2 3 2 ...
 $ JobLevel                : Factor w/ 5 levels "1","2","3","4",..: 2 5 3 3 1 3 1 2 1 2 ...
 $ JobRole                 : Factor w/ 9 levels "Healthcare Representative",..: 8 6 5 8 7 5 7 8 9 1 ...
 $ JobSatisfaction         : Factor w/ 4 levels "1","2","3","4": 4 3 4 4 4 1 3 4 3 3 ...
 $ MaritalStatus           : Factor w/ 3 levels "Divorced","Married",..: 1 3 3 2 3 1 2 1 2 2 ...
 $ MonthlyIncome           : int  4403 19626 9362 10422 3760 8793 2127 6694 2220 5063 ...
 $ MonthlyRate             : int  9250 17544 19944 24032 17218 4809 5561 24223 18410 15332 ...
 $ NumCompaniesWorked      : int  2 1 2 1 1 1 2 2 1 1 ...
 $ Over18                  : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
 $ OverTime                : Factor w/ 2 levels "No","Yes": 1 1 1 1 2 1 2 2 2 1 ...
 $ PercentSalaryHike       : int  11 14 11 19 13 21 12 14 19 14 ...
 $ PerformanceRating       : Factor w/ 2 levels "3","4": 1 1 1 1 1 2 1 1 1 1 ...
 $ RelationshipSatisfaction: Factor w/ 4 levels "1","2","3","4": 3 1 3 3 3 3 1 3 4 2 ...
 $ StandardHours           : int  80 80 80 80 80 80 80 80 80 80 ...
 $ StockOptionLevel        : Factor w/ 4 levels "0","1","2","3": 2 1 1 3 1 3 1 4 2 2 ...
 $ TotalWorkingYears       : int  8 21 10 14 6 9 7 8 1 8 ...
 $ TrainingTimesLastYear   : int  3 2 2 3 2 4 5 5 2 3 ...
 $ WorkLifeBalance         : Factor w/ 4 levels "1","2","3","4": 2 4 3 3 3 2 2 3 3 2 ...
 $ YearsAtCompany          : int  5 20 2 14 6 9 4 1 1 8 ...
 $ YearsInCurrentRole      : int  2 7 2 10 3 7 2 0 1 2 ...
 $ YearsSinceLastPromotion : int  0 4 2 5 1 1 0 0 0 7 ...
 $ YearsWithCurrManager    : int  3 9 2 7 3 7 3 0 0 7 ...

# get the proportion of attrition
summary(cs2_conv$Attrition)

 No Yes 
730 140 

NoAttProb = summary(cs2_conv$Attrition)["No"] / sum(summary(cs2_conv$Attrition))
NoAttProb

       No 
0.8390805 

AttProb = summary(cs2_conv$Attrition)["Yes"] / sum(summary(cs2_conv$Attrition))
AttProb

      Yes 
0.1609195 

# plot the distributions of numerical variables with respect to attrition group

# select all variables except ID, EmployeeCount (all=1), and StandardHours (all=80))
cs2_conv_subset = cs2_conv %>% select(-ID, -EmployeeCount, -StandardHours)
# check the modification
# str(cs2_conv_subset)

# filter the numerical variables
numVars = sapply(cs2_conv_subset, is.numeric)
cs2_numerical = cs2_conv_subset[, numVars] #this does not include integers that were converted to factors
# check the result
# str(cs2_numerical)

# function to calculate binwidth (by Freedman-Diaconis rule, Bin Width=2*IQR/(cuberoot(n)))
# and flexibly set a binwidth for each variable
calculate_binwidth = function(data) {
  IQR = quantile(data, 0.75) - quantile(data, 0.25)
  n = length(data)
  bw = 2 * IQR / (n^(1/3))
  return(bw)
}

# iterate over numerical variables and create plots
dist_plots = list()
for (col in names(cs2_numerical)) {
  # calculate binwidth for current variable
  bw = calculate_binwidth(cs2_conv[[col]])
  
  # create a histogram with density not frequency for each variable
  hist_plot = cs2_conv %>%
    ggplot(aes(x = .data[[col]], y = after_stat(density), fill = Attrition)) +
    geom_histogram(binwidth = bw) +
    facet_wrap(~Attrition)
    labs(title = paste("Histogram of", col))

  # save the histogram plot
  # ggsave(filename = paste0("plots/EDA/", col, "_histogram.png"), plot = hist_plot, device = "png")
  
  # create a frequency polygon plot for each variable
  freqpoly_plot = cs2_conv %>%
    ggplot(aes(x = .data[[col]], y = after_stat(density), color = Attrition)) +
    geom_freqpoly(binwidth = bw) +
    labs(title = paste("Frequency Polygon of", col))
  
  # save the frequency polygon plot
  # ggsave(filename = paste0("plots/EDA/", col, "_freqpoly.png"), plot = freqpoly_plot, device = "png")

  dist_plots[[col]] = list(hist_plot, freqpoly_plot)
}

# display plots
for (col in names(cs2_numerical)) {
  print(dist_plots[[col]][[1]]) #displays histogram
  print(dist_plots[[col]][[2]]) #displays frequency polygon
}

# make bar charts to visualize categorical variables with respect to attrition group
# filter categorical variables (factors)
cs2_categorical = cs2_conv %>%
  select(where(is.factor) & -Over18) #Over18(all=Y)
# check the result
# str(cs2_categorical)

# iterate over categorical variables and create bar plots
bar_plots = list()
for (col in names(cs2_categorical)) {
  if (col != "Attrition") { #check if the column is not "Attrition"
    # calculate proportions of each category within each level of Attrition
    prop_cat_data = cs2_categorical %>%
      group_by(Attrition = cs2_conv$Attrition, .data[[col]]) %>%
      dplyr::summarize(count = n(), .groups = "drop") %>% #this gets rid of the warning message about grouping
      group_by(Attrition) %>%
      mutate(proportion = count / sum(count))
    
    bar_plot = prop_cat_data %>%
      ggplot(aes(x = .data[[col]], y = proportion, fill = Attrition)) +
      geom_bar(position = "dodge", stat = "identity") +
      labs(title = paste("Bar Chart of", col)) + 
      coord_flip()
    
    # save the bar plot
    # ggsave(filename = paste0("plots/EDA/", col, "_barplot.png"), plot = bar_plot, device = "png")
    
    bar_plots[[col]] = bar_plot
  }
}

# display plots if they exist (there is no plot for attrition)
for (col in names(cs2_categorical)) {
  if (!is.null(bar_plots[[col]]))
    print(bar_plots[[col]])
}

# are there missing values
missing_count = sum(is.na(cs2_conv) | cs2_conv == "")
writeLines(sprintf("There are %d missing values in the dataset.", missing_count))

There are 0 missing values in the dataset.

create_report(cs2_conv, y = "Attrition")

# compute correlation matrix and p-values
cor_mat = rcorr(as.matrix(cs2_numerical))

# This function makes a table of each variable combination with the correlation coefficient and p-value
# ++++++++++++++++++++++++++++
# flattenCorrMatrix
# ++++++++++++++++++++++++++++
# cormat : matrix of the correlation coefficients
# pmat : matrix of the correlation p-values
flattenCorrMatrix = function(cormat, pmat) {
  ut <- upper.tri(cormat)
  data.frame(
    row = rownames(cormat)[row(cormat)[ut]],
    column = rownames(cormat)[col(cormat)[ut]],
    cor  =(cormat)[ut],
    p = pmat[ut]
    )
}

# call the function with extracted correlation and p-values
corrTable = flattenCorrMatrix(cor_mat$r, cor_mat$P)
kable(head(corrTable), caption = "correlation coefficients") %>% kable_styling(full_width = FALSE, position = "left")

# plot the correlations using corrplot
corrplot(cor_mat$r, type = "upper", order = "hclust", insig = "blank")

# If I include the p.mat argument I get an error.
# I think because pairs of the same variable create an NA.

# extract numerical column names from cs2_numerical
numerical_columns = colnames(cs2_numerical)

# initialize an empty list to store t-test results
t_test_results = list()

# initialize an empty dataframe to store summary statistics
summary_table = data.frame(variable = character(), 
                            mean_Attrition_Yes = numeric(), 
                            mean_Attrition_No = numeric(),
                            p_value = numeric(),
                            stringsAsFactors = FALSE)

# initialize empty lists to store variable names with p-value < 0.05 or < 0.001
significant_variables = list() #p-value < 0.05
super_sig_variables = list() # p-value < 0.001

# loop through each numerical variable
for (col in numerical_columns) {
  # get data for the current column
  data_col = cs2_conv[[col]]
    
  # run a t-test
  t_test_result = t.test(data_col ~ Attrition, data = cs2_conv)
      
  # store t-test result in the list
  t_test_results[[col]] = t_test_result
      
  # extract relevant information and add to summary table
  summary_table = summary_table %>%
    add_row(variable = col,
      mean_Attrition_Yes = mean(data_col[cs2_conv$Attrition == "Yes"], na.rm = TRUE),
      mean_Attrition_No = mean(data_col[cs2_conv$Attrition == "No"], na.rm = TRUE),
      p_value = t_test_result$p.value)
      
  # check if p-value is less than 0.05
  if (t_test_result$p.value < 0.05) {
  significant_variables[[col]] = t_test_result
  }
  # check if p-value is less than 0.001
  if (t_test_result$p.value < 0.001) {
  super_sig_variables[[col]] = t_test_result
  }
}

# print summary table
kable(summary_table, caption = "t-test results") %>% kable_styling(full_width = FALSE, position = "left")

# print list of variables with p-value < 0.05
significant_variable_names = names(significant_variables)
cat("\nVariables with p-value < 0.05:\n", paste(significant_variable_names, collapse = ", "))


Variables with p-value < 0.05:
 Age, DistanceFromHome, MonthlyIncome, TotalWorkingYears, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager

# print list of variables with p-value < 0.001
super_sig_variable_names = names(super_sig_variables)
cat("\nVariables with p-value < 0.001:\n", paste(super_sig_variable_names, collapse = ", "))


Variables with p-value < 0.001:
 Age, MonthlyIncome, TotalWorkingYears, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager

# print full t-test results for variables with p-value < 0.001
cat("\nT-test results for variables with p-value < 0.001:\n")


T-test results for variables with p-value < 0.001:

for (col in super_sig_variable_names) {
  cat("Variable:", col, "\n")
  print(super_sig_variables[[col]])
  cat("\n")
}

Variable: Age 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 4.1509, df = 184.91, p-value = 5.05e-05
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 1.902905 5.350324
sample estimates:
 mean in group No mean in group Yes 
         37.41233          33.78571 


Variable: MonthlyIncome 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 5.3249, df = 228.45, p-value = 2.412e-07
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 1220.382 2654.047
sample estimates:
 mean in group No mean in group Yes 
         6702.000          4764.786 


Variable: TotalWorkingYears 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 5.1364, df = 201.19, p-value = 6.596e-07
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 2.105259 4.728792
sample estimates:
 mean in group No mean in group Yes 
        11.602740          8.185714 


Variable: YearsAtCompany 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 3.7256, df = 191.55, p-value = 0.0002563
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 0.9922099 3.2248155
sample estimates:
 mean in group No mean in group Yes 
         7.301370          5.192857 


Variable: YearsInCurrentRole 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 4.9513, df = 208, p-value = 1.522e-06
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 0.9306052 2.1619584
sample estimates:
 mean in group No mean in group Yes 
         4.453425          2.907143 


Variable: YearsWithCurrManager 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 4.6826, df = 209.75, p-value = 5.084e-06
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 0.8262439 2.0277679
sample estimates:
 mean in group No mean in group Yes 
         4.369863          2.942857 

# extract categorical column names from cs2_categorical, excluding Attrition
categorical_columns = colnames(cs2_categorical)
categorical_columns = categorical_columns[categorical_columns != "Attrition"]

# initialize an empty list to store chi-square test results
chisq_test_results = list()

# initialize an empty dataframe to store summary statistics
summary_table2 = data.frame(variable = character(), 
                            p_value = numeric(),
                            stringsAsFactors = FALSE)

# initialize empty lists to store variable names with p-value < 0.05 or < 0.001
significant_variables2 = list()
super_sig_variables2 = list()

# loop through each categorical variable
for (col in categorical_columns) {
  # create a contingency table for the chi-square test
  contingency_table = table(cs2_conv[[col]], cs2_conv$Attrition)
  # print(contingency_table)
  
  # run a chi-square test
  chisq_test_result = chisq.test(contingency_table)
      
  # store chi-square test result in the list
  chisq_test_results[[col]] = chisq_test_result
      
  # extract relevant information and add to summary table
  summary_table2 = summary_table2 %>%
    add_row(variable = col,
      p_value = chisq_test_result$p.value)
      
  # check if p-value is less than 0.05
  if (chisq_test_result$p.value < 0.05) {
  significant_variables2[[col]] = chisq_test_result
  }
  # check if p-value is less than 0.001
  if (chisq_test_result$p.value < 0.001) {
  super_sig_variables2[[col]] = chisq_test_result
  }
}

# print summary table
kable(summary_table2, caption = "chi-square test results") %>% kable_styling(full_width = FALSE, position = "left")

# print list of variables with p-value < 0.05
significant_variable_names2 = names(significant_variables2)
cat("\nVariables with p-value < 0.05:\n", paste(significant_variable_names2, collapse = ", "))


Variables with p-value < 0.05:
 BusinessTravel, Department, EnvironmentSatisfaction, JobInvolvement, JobLevel, JobRole, JobSatisfaction, MaritalStatus, OverTime, StockOptionLevel, WorkLifeBalance

# print list of variables with p-value < 0.001
super_sig_variable_names2 = names(super_sig_variables2)
cat("\nVariables with p-value < 0.001:\n", paste(super_sig_variable_names2, collapse = ", "))


Variables with p-value < 0.001:
 JobInvolvement, JobLevel, JobRole, MaritalStatus, OverTime, StockOptionLevel

# print full chi-square test results for variables with p-value < 0.001
cat("\nChi-square test results for variables with p-value < 0.001:\n")


Chi-square test results for variables with p-value < 0.001:

for (col in super_sig_variable_names2) {
  cat("Variable:", col, "\n")
  print(super_sig_variables2[[col]])
  cat("\n")
}

Variable: JobInvolvement 

    Pearson's Chi-squared test

data:  contingency_table
X-squared = 41.465, df = 3, p-value = 5.211e-09


Variable: JobLevel 

    Pearson's Chi-squared test

data:  contingency_table
X-squared = 41.533, df = 4, p-value = 2.085e-08


Variable: JobRole 

    Pearson's Chi-squared test

data:  contingency_table
X-squared = 60.543, df = 8, p-value = 3.647e-10


Variable: MaritalStatus 

    Pearson's Chi-squared test

data:  contingency_table
X-squared = 34.406, df = 2, p-value = 3.379e-08


Variable: OverTime 

    Pearson's Chi-squared test with Yates' continuity correction

data:  contingency_table
X-squared = 62.762, df = 1, p-value = 2.333e-15


Variable: StockOptionLevel 

    Pearson's Chi-squared test

data:  contingency_table
X-squared = 56.245, df = 3, p-value = 3.724e-12

# look at co-variation among numerical variables

# function to create scatter plots for each pair of variables
make_scatterplot = function(var1, var2) {
  cs2_conv %>% 
    ggplot(aes(x = .data[[var1]], y = .data[[var2]], color = Attrition)) +
    geom_point(alpha = 0.5, position = "jitter") +
    geom_smooth() +
    labs(title = paste(var1, "vs", var2))
}

# loop through each variable
for (i in 1:(length(super_sig_variable_names) - 1)) {
  var1 = super_sig_variable_names[i]
  
  # plot var1 with every other variable that comes after it in the list
  for (j in (i + 1):length(super_sig_variable_names)) {
    var2 = super_sig_variable_names[j]
    scatter = make_scatterplot(var1, var2)
    
    # display and save the individual plots
    print(scatter) # using print() so it's easier to find where I call the plot
    filename = paste0("plots/EDA/scatter_", var1, "_vs_", var2, ".png")
    # ggsave(filename, plot = scatter, device = "png")
  }
}

# look at co-variation between numerical and categorical variables

# function to create boxplots for each pair of variables
make_boxplot = function(catvar, numvar) {
  cs2_conv %>% group_by(Attrition) %>% 
    ggplot(aes(x = .data[[catvar]], y = .data[[numvar]], fill = Attrition)) +
    geom_boxplot() +
    coord_flip() +
    labs(title = paste(catvar, "vs", numvar))
}

# loop through each variable
for (i in 1:(length(super_sig_variable_names2))) {
  catvar = super_sig_variable_names2[i]
  
  # plot catvar with every numvar
  for (j in 1:length(super_sig_variable_names)) {
    numvar = super_sig_variable_names[j]
    boxplt = make_boxplot(catvar, numvar)
    
    # display and save the individual plots
    # I tried to display them in a grid in the interest of space, but they are just too small.
    print(boxplt)
    filename = paste0("plots/EDA/boxplt_", catvar, "_vs_", numvar, ".png")
    # ggsave(filename, plot = boxplt, device = "png")
  }
}

# look at co-variation among categorical variables

# It probably is easier to see relationships if I were to calculate proportions a different way to normalize the data.
# Currently, proportions are calculated like this. For each attrition group, and each level of variable 1, the count of each level of variable 2 (the fill variable) is divided by the sum of the total count for all levels of that variable (within the attrition and variable 1 level).

make_barchart = function(var1, var2) {
  cs2_conv %>% 
    group_by(Attrition, .data[[var1]], .data[[var2]]) %>%
    dplyr::summarize(n = n(), .groups = 'drop') %>%  #count occurrences within each group
    group_by(Attrition, .data[[var1]]) %>%  # group by Attrition and var1
    mutate(prop = n / sum(n)) %>% #calculate proportion within each group
    ggplot(aes(y = .data[[var1]], x = prop, fill = .data[[var2]])) +  #use prop as fill
    geom_bar(stat = "identity", position = position_dodge2(preserve = "single")) +
    facet_wrap(~Attrition, labeller = labeller(Attrition = c("No" = "No Attrition", "Yes" = "Yes Attrition"))) +
    labs(title = paste(var1, "vs", var2),
         y = var1,
         x = paste0("Proportion of ", var2, " within Attrition and ", var1, " level"),
         fill = var2) +
    theme_bw() +
    theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
    scale_fill_brewer(palette = "Set1")
}

# loop through each variable
for (i in 1:(length(super_sig_variable_names2) - 1)) {
  var1 = super_sig_variable_names2[i]
    
  for (j in (i + 1):length(super_sig_variable_names2)) {
    var2 = super_sig_variable_names2[j]
    barplt = make_barchart(var1, var2)
    
    # display and save the individual plots
    print(barplt)
    filename = paste0("plots/EDA/barplt_", var1, "_vs_", var2, ".png")
    # ggsave(filename, plot = barplt, device = "png")
  }
}

cs2_conv2 = cs2_conv %>% 
  mutate(
    PercentWrkYrsAtCompany = ifelse(TotalWorkingYears == 0, 0,
                                    round(YearsAtCompany / TotalWorkingYears * 100, 2)),
    PercentYrs_wManager = ifelse(TotalWorkingYears == 0, 0,
                                 round(YearsWithCurrManager / TotalWorkingYears * 100, 2)),
    PercentYrs_inRole = ifelse(TotalWorkingYears == 0, 0,
                               round(YearsInCurrentRole / TotalWorkingYears * 100, 2)),
    PercentYrs_inRoleAtComp = ifelse(YearsAtCompany == 0, 0,
                               round(YearsInCurrentRole / YearsAtCompany * 100, 2))
  )
# str(cs2_conv2)
# summary(cs2_conv2)

# plot these derived variables with other variables that seem relevant and alone to see the distributions
cs2_conv2 %>% ggplot(aes(x = Age, y = PercentWrkYrsAtCompany, color = Attrition)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()

cs2_conv2 %>% ggplot(aes(x = MonthlyIncome, y = PercentWrkYrsAtCompany, color = Attrition)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()

cs2_conv2 %>% ggplot(aes(x = Age, y = PercentYrs_inRoleAtComp, color = Attrition)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()

cs2_conv2 %>% ggplot(aes(x = MonthlyIncome, y = PercentYrs_inRoleAtComp, color = Attrition)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()

cs2_conv2 %>% ggplot(aes(x = MaritalStatus, y = PercentWrkYrsAtCompany, fill = Attrition)) +
  geom_boxplot(position = "dodge")

cs2_conv2 %>% ggplot(aes(x = JobLevel, y = PercentWrkYrsAtCompany, fill = Attrition)) +
  geom_boxplot(position = "dodge")

cs2_conv2 %>% ggplot(aes(x = MaritalStatus, y = PercentYrs_inRoleAtComp, fill = Attrition)) +
  geom_boxplot(position = "dodge")

cs2_conv2 %>% ggplot(aes(x = JobLevel, y = PercentYrs_inRoleAtComp, fill = Attrition)) +
  geom_boxplot(position = "dodge")

cs2_conv2 %>% ggplot(aes(x = PercentWrkYrsAtCompany, after_stat(density), fill = Attrition)) +
  geom_histogram(binwidth = 10) + facet_wrap(~Attrition)

cs2_conv2 %>% ggplot(aes(x = PercentYrs_inRoleAtComp, y = after_stat(density), fill = Attrition)) +
  geom_histogram(binwidth = 10) + facet_wrap(~Attrition)

# run t-tests to check for possible differences
t.test(PercentWrkYrsAtCompany ~ Attrition, data = cs2_conv2)


    Welch Two Sample t-test

data:  PercentWrkYrsAtCompany by Attrition
t = 0.94099, df = 187.08, p-value = 0.3479
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 -3.316668  9.366557
sample estimates:
 mean in group No mean in group Yes 
         68.70130          65.67636 

t.test(PercentYrs_wManager ~ Attrition, data = cs2_conv2)


    Welch Two Sample t-test

data:  PercentYrs_wManager by Attrition
t = 3.2429, df = 188.9, p-value = 0.001399
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
  3.638589 14.938990
sample estimates:
 mean in group No mean in group Yes 
         41.57358          32.28479 

t.test(PercentYrs_inRole ~ Attrition, data = cs2_conv2)


    Welch Two Sample t-test

data:  PercentYrs_inRole by Attrition
t = 3.058, df = 189.5, p-value = 0.00255
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
  3.079205 14.270408
sample estimates:
 mean in group No mean in group Yes 
         42.37452          33.69971 

t.test(PercentYrs_inRoleAtComp ~ Attrition, data = cs2_conv2)


    Welch Two Sample t-test

data:  PercentYrs_inRoleAtComp by Attrition
t = 3.55, df = 177.46, p-value = 0.0004933
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
  5.468542 19.158856
sample estimates:
 mean in group No mean in group Yes 
          59.0657           46.7520 

cs2_conv2 %>% ggplot(aes(x = PercentYrs_inRoleAtComp, y = MonthlyIncome, color = JobLevel)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()

cs2_conv2 %>% ggplot(aes(x = PercentYrs_inRoleAtComp, y = Age, color = JobLevel)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()

cs2_conv2 %>% ggplot(aes(x = MonthlyIncome, y = Age, color = JobLevel)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()

modelIdx = c(2,15,16,17,19,20,24,29,30,33,34,36) #indexes of predicted top features
# these are the indexes for Age, JobInvolvement, JobLevel, JobRole, MaritalStatus, MonthlyIncome, OverTime, StockOptionLevel, TotalWorkingYears, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager

# initialize an empty data frame to store results
results = data.frame(Index1 = integer(), Index2 = integer(), Index3 = integer(), Sensitivity = numeric(), Specificity = numeric(), Accuracy = numeric(), stringsAsFactors = FALSE)

# number of different splits
iters = 50

# 70-30 train/test split
splitPerc = 0.7

# generate all combinations of 3 indexes
index_combinations = combinat::combn(modelIdx, 3)

# loop through each combination of 3 indexes
for (i in 1:ncol(index_combinations)) {
  index_set = index_combinations[, i]

  # create holders for the sensitivity, specificity, and accuracy for each iteration
  masterSens = numeric(iters)
  masterSpec = numeric(iters)
  masterAcc = numeric(iters)

  # iterate over the specified number of iterations
  for (j in 1:iters) {
    set.seed(j)

    # sample 70% for training
    trainIdx = sample(1:dim(cs2_conv2)[1], round(splitPerc * dim(cs2_conv2)[1]))
    # select the rows for training
    AttritionTrn = cs2_conv2[trainIdx, ]
    # select the remaining rows for testing
    AttritionTst = cs2_conv2[-trainIdx, ]

    # temporarily set the current indexes for modeling
    temp_modelIdx = index_set

    # train the model
    modelNB = naiveBayes(AttritionTrn[, temp_modelIdx], AttritionTrn$Attrition, laplace = 1)

    # predict using the model
    preds = predict(modelNB, AttritionTst[, temp_modelIdx])

    # make a confusion matrix
    CM = confusionMatrix(table(preds, AttritionTst$Attrition))

    # store sensitivity, specificity, and accuracy
    masterSens[j] = CM$byClass["Sensitivity"]
    masterSpec[j] = CM$byClass["Specificity"]
    masterAcc[j] = CM$overall["Accuracy"]
  }

  # calculate average sensitivity, specificity, and accuracy
  avg_sensitivity = mean(masterSens)
  avg_specificity = mean(masterSpec)
  avg_accuracy = mean(masterAcc)

  # store the results including the three indexes
  results = rbind(results, list(Index1 = index_set[1], Index2 = index_set[2], Index3 = index_set[3], Sensitivity = avg_sensitivity, Specificity = avg_specificity, Accuracy = avg_accuracy))
}

# output the results
results = results %>% arrange(-Specificity)
kable(head(results, 10), caption = "3 variable combos to predict attrition") %>% kable_styling(full_width = FALSE, position = "left")

# plot positive predictors example: Job Level for presentation
# also plot negative predictor: Gender

# I revert to using my original converted dataset `cs2_conv`.

# plot positive predictor example: job level and attrition
# calculation of proportion of employees: employees in job level attrition yes / total employees in job level, to normalize each job level 
jobLevel_bar = cs2_conv %>%
  group_by(JobLevel, Attrition) %>%
  dplyr::summarize(n = n()) %>%
  mutate(prop = n / sum(n)) %>%
  filter(Attrition == "Yes") %>% 
  ggplot(aes(y = JobLevel, x = prop, fill = JobLevel)) +
  geom_bar(stat = "identity") +
  labs(y = "Job Level", x = "Proportion of Attrition",
       fill = "Job Level",
       title = "Proportion of Attrition within Each Job Level",
       caption = "Normalized by Total Employees per Job Level") +
  theme_bw() +
  scale_fill_brewer(palette = "Set1")
print(jobLevel_bar)

# ggsave(jobLevel_bar, filename = "plots/top3_jobLevel_bar.png")

# plot negative predictor example: gender and attrition
genderBar = cs2_conv %>% 
  group_by(Gender, Attrition) %>%
  dplyr::summarize(n = n()) %>%
  mutate(prop = n / sum(n)) %>%
  filter(Attrition == "Yes") %>% 
  ggplot(aes(y = Gender, x = prop)) +
  geom_bar(stat = "identity", fill = "#377EB8") + #fill color = Attrition group blue
  labs(y = "Gender", x = "Proportion of Attrition",
       fill = "Gender",
       title = "Proportion of Attrition within Each Gender",
       caption = "Normalized by Total Employees per Gender") +
  theme_bw() +
  theme(text = element_text(size = 12))
genderBar

# ggsave(genderBar, filename = "plots/top3negExample_genderBar.png")

# plot the other positive predictors for presentation: Monthly Income, Job Level and Overtime

# plot monthly income and attrition with a boxplot and two histograms
incomeBox = cs2_conv %>% 
  ggplot(aes(x = MonthlyIncome, y = Attrition, fill = Attrition)) +
  geom_boxplot() +
  ylab("Attrition") +
  theme_bw() +
  theme(legend.position = "none",
        axis.title.x = element_blank()) +
  scale_fill_brewer(palette = "Set1")

yAtt_hist = cs2_conv %>% filter(Attrition == "Yes") %>% 
  ggplot(aes(x = MonthlyIncome)) +
  geom_histogram(binwidth = 1000, fill = "#377EB8") +
  labs(title = "Distribution of Monthly Income by Employee Attrition",
       y = "Yes") +
  theme_bw() +
    theme(legend.position = "none",
          axis.title.x = element_blank())
  
nAtt_hist = cs2_conv %>% filter(Attrition == "No") %>% 
  ggplot(aes(x = MonthlyIncome)) +
  geom_histogram(binwidth = 1000, fill = "#E41A1C") +
  labs(#title = "Employee Attrition and Monthly Income",
       y = "No") +
  theme_bw() + 
  theme(legend.position = "none")

incomePlt = yAtt_hist / incomeBox / nAtt_hist
print(incomePlt)

# ggsave(incomePlt, filename = "plots/top3_incomeDist.png")


# make co-variation plots split by attrition groups

# plot positive predictor: job level and monthly income
income_jobLevel_box = ggplot(cs2_conv, aes(x = JobLevel, y = MonthlyIncome, fill = Attrition)) +
  geom_boxplot() +
  labs(x = "Job Level", y = "Monthly Income", fill = "Attrition") +
  ggtitle("Monthly Income by Job Level and Attrition") +
  theme_bw() + 
  scale_fill_brewer(palette = "Set1")
income_jobLevel_box

# ggsave(income_jobLevel_box, filename = "plots/top3_income_jobLevel_box.png")


# plot positive predictor: job level and attrition, with NO overtime
# employees NOT working overtime
jobLevel_OTno_bar = cs2_conv %>%
  group_by(OverTime, JobLevel, Attrition) %>%
  dplyr::summarize(n = n()) %>%
  mutate(prop = n / sum(n)) %>%
  filter(Attrition == "Yes" & OverTime == "No") %>%
  ggplot(aes(y = JobLevel, x = prop, fill = JobLevel)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(y = "Job Level", x = "Proportion of Attrition",
       fill = "Job Level",
       subtitle = "Proportion of Attrition within Each Job Level",
       title = "Employees with No Overtime Hours",
       caption = "Normalized by Total Employees per Job Level") +
  xlim(0.00, 0.55) +
  theme_bw() +
  theme(text = element_text(size = 12)) +
  scale_fill_brewer(palette = "Set1")
print(jobLevel_OTno_bar)

# ggsave(jobLevel_OTno_bar, filename = "plots/top3_jobLevel_OTno_bar.png")

# plot positive predictor: job level and attrition, with overtime
# employees working at least an hour of overtime
jobLevel_OTyes_bar = cs2_conv %>%
  group_by(OverTime, JobLevel, Attrition) %>%
  dplyr::summarize(n = n()) %>%
  mutate(prop = n / sum(n)) %>%
  filter(Attrition == "Yes" & OverTime == "Yes") %>%
  ggplot(aes(y = JobLevel, x = prop, fill = JobLevel)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(y = "Job Level", x = "Proportion of Attrition",
       fill = "Job Level",
       subtitle = "Proportion of Attrition within Each Job Level",
       title = "Employees Working Overtime",
       caption = "Normalized by Total Employees per Job Level") +
  xlim(0.00, 0.55) +
  theme_bw() +
  theme(text = element_text(size = 12)) +
  scale_fill_brewer(palette = "Set1")
print(jobLevel_OTyes_bar)

# ggsave(jobLevel_OTyes_bar, filename = "plots/top3_jobLevel_OTyes_bar.png")

# find 25th, 50th and 75th percentile of monthly incomes for each attrition group and job level
# is there a stay/go cut off for job level 4
mid50_income = cs2_conv %>%
  group_by(Attrition, JobLevel) %>%
  dplyr::summarise(q25 = quantile(MonthlyIncome, 0.25),
            median = median(MonthlyIncome),
            q75 = quantile(MonthlyIncome, 0.75))
kable(mid50_income, caption = "monthly income q25, median, q75 for each job level and attrition group") %>% kable_styling(full_width = FALSE, position = "left")

# extra plots for the appendix

# plot positive predictor example: overtime and attrition
# calculation of proportion of employees: employees in overtime group & attrition yes / total employees in overtime group, to normalize each overtime group 
overtime_bar = cs2_conv %>%
  group_by(OverTime, Attrition) %>%
  dplyr::summarize(n = n()) %>%
  mutate(prop = n / sum(n)) %>%
  filter(Attrition == "Yes") %>% 
  ggplot(aes(y = OverTime, x = prop)) +
  geom_bar(stat = "identity", fill = "#377EB8") +
  labs(y = "Overtime", x = "Proportion of Attrition",
       fill = "Overtime",
       title = "Proportion of Attrition for Employees With and Without Overtime",
       caption = "Normalized by Total Employees per OT Group") +
  theme_bw() +
  scale_fill_brewer(palette = "Set1")
print(overtime_bar)

# ggsave(overtime_bar, filename = "plots/appendix/top3_overtime_bar.png")

# plot positive predictor: monthly income and overtime
income_OT_box = ggplot(cs2_conv, aes(x = OverTime, y = MonthlyIncome, fill = Attrition)) +
  geom_boxplot() +
  labs(x = "Overtime", y = "Monthly Income", fill = "Attrition") +
  ggtitle("Monthly Income by Overtime and Attrition") +
  theme_bw() +
  scale_fill_brewer(palette = "Set1")
print(income_OT_box)

# ggsave(income_OT_box, filename = "plots/appendix/top3_income_OT_box.png")

# reorder levels of JobRole from low income/level to high
cs2_conv$JobRole = factor(cs2_conv$JobRole, levels = c("Sales Representative", "Laboratory Technician", "Human Resources", "Research Scientist", "Sales Executive", "Healthcare Representative", "Manufacturing Director", "Research Director", "Manager"))

# rename numerical and categorical variables for nicer axis titles
custom_labels = list(
  JobLevel = "Job Level",
  JobRole = "Job Role",
  MaritalStatus = "Marital Status",
  MonthlyIncome = "Monthly Income",
  OverTime = "Overtime",
  StockOptionLevel = "Stock Option Level",
  TotalWorkingYears = "Total Working Years",
  YearsAtCompany = "Years At Company",
  YearsInCurrentRole = "Years in Current Role",
  YearsWithCurrManager = "Years with Current Manager"
)

# a function to get the appropriate label from the list above
get_label = function(var) {
  if (var %in% names(custom_labels)) {
    return(custom_labels[[var]])
  } else {
    return(var)
  }
}

# numerical_columns = colnames(cs2_numerical)
for (numvar in numerical_columns) {
  boxplot = cs2_conv %>%  
    ggplot(aes(x = .data[[numvar]], y = JobRole, fill = JobRole)) +
    geom_boxplot() +
    labs(title = paste("Job Role vs", get_label(numvar)),
         x = get_label(numvar), y = "Job Role") +
    theme_bw() +
    theme(legend.position = "none",
          text = element_text(size = 12)) +
    scale_fill_brewer(palette = "Spectral")
  
  # display each plot
  print(boxplot)
  
  # create a unique filename for each plot
  filename = paste0("plots/JobRole/boxplt_JobRole_vs_", numvar, ".png")
  
  # save the plots
  # ggsave(filename, plot = boxplot, device = "png")
}

# categorical_columns = colnames(cs2_categorical)
cat_cols = categorical_columns[!categorical_columns %in% "JobRole"]

for (catvar in cat_cols) {
  barplot = cs2_conv %>%
    group_by(JobRole, .data[[catvar]], .drop = FALSE) %>%
    dplyr::summarize(count = n(), .groups = 'drop') %>%
    group_by(JobRole) %>%
    mutate(prop = count / sum(count)) %>%
    ggplot(aes(y = JobRole, x = prop, fill = .data[[catvar]])) +
    geom_bar(stat = "identity", position = "dodge") +
    labs(title = paste("Job Role vs", get_label(catvar)),
         y = "Job Role", x = "Proportion", fill = get_label(catvar)) +
    theme_bw() +
    theme(legend.position = "right",
          text = element_text(size = 12)) +
    scale_fill_brewer(palette = "Set1")
  
  #display each plot
  print(barplot)
  
  # create a unique filename for each plot
  filename = paste0("plots/JobRole/barplot_JobRole_vs_", catvar, ".png")
  
  # save the plots
  # ggsave(filename, plot = barplot, device = "png")
}

# reorder levels of JobRole
cs2_conv2$JobRole = factor(cs2_conv2$JobRole, levels = c("Sales Representative", "Laboratory Technician", "Human Resources", "Research Scientist", "Sales Executive", "Healthcare Representative", "Manufacturing Director", "Research Director", "Manager"))

# group roles by median income level (low, med, high)
# test difference in salary between low and mid and mid and high
cs2_conv2 = cs2_conv2 %>% 
  mutate(incomeGroup = case_when(
      JobRole %in% c("Sales Representative", "Research Scientist", "Human Resources", "Laboratory Technician") ~ "Low",
      JobRole %in% c("Sales Executive", "Manufacturing Director", "Healthcare Representative") ~ "Medium",
      TRUE ~ "High"
    )
  ) %>%
  mutate(incomeGroup = factor(incomeGroup, levels = c("Low", "Medium", "High")))

# check the conversion
# head(cs2_conv2)

# filter the data
cs2_LowMid = cs2_conv2 %>% filter(incomeGroup != "High")
cs2_MidHigh = cs2_conv2 %>% filter(incomeGroup != "Low")

# perform t-tests
t_test_LowMid = t.test(MonthlyIncome ~ incomeGroup, data = cs2_LowMid)
t_test_MidHigh = t.test(MonthlyIncome ~ incomeGroup, data = cs2_MidHigh)

# print the results
t_test_LowMid


    Welch Two Sample t-test

data:  MonthlyIncome by incomeGroup
t = -27.646, df = 522.61, p-value < 2.2e-16
alternative hypothesis: true difference in means between group Low and group Medium is not equal to 0
95 percent confidence interval:
 -4268.293 -3701.937
sample estimates:
   mean in group Low mean in group Medium 
            3167.491             7152.606 

t_test_MidHigh


    Welch Two Sample t-test

data:  MonthlyIncome by incomeGroup
t = -31.529, df = 152.77, p-value < 2.2e-16
alternative hypothesis: true difference in means between group Medium and group High is not equal to 0
95 percent confidence interval:
 -9904.980 -8736.867
sample estimates:
mean in group Medium   mean in group High 
            7152.606            16473.529 

# Naive Bayes classifier
# start with lots of explanatory variables and distill down manually one at a time using domain knowledge

# str(cs2_conv2) #this is the dataframe with my derived variables too


# list indexes of explanatory variables 

# for reference:
# modelIdx = c(2,4:9,11:19,21,22,25:27,29:40) #list of all possible features
# modelIdx = c(16,19,20,24,29) #top 5 features

# start here: list of indexes of 18 significant variables (alpha = 0.05) from t-tests and chi-square tests
# modelIdx = c(2,4,6,7,12,15,16,17,18,19,20,24,29,30,32,33,34,36) #significant features: sens 85.6%, spec 60.7%

# end here: list of indexes which produced highest specificity, derived manually
modelIdx = c(12,15,16,17,19,20,24,29,30,32,33,34,36) #sensitivity: 84.4% specificity: 62.3%

# other promising combinations:
# modelIdx = c(2,12,15,16,17,19,20,24,29,30,32,33,34,36) #84.2, 61.4
# modelIdx = c(12,15,16,17,20,24,29,30,32,33,34,36) #84.6, 61.3
# modelIdx = c(15,16,17,20,24,29,30,32,33,34,36) #84, 60.5


# list the explanatory variables used
names(cs2_conv2[,modelIdx])

 [1] "EnvironmentSatisfaction" "JobInvolvement"          "JobLevel"                "JobRole"                
 [5] "MaritalStatus"           "MonthlyIncome"           "OverTime"                "StockOptionLevel"       
 [9] "TotalWorkingYears"       "WorkLifeBalance"         "YearsAtCompany"          "YearsInCurrentRole"     
[13] "YearsWithCurrManager"   

# how many explanatory variables are used
length(modelIdx)

[1] 13

# 100 different splits
iters = 100

# make holders for the stats from each iteration
masterAccu = matrix(nrow = iters, ncol = 2)
masterPval = matrix(nrow = iters, ncol = 2)
masterSens = matrix(nrow = iters, ncol = 2)
masterSpec = matrix(nrow = iters, ncol = 2)

# 70-30 train/test split
splitPerc = .7

for(i in 1:iters)
{
  set.seed(i)
  
  # sample 70%
  trainIdx = sample(1:dim(cs2_conv2)[1], round(splitPerc*dim(cs2_conv2)[1]))
  # choose the rows that match those sampled numbers for training
  AttritionTrn = (cs2_conv2[trainIdx,])
  # and the others for testing
  AttritionTst = (cs2_conv2[-trainIdx,])
  
  # head(AttritionTrn)
  # head(AttritionTst)
  
  # give the model the training variables, training labels
  modelNB = naiveBayes(AttritionTrn[,modelIdx], AttritionTrn$Attrition, laplace = 1)
  
  # use the model and testing explanatory variables (modelIdx) to predict the testing labels
  preds = predict(modelNB, AttritionTst[,modelIdx])
  
  # make a confusion matrix comparing the predicted labels to the true labels
  # predicted labels = rows, true labels = cols
  CM = confusionMatrix(table(preds, AttritionTst$Attrition))
  
  masterAccu[i,] = c(i, CM$overall["Accuracy"])
  masterPval[i,] = c(i, CM$overall["AccuracyPValue"])
  masterSens[i,] = c(i, CM$byClass["Sensitivity"])
  masterSpec[i,] = c(i, CM$byClass["Specificity"])
}

# organize the output data
colnames(masterAccu) = c("Seed", "Accuracy")
colnames(masterPval) = c("Seed", "AccuracyPValue")
colnames(masterSens) = c("Seed", "Sensitivity")
colnames(masterSpec) = c("Seed", "Specificity")
NB_results = merge(as.data.frame(masterAccu), as.data.frame(masterPval), by = "Seed", all = TRUE)
NB_results = merge(NB_results, as.data.frame(masterSens), by = "Seed", all = TRUE)
NB_results = merge(NB_results, as.data.frame(masterSpec), by = "Seed", all = TRUE)

NB_stats = colMeans(NB_results[,2:5])
NB_stats = data.frame(
  Metric = c("Accuracy", "AccuracyPValue", "Sensitivity", "Specificity"),
  Value = c(sprintf("%.1f%%", NB_stats[1]*100),
            sprintf("%.2e", NB_stats[2]),
            sprintf("%.1f%%", NB_stats[3]*100),
            sprintf("%.1f%%", NB_stats[4]*100)))

# output the metrics of the naive bayes model
cat("Naive Bayes \n")

Naive Bayes 

cat("Accuracy:", NB_stats[1,2], "\n")

Accuracy: 80.9% 

cat("Accuracy P-Value:", NB_stats[2,2], "\n")

Accuracy P-Value: 7.83e-01 

cat("Sensitivity:", NB_stats[3,2], "\n")

Sensitivity: 84.4% 

cat("Specificity:", NB_stats[4,2], "\n")

Specificity: 62.3% 

# perhaps it would be more efficient to do the train test splits on the outer loop?
# also I should place the progress reporter (Sys.time()) in a different place in the code

# Function to calculate sensitivity, specificity for all combinations of a given number of variables
calculate_combinations <- function(modelIdx, max_vars = 18, iters = 10, splitPerc = 0.7) {
  
  # Initialize an empty list to store results
  results_list <- list()
  
  # Initialize a variable to keep track of the maximum specificity reached
  max_specificity_so_far <- 0
  
  # Initialize a variable to store the maximum mean specificity from previous iterations
  max_mean_specificity_previous <- 0

  # Loop over different number of variables
  for (num_vars in seq(8, max_vars)) {
    cat("Number of variables:", num_vars, "\n")
    start_time <- Sys.time()
    
    # Generate all combinations of variables
    index_combinations <- combinat::combn(modelIdx, num_vars)
    
    # Initialize an empty list to store results for this iteration
    temp_results_list <- list()
    
    # Loop through each combination of variables
    for (i in 1:ncol(index_combinations)) {
      index_set <- index_combinations[, i]
      
      # Create holders for the sensitivity, specificity for each iteration
      masterSens <- numeric(iters)
      masterSpec <- numeric(iters)
      
      # Iterate over the specified number of iterations
      for (j in 1:iters) {
        set.seed(j)
        
        # Sample 70% for training
        trainIdx <- sample(1:dim(cs2_conv2)[1], round(splitPerc * dim(cs2_conv2)[1]))
        # Select the rows for training
        AttritionTrn <- cs2_conv2[trainIdx, ]
        # Select the remaining rows for testing
        AttritionTst <- cs2_conv2[-trainIdx, ]
        
        # Temporarily set the current indexes for modeling
        temp_modelIdx <- index_set
        
        # Train the model
        modelNB <- naiveBayes(AttritionTrn[, temp_modelIdx], AttritionTrn$Attrition, laplace = 1)
        
        # Predict using the model
        preds <- predict(modelNB, AttritionTst[, temp_modelIdx])
        
        # Confusion matrix
        CM <- confusionMatrix(table(preds, AttritionTst$Attrition))
        
        # Store sensitivity, specificity
        masterSens[j] <- CM$byClass["Sensitivity"]
        masterSpec[j] <- CM$byClass["Specificity"]
      }
      
      # Average sensitivity, specificity
      avg_sensitivity <- mean(masterSens)
      avg_specificity <- mean(masterSpec)
      
      # Store the results including the combination of variables
      temp_results_list[[i]] <- list(variables = index_set, Sensitivity = avg_sensitivity, Specificity = avg_specificity)
    }
    
    end_time <- Sys.time()
    time_taken <- end_time - start_time
    cat("Time taken:", time_taken, "\n")
    
    # Store the results for this iteration
    results_list[[num_vars]] <- temp_results_list
    
    # Get the maximum mean specificity for this number of variables
    max_mean_specificity_current <- max(sapply(temp_results_list, function(x) x$Specificity))
    
    # Check if the maximum mean specificity for the current number of variables is less than the previous maximum
    if (max_mean_specificity_current < max_mean_specificity_previous) {
      cat("Maximum specificity reached for", num_vars, "variables is less than previous maximum. Stopping further iterations.\n")
      break
    }
    
    # Update the maximum mean specificity from previous iterations
    max_mean_specificity_previous <- max_mean_specificity_current
  }
  
  return(results_list)
}

# Define the list of indexes to loop through
modelIdx <- c(2,4,6,7,12,15,16,17,18,19,20,24,29,30,32,33,34,36) #significant features

# Define the maximum number of variables
max_vars <- 18

# Call the function to calculate combinations
results <- calculate_combinations(modelIdx, max_vars)

# Determine the maximum expected number of combinations
max_combinations <- max_vars * 10  # Assuming a maximum of 10 combinations per number of variables

# Preallocate the output data frame with maximum expected number of rows
output_df <- data.frame(Number_of_Variables = integer(max_combinations),
                        Variable_Indexes = character(max_combinations),
                        Mean_Sensitivity = numeric(max_combinations),
                        Mean_Specificity = numeric(max_combinations),
                        Sum_of_Sensitivity_and_Specificity = numeric(max_combinations),
                        stringsAsFactors = FALSE)

# Loop over different number of variables
for (num_vars in seq(8, max_vars)) {
  cat("\nTop 10 combinations with the highest specificity for", num_vars, "variables:\n")

  sorted_indices <- order(sapply(results[[num_vars]], function(x) x$Specificity), decreasing = TRUE)
  for (i in 1:min(10, length(sorted_indices))) {
    index <- sorted_indices[i]
    cat("Combination", i, ": Variables =", results[[num_vars]][[index]]$variables, ", Specificity =", results[[num_vars]][[index]]$Specificity, "\n")

    # Assign the results to the preallocated rows in the output data frame
    row_index <- (num_vars - 10) * 10 + i  # Calculate the row index
    output_df$Number_of_Variables[row_index] <- num_vars
    output_df$Variable_Indexes[row_index] <- paste(results[[num_vars]][[index]]$variables, collapse = ", ")
    output_df$Mean_Sensitivity[row_index] <- results[[num_vars]][[index]]$Sensitivity
    output_df$Mean_Specificity[row_index] <- results[[num_vars]][[index]]$Specificity
    output_df$Sum_of_Sensitivity_and_Specificity[row_index] <- results[[num_vars]][[index]]$Sensitivity + results[[num_vars]][[index]]$Specificity
  }
}

# Print the final output data frame
print(output_df)

# computationally expensive, not sure how to do it a better way

# define parameters (the ones I really used)
# modelIdx_list = list(
#   c(2, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36),      # Combination 1
#   c(12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36),         # Combination 2
#   c(6, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36),      # Combination 3
#   c(4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36),   # Combination 4
#   c(4, 6, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36) # Combination 5
# )
# alphas = seq(0.1, 1, 0.1) #smoothing parameters to try
# thresholds = seq(0.1, 0.6, 0.02) #classifier thresholds to try for "Yes" based on ~0.16 proportion yes to no
# iters = 100  #train/test split iterations
# splitPerc = 0.7  #percentage of data for training

# define shortened parameters for demo purposes
modelIdx_list = list(
  c(12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36),         # Combination 2 (my hand-picked variables)
  c(4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36)    # Combination 4 (the *best*)
)
alphas = seq(0.1, 0.9, 0.2) #smoothing parameters to try
thresholds = seq(0.3, 0.5, 0.05) #classifier thresholds to try for "Yes" based on ~0.16 proportion yes to no
iters = 10  #train/test split iterations
splitPerc = 0.7  #percentage of data for training

# initialize a list to store results
results_list = list()

# time the loop 
loop_start = Sys.time()

# loop through modelIdx combinations
for (modelIdx in modelIdx_list) {
  
  # loop through the alphas
  for (alpha in alphas) {
    
    # loop through the thresholds
    for (threshold in thresholds) {
      
      # time the threshold loop
      thresh_start = Sys.time()
      
      # make holders for the stats from each iteration for this modelIdx, alpha, and threshold
      iteration_stats = matrix(nrow = iters, ncol = 5)
      colnames(iteration_stats) = c("Seed", "Threshold", "Alpha", "Sensitivity", "Specificity")
      
      # counter for row index in iteration_stats
      row_counter = 1
      
      # external cross-validation loop
      for (i in 1:iters) {

        set.seed(i)

        # generate the test train split
        trainIdx = sample(1:nrow(cs2_conv), round(splitPerc * nrow(cs2_conv)))
        AttritionTrn = cs2_conv[trainIdx, ]
        AttritionTst = cs2_conv[-trainIdx, ]

        # train Naive Bayes model with current alpha and feature (modelIdx) set
        modelNB = naiveBayes(AttritionTrn[, modelIdx], AttritionTrn$Attrition, laplace = alpha)

        # predict on testing set
        preds = predict(modelNB, AttritionTst[, modelIdx], type = "raw") # raw returns the probabilities

        attrition_probs = preds[, "Yes"]

        predictions = ifelse(attrition_probs >= threshold, "Yes", "No")

        # calculate confusion matrix
        CM_no = confusionMatrix(table(predictions, AttritionTst$Attrition))

        # get sensitivity and specificity for "No" class
        sens_no = CM_no[4]$byClass["Sensitivity"] # because reference (positive class) is set to no
        spec_no = CM_no[4]$byClass["Specificity"]

        # store results for that iteration
        iteration_stats[row_counter, ] = c(i, threshold, alpha, sens_no, spec_no)
        row_counter = row_counter + 1

      } # complete external cross-validation loop
      
      # initialize variables to store predictions and actual values to calculate confusion matrix after all LOO
      all_predictions = c()
      all_actual = c()
      
      # internal cross-validation loop (Leave-One-Out Cross-Validation)
      for (row in 1:nrow(cs2_conv)) {
        
        # generate the test train split
        AttritionTrn = cs2_conv[-row, ]
        AttritionTst = cs2_conv[row, ]
        
        # train Naive Bayes model with current alpha and feature (modelIdx) set
        modelNB = naiveBayes(AttritionTrn[, modelIdx], AttritionTrn$Attrition, laplace = alpha)
        
        # predict on testing set
        preds = predict(modelNB, AttritionTst[, modelIdx], type = "raw") # raw returns the probabilities
        
        attrition_probs = preds[,"Yes"]
        attrition_probs = attrition_probs[["Yes"]] # get just the probability from the named number

        predictions = ifelse(attrition_probs >= threshold, "Yes", "No")
        
        # accumulate predictions and actual values
        all_predictions = c(all_predictions, predictions)
        all_actual = c(all_actual, as.character(AttritionTst$Attrition)) # turn factors to characters to match all_actual
        
      } # complete internal cross-validation loop

      # calculate confusion matrix using all predictions and actual values
      CM_no = confusionMatrix(table(all_predictions, all_actual))
      
      # get sensitivity and specificity for "No" class
      sens_icv = CM_no[4]$byClass["Sensitivity"] # because reference (positive class) is set to no
      spec_icv = CM_no[4]$byClass["Specificity"]
      
      # calculate mean sensitivity and specificity over ECV and ICV for this combination of modelIdx, alpha, and threshold
      # not sure if this is the best way since there are many more test/train splits in ICV
      # also don't know if people ever really average ECV and ICV results
      avg_sens = mean(c(mean(iteration_stats[, "Sensitivity"]), sens_icv))
      avg_spec = mean(c(mean(iteration_stats[, "Specificity"]), spec_icv))
      
      # store results for this combination of modelIdx, alpha, and threshold
      results_list = c(results_list, list(
        data.frame(
          ModelIdx = toString(modelIdx),
          Alpha = alpha,
          Threshold = threshold,
          AvgSensitivity = avg_sens,
          AvgSpecificity = avg_spec,
          AvgSum = avg_sens + avg_spec
        )
      ))

        # time the threshold loop
        thresh_end = Sys.time()
        time_taken_thresh = difftime(thresh_end, thresh_start, units = "secs")
        cat("Threshold Loop Time:", time_taken_thresh, "secs \n")
        cat("ModelIdx:", toString(modelIdx), "- Alpha:", alpha, "- Threshold:", threshold, "\n")
      
    } # complete threshold loop

  } # complete alpha loop
  
} # complete modelIdx loop

Threshold Loop Time: 5.592388 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.3 
Threshold Loop Time: 6.021531 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.35 
Threshold Loop Time: 5.547989 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.4 
Threshold Loop Time: 5.553841 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.45 
Threshold Loop Time: 6.12177 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.5 
Threshold Loop Time: 6.420382 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.3 
Threshold Loop Time: 5.520584 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.35 
Threshold Loop Time: 7.136181 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.4 
Threshold Loop Time: 6.214353 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.45 
Threshold Loop Time: 5.380049 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.5 
Threshold Loop Time: 6.685035 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.3 
Threshold Loop Time: 4.998083 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.35 
Threshold Loop Time: 4.644609 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.4 
Threshold Loop Time: 5.171444 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.45 
Threshold Loop Time: 4.761993 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.5 
Threshold Loop Time: 4.782534 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.3 
Threshold Loop Time: 5.089848 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.35 
Threshold Loop Time: 4.768193 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.4 
Threshold Loop Time: 4.86963 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.45 
Threshold Loop Time: 4.742829 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.5 
Threshold Loop Time: 4.720387 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.3 
Threshold Loop Time: 4.678431 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.35 
Threshold Loop Time: 5.60258 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.4 
Threshold Loop Time: 5.327845 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.45 
Threshold Loop Time: 4.64058 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.5 
Threshold Loop Time: 6.054231 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.3 
Threshold Loop Time: 5.122041 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.35 
Threshold Loop Time: 5.147665 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.4 
Threshold Loop Time: 5.249031 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.45 
Threshold Loop Time: 5.486604 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.5 
Threshold Loop Time: 5.605057 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.3 
Threshold Loop Time: 5.666585 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.35 
Threshold Loop Time: 5.104779 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.4 
Threshold Loop Time: 5.114549 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.45 
Threshold Loop Time: 5.132987 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.5 
Threshold Loop Time: 5.240235 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.3 
Threshold Loop Time: 5.867367 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.35 
Threshold Loop Time: 5.544347 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.4 
Threshold Loop Time: 4.961782 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.45 
Threshold Loop Time: 5.413003 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.5 
Threshold Loop Time: 5.472714 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.3 
Threshold Loop Time: 5.191352 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.35 
Threshold Loop Time: 5.131339 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.4 
Threshold Loop Time: 5.16242 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.45 
Threshold Loop Time: 5.0915 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.5 
Threshold Loop Time: 5.148092 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.3 
Threshold Loop Time: 5.51221 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.35 
Threshold Loop Time: 5.823147 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.4 
Threshold Loop Time: 5.233849 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.45 
Threshold Loop Time: 5.136843 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.5 

# loop time
loop_end = Sys.time()
time_taken_loop = difftime(loop_end, loop_start, units = "mins")
cat("Total Loop Time:", time_taken_loop, "mins \n")

Total Loop Time: 4.477766 mins 

# convert results_list to a data frame
results_df = do.call(rbind, results_list)

# output top 10 combinations for each ModelIdx
top_10_combos = results_df %>%
  arrange(ModelIdx, desc(AvgSum), desc(AvgSpecificity), desc(AvgSensitivity)) %>%
  group_by(ModelIdx) %>%
  #top_n(10, wt = AvgSum)
  #make a shorter version for demo purpose
  top_n(5, wt = AvgSum)
kable(top_10_combos, caption = "demo top 10 sensitivity + specificity tuned parameter combos") %>% kable_styling(full_width = FALSE, position = "left")

# starting with the original dataset `cs2` since the ordinal categorical variables are in an integer class
# there are a few other variables that I could transform into ranked like business travel
# not sure it is valid to do it for marital status or overtime

# make a copy of the original dataset
numerical_df = cs2

# check the data
# head(numerical_df$BusinessTravel)

# reorder factor levels
numerical_df$BusinessTravel = factor(numerical_df$BusinessTravel, levels = c("Non-Travel", "Travel_Rarely", "Travel_Frequently"), labels = c("Non-Travel", "Travel_Rarely", "Travel_Frequently"))

# rename the levels to numbers
levels(numerical_df$BusinessTravel) = c(1:3)

# convert factor to integer
numerical_df$BusinessTravel = as.integer(numerical_df$BusinessTravel)

# check the conversion
# head(numerical_df$BusinessTravel)

# repeat for marital status and overtime :/
# head(numerical_df$MaritalStatus)
numerical_df$MaritalStatus = factor(numerical_df$MaritalStatus, levels = c("Single", "Married", "Divorced"), labels = c("Single", "Married", "Divorced"))
levels(numerical_df$MaritalStatus) = c(1:3)
numerical_df$MaritalStatus = as.integer(numerical_df$MaritalStatus)
# head(numerical_df$MaritalStatus)

# head(numerical_df$OverTime)
numerical_df$OverTime = factor(numerical_df$OverTime, levels = c("Yes", "No"), labels = c("Yes", "No"))
levels(numerical_df$OverTime) = c(1:2)
numerical_df$OverTime = as.integer(numerical_df$OverTime)
# head(numerical_df$OverTime)

# scale the variables
# str(numerical_df)
# list of columns to exclude from scaling
exclude_columns = c("ID", "EmployeeCount", "EmployeeNumber", "StandardHours")
# scale the numeric variables and reassign values to same columns
numerical_df = numerical_df %>%
  mutate_at(vars(-matches(paste(exclude_columns, collapse = "|"))), 
            .funs = function(x) if(is.numeric(x)) scale(x) else x)
# str(numerical_df)

# this is a computationally heavy, lengthy process depending on iterations.

modelIdx_num = c(2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36) # sig numeric vars (16)

# Function to calculate sensitivity, specificity for all combinations of a given number of variables
calculate_combinations <- function(modelIdx, max_vars = 15, iters = 10, splitPerc = 0.7) {
  # Initialize an empty list to store results
  results_list <- list()
  
  # Initialize a variable to keep track of the maximum specificity reached
  # max_specificity_so_far <- 0
  
  # Initialize a variable to store the maximum mean specificity from previous iterations
  # max_mean_specificity_previous <- 0

  # Loop over different number of variables
  for (num_vars in seq(8, max_vars)) {
    cat("Number of variables:", num_vars, "\n")
    start_time <- Sys.time()
    
    # Generate all combinations of variables
    index_combinations <- combinat::combn(modelIdx, num_vars)
    
    # Initialize an empty list to store results for this iteration
    temp_results_list <- list()
    
    # Loop through each combination of variables
    for (i in 1:ncol(index_combinations)) {
      index_set <- index_combinations[, i]
      
      # Create holders for the sensitivity, specificity for each iteration
      masterSens <- numeric(iters)
      masterSpec <- numeric(iters)
      
      # Iterate over the specified number of iterations
      for (j in 1:iters) {
        set.seed(j)
        
        # Sample 70% for training
        trainIdx <- sample(1:dim(numerical_df)[1], round(splitPerc * dim(numerical_df)[1]))
        # Select the rows for training
        AttritionTrn <- numerical_df[trainIdx, ]
        # Select the remaining rows for testing
        AttritionTst <- numerical_df[-trainIdx, ]
        
        # Temporarily set the current indexes for modeling
        temp_modelIdx <- index_set
        
        # Train the model
        classifications <- knn(AttritionTrn[, temp_modelIdx], AttritionTst[, temp_modelIdx], AttritionTrn$Attrition, prob = TRUE, k = 15)

        # Predict using the model
        # preds <- predict(modelNB, AttritionTst[, temp_modelIdx])

        # Confusion matrix
        CM <- confusionMatrix(table(classifications, AttritionTst$Attrition))
        
        # Store sensitivity, specificity
        masterSens[j] <- CM$byClass["Sensitivity"]
        masterSpec[j] <- CM$byClass["Specificity"]
      }
      
      # Average sensitivity, specificity
      avg_sensitivity <- mean(masterSens)
      avg_specificity <- mean(masterSpec)
      
      # Store the results including the combination of variables
      temp_results_list[[i]] <- list(variables = index_set, Sensitivity = avg_sensitivity, Specificity = avg_specificity)
    }
    
    end_time <- Sys.time()
    time_taken <- end_time - start_time
    cat("Time taken:", time_taken, "\n")
    
    # Store the results for this iteration
    results_list[[num_vars]] <- temp_results_list
    
    # Get the maximum mean specificity for this number of variables
    max_mean_specificity_current <- max(sapply(temp_results_list, function(x) x$Specificity))
    
    # Check if the maximum mean specificity for the current number of variables is less than the previous maximum
    # if (max_mean_specificity_current < max_mean_specificity_previous) {
    #   cat("Maximum specificity reached for", num_vars, "variables is less than previous maximum. Stopping further iterations.\n")
    #   break
    # }
    
    # Update the maximum mean specificity from previous iterations
    # max_mean_specificity_previous <- max_mean_specificity_current
  }
  
  return(results_list)
}

# Define the list of indexes to loop through
modelIdx <- c(2,4,7,12,15,16,18,19,20,24,29,30,32,33,34,36) #significant features

# Define the maximum number of variables
max_vars <- 15

# Call the function to calculate combinations
results <- calculate_combinations(modelIdx, max_vars)

# Determine the maximum expected number of combinations
max_combinations <- (max_vars - 8) * 10  # Assuming a maximum of 10 combinations per number of variables

# Preallocate the output data frame with maximum expected number of rows
output_df <- data.frame(Number_of_Variables = integer(max_combinations),
                        Variable_Indexes = character(max_combinations),
                        Mean_Sensitivity = numeric(max_combinations),
                        Mean_Specificity = numeric(max_combinations),
                        Sum_of_Sensitivity_and_Specificity = numeric(max_combinations),
                        stringsAsFactors = FALSE)

# Loop over different number of variables
for (num_vars in seq(8, max_vars)) {
  cat("\nTop 10 combinations with the highest specificity for", num_vars, "variables:\n")

  sorted_indices <- order(sapply(results[[num_vars]], function(x) x$Specificity), decreasing = TRUE)
  for (i in 1:min(10, length(sorted_indices))) {
    index <- sorted_indices[i]
    # cat("Combination", i, ": Variables =", results[[num_vars]][[index]]$variables, ", Specificity =", results[[num_vars]][[index]]$Specificity, "\n")

    # Assign the results to the preallocated rows in the output data frame
    row_index <- (num_vars - 8) * 10 + i  # Calculate the row index
    output_df$Number_of_Variables[row_index] <- num_vars
    output_df$Variable_Indexes[row_index] <- paste(results[[num_vars]][[index]]$variables, collapse = ", ")
    output_df$Mean_Sensitivity[row_index] <- results[[num_vars]][[index]]$Sensitivity
    output_df$Mean_Specificity[row_index] <- results[[num_vars]][[index]]$Specificity
    output_df$Sum_of_Sensitivity_and_Specificity[row_index] <- results[[num_vars]][[index]]$Sensitivity + results[[num_vars]][[index]]$Specificity
  }
}

# Print the final output data frame
print(output_df)

# I comment out some parameters to make a demo version of this code, so that it doesn't take so long to run.

# define parameters
modelIdx_list = list(
  c(2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36), # sig numeric vars (16)
  # c(12,16,19,24,29,33,34,36), #8var
  # c(16,18,20,24,29,33,34,36), #8var
  # c(2,12,16,19,24,29,33,34,36), #9var
  # c(2,12,16,19,24,29,30,33,34,36), #10var
  # c(2,12,16,19,20,24,29,30,33,34,36), #11var
  # c(2,7,16,18,19,20,24,29,30,33,34,36), #12var
  # c(2,7,12,16,18,19,20,24,29,30,33,34,36), #13var
  c(2,7,12,15,16,18,19,20,24,29,30,33,34,36), #14var
  # c(2,7,12,15,16,18,19,20,24,29,30,32,33,34,36), #15var
  # c(12,15,16,19,20,24,29,30,32,33,34,36),     # NB Combination 2 (my hand-picked variables) minus job role
  c(4,7,12,15,16,19,20,24,29,30,32,33,34,36)    # NB Combination 4 (the *best*) minus job role
  # c(2, 7, 20, 22, 25, 30, 31, 33, 34, 35, 36) # all numeric variables
)

# actual set of parameters used
# thresholds = seq(0.1, 0.6, 0.02) #classifier thresholds to try for "Yes" based on ~0.16 proportion yes to no
# numKs = seq(1, 49, 2) #odd Ks to try
# iters = 100  #train/test split iterations
# splitPerc = 0.7  #percentage of data for training

# demo set
thresholds = seq(0.1, 0.5, 0.05) #classifier thresholds to try for "Yes" based on ~0.16 proportion yes to no
numKs = seq(3, 49, 2) #odd Ks to try
iters = 10  #train/test split iterations
splitPerc = 0.7  #percentage of data for training

# for debugging
# modelIdx = c(2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36)
# threshold = 0.5
# k = 11
# i = 1

# initialize a list to store results
results_list = list()

# time the loop 
loop_start = Sys.time()
cat("Start time:", loop_start, "\n")

Start time: 1724516800 

# loop through modelIdx combinations
for (modelIdx in modelIdx_list) {
  
  # loop through the thresholds
  for (threshold in thresholds) {
    
    # loop through the Ks
    for (k in numKs) {
      
      # time the K loop
      k_start = Sys.time()
      
      # make holders for the stats from each iteration for this modelIdx, threshold and K
      iteration_stats = matrix(nrow = iters, ncol = 5)
      colnames(iteration_stats) = c("Seed", "Threshold", "K", "Sensitivity", "Specificity")
      
      # counter for row index in iteration_stats
      row_counter = 1
      
      # external cross-validation loop
      for (i in 1:iters) {

        set.seed(i)

        # generate the test train split
        trainIdx = sample(1:nrow(numerical_df), round(splitPerc * nrow(numerical_df)))
        AttritionTrn = numerical_df[trainIdx, ]
        AttritionTst = numerical_df[-trainIdx, ]

        # train kNN model with current k and feature (modelIdx) set
        classifications = knn(AttritionTrn[, modelIdx], AttritionTst[, modelIdx], AttritionTrn$Attrition, prob = T, k = k)
        # create a table of predicted vs actual values for assessing classification accuracy
        #table(classifications, AttritionTst$Attrition)
   
        # display the classifications and their attributes; useful for debugging and understanding model output
        classifications
        attributes(classifications)
        
        # compute probabilities specifically for the "YES" class, adjusting based on predicted labels
        probs = ifelse(classifications == "YES", attributes(classifications)$prob, 1 - attributes(classifications)$prob)

        # apply the new threshold to reclassify observations
        NewClass = ifelse(probs >= threshold, "Yes", "No")

        # this didn't work if all the predictions were No because the Yes row was missing 
        # tabulate the new classifications against actual values
        # table(NewClass, AttritionTst$Attrition)
        # calculate the confusion matrix
        # don't need to relevel the confusion matrix because I am looking at sensitivity + specificity
        # CM_no = confusionMatrix(table(relevel(as.factor(NewClass), ref = "No"), AttritionTst$Attrition), mode = "everything")
        
        # create a table with rows for both "Yes" and "No" classes (in the event there are zero "Yes"s)
        table_predicted_actual = matrix(0, nrow = 2, ncol = 2, dimnames = list(c("No", "Yes"), c("No", "Yes")))
        
        # populate the counts based on the predictions and actual classes
        table_predicted_actual["No", "No"] = sum(NewClass == "No" & AttritionTst$Attrition == "No")
        table_predicted_actual["No", "Yes"] = sum(NewClass == "No" & AttritionTst$Attrition == "Yes")
        table_predicted_actual["Yes", "No"] = sum(NewClass == "Yes" & AttritionTst$Attrition == "No")
        table_predicted_actual["Yes", "Yes"] = sum(NewClass == "Yes" & AttritionTst$Attrition == "Yes")

        # calculate the confusion matrix for this iteration
        CM_no = confusionMatrix(table_predicted_actual, mode = "everything")
        
        # get sensitivity and specificity for "No" class
        sens_no = CM_no[4]$byClass["Sensitivity"] # because reference (positive class) is set to no
        spec_no = CM_no[4]$byClass["Specificity"]

        # store results for that iteration
        iteration_stats[row_counter, ] = c(i, threshold, k, sens_no, spec_no)
        row_counter = row_counter + 1

      } # complete external cross-validation loop
      
      # initialize variables to store predictions and actual values to calculate confusion matrix after all LOO
      all_predictions = c()
      all_actual = c()
      
      # internal cross-validation (Leave-One-Out Cross-Validation)
      classifications = knn.cv(numerical_df[, modelIdx], numerical_df$Attrition,
                         prob = TRUE, k = k)
      # create a table of predicted vs actual values for assessing classification accuracy
      #table(classifications, AttritionTst$Attrition)
   
      # display the classifications and their attributes; useful for debugging and understanding model output
      classifications
      attributes(classifications)
        
      # compute probabilities specifically for the "YES" class, adjusting based on predicted labels
      probs = ifelse(classifications == "YES", attributes(classifications)$prob, 1 - attributes(classifications)$prob)

      # apply the new threshold to reclassify observations
      NewClass = ifelse(probs >= threshold, "Yes", "No")
      
      # tabulate the new classifications against actual values
      # table(NewClass, AttritionTst$Attrition)
      # calculate the confusion matrix
      # don't need to relevel the confusion matrix because I am looking about sensitivity + specificity
      # CM_no = confusionMatrix(table(relevel(as.factor(NewClass), ref = "No"), cs2_conv$Attrition), mode = "everything")
      
      # create a table with rows for both "Yes" and "No" classes (in the event there are zero "Yes"s)
      table_predicted_actual = matrix(0, nrow = 2, ncol = 2, dimnames = list(c("No", "Yes"), c("No", "Yes")))
        
      # populate the counts based on the predictions and actual classes
      table_predicted_actual["No", "No"] = sum(NewClass == "No" & cs2_conv$Attrition == "No")
      table_predicted_actual["No", "Yes"] = sum(NewClass == "No" & cs2_conv$Attrition == "Yes")
      table_predicted_actual["Yes", "No"] = sum(NewClass == "Yes" & cs2_conv$Attrition == "No")
      table_predicted_actual["Yes", "Yes"] = sum(NewClass == "Yes" & cs2_conv$Attrition == "Yes")
        
      # calculate the confusion matrix for this iteration
      CM_no = confusionMatrix(table_predicted_actual, mode = "everything")
        
      # get sensitivity and specificity for "No" class
      sens_icv = CM_no[4]$byClass["Sensitivity"] # because reference (positive class) is set to no
      spec_icv = CM_no[4]$byClass["Specificity"]

      # calculate mean sensitivity and specificity over ECV and ICV for this combination of modelIdx, threshold and k
      # not sure if I should even average these??
      avg_sens = mean(c(mean(iteration_stats[, "Sensitivity"]), sens_icv))
      avg_spec = mean(c(mean(iteration_stats[, "Specificity"]), spec_icv))
      
      # store results for this combination of modelIdx, threshold and K
      results_list = c(results_list, list(
        data.frame(
          ModelIdx = toString(modelIdx),
          Threshold = threshold,
          K = k,
          AvgSensitivity = avg_sens,
          AvgSpecificity = avg_spec,
          AvgSum = avg_sens + avg_spec
        )
      ))

        # time the k loop
        k_end = Sys.time()
        time_taken_thresh = difftime(k_end, k_start, units = "secs")
        # cat("K Loop Time:", time_taken_thresh, "secs \n")
        # cat("ModelIdx:", toString(modelIdx), "- Threshold:", threshold, "- K:", k, "\n")
      
    } # complete k loop

  } # complete threshold loop
  
  # print progress report
  progress_time = Sys.time()
  progress = difftime(progress_time, loop_start, units = "mins")
  cat("Total Elapsed Time:", progress, "mins \n")
  
} # complete modelIdx loop

Total Elapsed Time: 0.3571209 mins 
Total Elapsed Time: 0.7068673 mins 
Total Elapsed Time: 1.113254 mins 

# loop time
# loop_end = Sys.time()
# time_taken_loop = difftime(loop_end, loop_start, units = "mins")
# cat("Total Loop Time:", time_taken_loop, "mins \n")

# convert results_list to a data frame
results_df = do.call(rbind, results_list)

# plot the optimal k (though not particularly helpful or needed with the other tuning)
# aggregate results by K
results_agg = results_df %>%
  group_by(K) %>%
  dplyr::summarize(Mean_Sensitivity = mean(AvgSensitivity),
            Mean_Specificity = mean(AvgSpecificity))
# plot the average sensitivity and specificity for each K
ggplot(results_agg, aes(x = K)) +
  geom_line(aes(y = Mean_Sensitivity, color = "Mean Sensitivity")) +
  geom_line(aes(y = Mean_Specificity, color = "Mean Specificity")) +
  labs(title = "Mean sensitivity and specificity for different values of K",
       x = "K parameter", y = "Metric", color = "Metric") +
  scale_color_manual(values = c("Mean Sensitivity" = "darkgreen", "Mean Specificity" = "darkblue")) +
  theme_bw()

# output top 10 combinations for each ModelIdx
top_10_combos = results_df %>%
  arrange(ModelIdx, desc(AvgSum), desc(AvgSpecificity), desc(AvgSensitivity)) %>%
  group_by(ModelIdx) %>%
  top_n(10, wt = AvgSum)
kable(top_10_combos, caption = "demo top 10 sensitivity + specificity tuned knn parameters") %>% kable_styling(full_width = FALSE, position = "left")

# make predictions with Naive Bayes model

# variables used: `BusinessTravel`, `DistanceFromHome`, `EnvironmentSatisfaction`, `JobInvolvement`, `JobLevel`, `JobRole`, `MaritalStatus`, `MonthlyIncome`, `OverTime`, `StockOptionLevel`, `TotalWorkingYears`, `WorkLifeBalance`, `YearsAtCompany`, `YearsInCurrentRole`, `YearsWithCurrManager`

# parameters
# train_dataframe = cs2_conv
# adjust index numbers based on missing Attrition column #3 or add column to competition set
ModelIdx = c(4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36)
alpha = 0.7
threshold = 0.46 # "Yes" >=

# import data: CaseStudy2CompSet No Attrition.csv from AWS S3 msdsds6306 bucket

url = "https://msdsds6306.s3.us-east-2.amazonaws.com/CaseStudy2CompSet+No+Attrition.csv"
# encoded_url = URLencode(url) # need to encode the spaces as %20 (or do it manually)
competition = read.table(textConnection(getURL(url)), sep = ",", header = TRUE, stringsAsFactors = TRUE)

# save a copy of the competition unlabeled data
# write.csv(competition, file = "data/CaseStudy2CompSet No Attrition.csv", row.names = FALSE)

# get a sense of the data
str(competition)

'data.frame':   300 obs. of  35 variables:
 $ ID                      : int  1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 ...
 $ Age                     : int  35 33 26 55 29 51 52 39 31 31 ...
 $ BusinessTravel          : Factor w/ 3 levels "Non-Travel","Travel_Frequently",..: 3 3 3 3 3 2 1 3 3 2 ...
 $ DailyRate               : int  750 147 1330 1311 1246 1456 585 1387 1062 534 ...
 $ Department              : Factor w/ 3 levels "Human Resources",..: 2 1 2 2 3 2 3 2 2 2 ...
 $ DistanceFromHome        : int  28 2 21 2 19 1 29 10 24 20 ...
 $ Education               : int  3 3 3 3 3 4 4 5 3 3 ...
 $ EducationField          : Factor w/ 6 levels "Human Resources",..: 2 1 4 2 2 4 2 4 4 2 ...
 $ EmployeeCount           : int  1 1 1 1 1 1 1 1 1 1 ...
 $ EmployeeNumber          : int  1596 1207 1107 505 1497 145 2019 1618 1252 587 ...
 $ EnvironmentSatisfaction : int  2 2 1 3 3 1 1 2 3 1 ...
 $ Gender                  : Factor w/ 2 levels "Female","Male": 2 2 2 1 2 1 2 2 1 2 ...
 $ HourlyRate              : int  46 99 37 97 77 30 40 76 96 66 ...
 $ JobInvolvement          : int  4 3 3 3 2 2 3 3 2 3 ...
 $ JobLevel                : int  2 1 1 4 2 3 1 2 2 3 ...
 $ JobRole                 : Factor w/ 9 levels "Healthcare Representative",..: 3 2 3 4 8 1 9 5 1 1 ...
 $ JobSatisfaction         : int  3 3 3 4 3 1 4 1 1 3 ...
 $ MaritalStatus           : Factor w/ 3 levels "Divorced","Married",..: 2 2 1 3 1 3 1 2 3 2 ...
 $ MonthlyIncome           : int  3407 3600 2377 16659 8620 7484 3482 5377 6812 9824 ...
 $ MonthlyRate             : int  25348 8429 19373 23258 23757 25796 19788 3835 17198 22908 ...
 $ NumCompaniesWorked      : int  1 1 1 2 1 3 2 2 1 3 ...
 $ Over18                  : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
 $ OverTime                : Factor w/ 2 levels "No","Yes": 1 1 1 2 1 1 1 1 1 1 ...
 $ PercentSalaryHike       : int  17 13 20 13 14 20 15 13 19 12 ...
 $ PerformanceRating       : int  3 3 4 3 3 4 3 3 3 3 ...
 $ RelationshipSatisfaction: int  4 4 3 3 3 3 2 4 2 1 ...
 $ StandardHours           : int  80 80 80 80 80 80 80 80 80 80 ...
 $ StockOptionLevel        : int  2 1 1 0 2 0 2 3 0 0 ...
 $ TotalWorkingYears       : int  10 5 1 30 10 23 16 10 10 12 ...
 $ TrainingTimesLastYear   : int  3 2 0 2 3 1 3 3 2 2 ...
 $ WorkLifeBalance         : int  2 3 2 3 3 2 2 3 3 3 ...
 $ YearsAtCompany          : int  10 5 1 5 10 13 9 7 10 1 ...
 $ YearsInCurrentRole      : int  9 4 1 4 7 12 8 7 9 0 ...
 $ YearsSinceLastPromotion : int  6 1 0 1 0 12 0 7 1 0 ...
 $ YearsWithCurrManager    : int  8 4 0 2 4 8 0 7 8 0 ...

summary(competition)

       ID            Age                  BusinessTravel   DailyRate                       Department  DistanceFromHome
 Min.   :1171   Min.   :19.00   Non-Travel       : 32    Min.   : 102.0   Human Resources       : 11   Min.   : 1.00   
 1st Qu.:1246   1st Qu.:31.00   Travel_Frequently: 57    1st Qu.: 448.0   Research & Development:209   1st Qu.: 2.00   
 Median :1320   Median :36.00   Travel_Rarely    :211    Median : 775.0   Sales                 : 80   Median : 7.00   
 Mean   :1320   Mean   :37.86                            Mean   : 784.8                                Mean   : 9.26   
 3rd Qu.:1395   3rd Qu.:44.00                            3rd Qu.:1117.0                                3rd Qu.:14.00   
 Max.   :1470   Max.   :60.00                            Max.   :1490.0                                Max.   :29.00   
                                                                                                                       
   Education              EducationField EmployeeCount EmployeeNumber   EnvironmentSatisfaction    Gender      HourlyRate    
 Min.   :1.000   Human Resources :  7    Min.   :1     Min.   :   2.0   Min.   :1.000           Female:105   Min.   : 30.00  
 1st Qu.:2.000   Life Sciences   :130    1st Qu.:1     1st Qu.: 508.8   1st Qu.:2.000           Male  :195   1st Qu.: 50.00  
 Median :3.000   Marketing       : 27    Median :1     Median : 994.5   Median :3.000                        Median : 66.00  
 Mean   :2.973   Medical         : 94    Mean   :1     Mean   :1020.9   Mean   :2.733                        Mean   : 66.07  
 3rd Qu.:4.000   Other           : 12    3rd Qu.:1     3rd Qu.:1542.5   3rd Qu.:4.000                        3rd Qu.: 83.00  
 Max.   :5.000   Technical Degree: 30    Max.   :1     Max.   :2065.0   Max.   :4.000                        Max.   :100.00  
                                                                                                                             
 JobInvolvement     JobLevel                        JobRole   JobSatisfaction  MaritalStatus MonthlyIncome    MonthlyRate   
 Min.   :1.000   Min.   :1.0   Research Scientist       :61   Min.   :1.000   Divorced: 65   Min.   : 1232   Min.   : 2097  
 1st Qu.:2.000   1st Qu.:1.0   Sales Executive          :57   1st Qu.:2.000   Married :128   1st Qu.: 3034   1st Qu.: 8420  
 Median :3.000   Median :2.0   Laboratory Technician    :55   Median :3.000   Single  :107   Median : 5208   Median :15091  
 Mean   :2.743   Mean   :2.2   Manufacturing Director   :31   Mean   :2.767                  Mean   : 7103   Mean   :14499  
 3rd Qu.:3.000   3rd Qu.:3.0   Manager                  :30   3rd Qu.:4.000                  3rd Qu.: 9750   3rd Qu.:20330  
 Max.   :4.000   Max.   :5.0   Healthcare Representative:29   Max.   :4.000                  Max.   :19973   Max.   :26914  
                               (Other)                  :37                                                                 
 NumCompaniesWorked Over18  OverTime  PercentSalaryHike PerformanceRating RelationshipSatisfaction StandardHours StockOptionLevel
 Min.   :0.000      Y:300   No :212   Min.   :11.00     Min.   :3.000     Min.   :1.000            Min.   :80    Min.   :0.0000  
 1st Qu.:1.000              Yes: 88   1st Qu.:12.00     1st Qu.:3.000     1st Qu.:2.000            1st Qu.:80    1st Qu.:0.0000  
 Median :2.000                        Median :14.00     Median :3.000     Median :3.000            Median :80    Median :1.0000  
 Mean   :2.547                        Mean   :15.17     Mean   :3.153     Mean   :2.803            Mean   :80    Mean   :0.7833  
 3rd Qu.:4.000                        3rd Qu.:18.00     3rd Qu.:3.000     3rd Qu.:4.000            3rd Qu.:80    3rd Qu.:1.0000  
 Max.   :9.000                        Max.   :25.00     Max.   :4.000     Max.   :4.000            Max.   :80    Max.   :3.0000  
                                                                                                                                 
 TotalWorkingYears TrainingTimesLastYear WorkLifeBalance YearsAtCompany   YearsInCurrentRole YearsSinceLastPromotion
 Min.   : 0.00     Min.   :0.000         Min.   :1.000   Min.   : 0.000   Min.   : 0.00      Min.   : 0.00          
 1st Qu.: 6.00     1st Qu.:2.000         1st Qu.:2.000   1st Qu.: 3.000   1st Qu.: 2.00      1st Qu.: 0.00          
 Median :10.00     Median :2.000         Median :3.000   Median : 5.000   Median : 3.00      Median : 1.00          
 Mean   :12.44     Mean   :2.683         Mean   :2.747   Mean   : 7.527   Mean   : 4.33      Mean   : 2.29          
 3rd Qu.:18.00     3rd Qu.:3.000         3rd Qu.:3.000   3rd Qu.:10.000   3rd Qu.: 7.00      3rd Qu.: 3.00          
 Max.   :38.00     Max.   :6.000         Max.   :4.000   Max.   :37.000   Max.   :18.00      Max.   :15.00          
                                                                                                                    
 YearsWithCurrManager
 Min.   : 0.00       
 1st Qu.: 2.00       
 Median : 3.00       
 Mean   : 4.38       
 3rd Qu.: 7.00       
 Max.   :17.00       
                     

# convert numerical ranked variables to factors
numVars_to_fact = c("Education", "EnvironmentSatisfaction",
                    "JobInvolvement", "JobLevel", "JobSatisfaction",
                    "PerformanceRating", "RelationshipSatisfaction",
                    "StockOptionLevel", "WorkLifeBalance")
competition = competition %>%
  mutate(across(all_of(numVars_to_fact), as.factor))
# check the conversion
# str(competition)

# add the Attrition column between Age and BusinessTravel
competition = competition %>%
  mutate(Attrition = NA, .after = "Age")
# str(competition)

# train the Naive Bayes model
fullsetNBmodel = naiveBayes(cs2_conv[, modelIdx], cs2_conv$Attrition, laplace = alpha)

# predict the labels on the competition set
preds = predict(fullsetNBmodel, competition[, modelIdx], type = "raw") # raw returns the probabilities

# get the Yes probabilities to adjust threshold
attrition_probs = preds[, "Yes"]

# classify with new threshold
predictions = ifelse(attrition_probs >= threshold, "Yes", "No")

# add the labels to the Attrition column
competition = competition %>% mutate(Attrition = factor(predictions))
# str(competition)

# get the proportion of attrition for curiousity
summary(competition$Attrition)

 No Yes 
242  58 

NoAttProb = summary(competition$Attrition)["No"] / sum(summary(competition$Attrition))
NoAttProb

       No 
0.8066667 

AttProb = summary(competition$Attrition)["Yes"] / sum(summary(competition$Attrition))
AttProb

      Yes 
0.1933333 

# make dataframe with just competition set ordered IDs and labels
competitionLabels = competition %>% select(ID, Attrition)
str(competitionLabels)

'data.frame':   300 obs. of  2 variables:
 $ ID       : int  1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 ...
 $ Attrition: Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...

# save to file
# write.csv(competitionLabels, file = "data/Case2PredictionsHenderson Attrition.csv", row.names = FALSE)

# starting with the original dataset `cs2` since the ordinal categorical variables are in an integer class
# there are a few other variables that I could transform into ranked variables, like business travel
# not sure it is valid to do it for marital status or overtime

# make a copy of the original dataset
numerical_df = cs2

# check the data
head(numerical_df$BusinessTravel)

[1] Travel_Rarely     Travel_Rarely     Travel_Frequently Travel_Rarely     Travel_Frequently Travel_Frequently
Levels: Non-Travel Travel_Frequently Travel_Rarely

# reorder factor levels
numerical_df$BusinessTravel = factor(numerical_df$BusinessTravel, levels = c("Non-Travel", "Travel_Rarely", "Travel_Frequently"), labels = c("Non-Travel", "Travel_Rarely", "Travel_Frequently"))

# rename the levels to numbers
levels(numerical_df$BusinessTravel) = c(1:3)

# convert factor to integer
numerical_df$BusinessTravel = as.integer(numerical_df$BusinessTravel)

# check the conversion
head(numerical_df$BusinessTravel)

[1] 2 2 3 2 3 3

# repeat for marital status and overtime and attrition :/
head(numerical_df$MaritalStatus)

[1] Divorced Single   Single   Married  Single   Divorced
Levels: Divorced Married Single

numerical_df$MaritalStatus = factor(numerical_df$MaritalStatus, levels = c("Single", "Married", "Divorced"), labels = c("Single", "Married", "Divorced"))
levels(numerical_df$MaritalStatus) = c(1:3)
numerical_df$MaritalStatus = as.integer(numerical_df$MaritalStatus)
head(numerical_df$MaritalStatus)

[1] 3 1 1 2 1 3

head(numerical_df$OverTime)

[1] No  No  No  No  Yes No 
Levels: No Yes

numerical_df$OverTime = factor(numerical_df$OverTime, levels = c("Yes", "No"), labels = c("Yes", "No"))
levels(numerical_df$OverTime) = c(1:2)
numerical_df$OverTime = as.integer(numerical_df$OverTime)
head(numerical_df$OverTime)

[1] 2 2 2 2 1 2

head(numerical_df$Attrition)

[1] No No No No No No
Levels: No Yes

numerical_df$Attrition = factor(numerical_df$Attrition, levels = c("Yes", "No"), labels = c("Yes", "No"))
levels(numerical_df$Attrition) = c(1:2)
numerical_df$Attrition = as.integer(numerical_df$Attrition)
head(numerical_df$Attrition)

[1] 2 2 2 2 2 2

# make a new DF, transform x variable (squaring term) and add it as a new column
cs2_regres = numerical_df %>%
  mutate(
    YearsInCurrentRole2 = YearsInCurrentRole^2,
    YearsWithCurrManager2 = YearsWithCurrManager^2)

#indexes from cs2_regres dataframe
ModelIdx = c(2,3,4,5,7,8,12,14,15,16,18,19,21,22,24,25,26,27,29,30,31,32,33,34,35,36,37,38)

# unused indexes from cs2_regres dataframe 
ModelIdx = c(2,3,4,5,8,14,18,19,21,22,24,25,26,27,29,31,32,33,34,35,37)
  
# initialize an empty dataframe to store results
results = data.frame(Index = numeric(length(ModelIdx)), Variable = character(length(ModelIdx)), RMSE = numeric(length(ModelIdx)))

# get number of rows in data frame
n = nrow(cs2_regres)

# loop through each explanatory variable separately
for (i in seq_along(ModelIdx)) {
  
  # create formula with the current explanatory variable 
  model_formula = as.formula(paste("MonthlyIncome ~ JobLevel + TotalWorkingYears + YearsWithCurrManager + YearsWithCurrManager2 + DistanceFromHome + JobInvolvement + EnvironmentSatisfaction + ", names(cs2_regres)[ModelIdx[i]]))
  # indexes of variables used in model c(16,30,36,7,15,38,12)

  # initialize vector to store squared error from each leave-one-out loop
  cv_error_model = numeric(n)
  
  # loop through setting each row as test set for internal n-fold CV
  for (j in 1:n) {
    # leave out the j-th observation
    test_row = cs2_regres[j, ]
    
    # use the remaining data for training       
    train_data = cs2_regres[-j, ]
    
    # fit the model with train_data
    model = lm(model_formula, data = train_data)
    
    # predict on the left-out observation
    pred = predict(model, newdata = test_row)
    
    # calculate the squared error
    cv_error_model[j] = (test_row$MonthlyIncome - pred)^2
  }
  
  # calculate the root mean squared error (RMSE) for the current model
  RMSE = sqrt(mean(cv_error_model))
  
  # store the variable index, name, and RMSE in the results dataframe
  results[i, "Index"] = ModelIdx[i]
  results[i, "Variable"] = names(cs2_regres)[ModelIdx[i]]
  results[i, "RMSE"] = RMSE
}

# sort results by RMSE in ascending order
results = results[order(results$RMSE), ]

# print the sorted table
kable(results, caption = "demo of resulting RSME for each 1 added variable") %>% kable_styling(full_width = FALSE, position = "left")

# model formula from variable indexes (16,30,36,7,15,38,12)
model_formula = as.formula("MonthlyIncome ~ JobLevel + TotalWorkingYears + YearsWithCurrManager + YearsWithCurrManager2 + DistanceFromHome + JobInvolvement + EnvironmentSatisfaction")

# number of train/test splits
iters = 100

# split percentage
split_perc = 0.7

# initialize vector to store squared error from each train/test split loop for training and validation sets
cv_error_train = numeric(iters)
cv_error_test = numeric(iters)
  
# external cross-validation loop
for (i in 1:iters) {
  
  set.seed(i)

  # generate the test train split
  trainIdx = sample(1:nrow(cs2_regres), round(splitPerc * nrow(cs2_regres)))
  IncomeTrn = cs2_regres[trainIdx, ]
  IncomeTst = cs2_regres[-trainIdx, ]
    
  # fit the model with train_data
  model = lm(model_formula, data = IncomeTrn)
    
  # predict on the training set (same data used to make model)
  predTrn = predict(model, newdata = IncomeTrn)
  
  # calculate the mean squared error of training pred
  cv_error_train[i] = mean((IncomeTrn$MonthlyIncome - predTrn)^2)
  
  # predict on the training set (same data used to make model)
  predTst = predict(model, newdata = IncomeTst)
    
  # calculate the mean squared error of training pred
  cv_error_test[i] = mean((IncomeTst$MonthlyIncome - predTst)^2)
}
  
# calculate the root mean squared error (RMSE) for the training set
RMSE_trn = sqrt(mean(cv_error_train)) # root of avg of error from each iteration 
  
# calculate the root mean squared error (RMSE) for the validation set
RMSE_tst = sqrt(mean(cv_error_test))
  
# print the results
cat("\nRMSE of training set: ", RMSE_trn, "\n")


RMSE of training set:  1357.371 

cat("\nRMSE of validation set: ", RMSE_tst, "\n")


RMSE of validation set:  1381.737 

# Stepwise Selection
# data = cs2_regres

library(boot)

# Check for variables with only one level
vars_one_level <- sapply(cs2_regres, function(x) length(unique(x)) == 1)

# List variables with only one level
names(cs2_regres)[vars_one_level]

# Remove variables with only one level
cs2_regres_clean <- cs2_regres[, !vars_one_level]

library(boot)

# Define a function to perform stepwise selection and return the selected model
perform_stepwise_selection <- function(data) {
  stepwise_model <- step(lm(MonthlyIncome ~ ., data = data))
  return(stepwise_model)
}

# Define a function to calculate RMSE
calculate_rmse <- function(actual, predicted) {
  return(sqrt(mean((actual - predicted)^2)))
}

# Define the number of iterations for cross-validation
num_iterations <- 100

# Initialize a data frame to store RMSEs and variable combinations
results <- data.frame(RMSE = numeric(num_iterations),
                      Variables = character(num_iterations))

# Perform cross-validation with multiple iterations
for (i in 1:num_iterations) {
  # Split data into training and validation sets (adjust as per your data)
  set.seed(i)  # Set seed for reproducibility
  train_indices <- sample(nrow(cs2_regres_clean), 0.7 * nrow(cs2_regres_clean))
  train_data <- cs2_regres_clean[train_indices, ]
  validation_data <- cs2_regres_clean[-train_indices, ]
  
  # Perform stepwise selection on the training data
  selected_model <- perform_stepwise_selection(train_data)
  
  # Make predictions on the validation set
  predicted_values <- predict(selected_model, newdata = validation_data)
  
  # Calculate RMSE for this iteration
  rmse <- calculate_rmse(validation_data$MonthlyIncome, predicted_values)
  
  # Store RMSE and variable combination
  results[i, "RMSE"] <- rmse
  results[i, "Variables"] <- paste(names(coefficients(selected_model)), collapse = ", ")
}

# Sort results by RMSE
results <- results[order(results$RMSE), ]

# Output top five RMSEs and their variable combinations
top_five <- head(results, 5)
print(top_five)

# make predictions with linear regression model

# variables used: `JobLevel`, `TotalWorkingYears`, `YearsWithCurrManager`, `YearsWithCurrManager2`, `DistanceFromHome`, `JobInvolvement`, `EnvironmentSatisfaction`

# parameters
# train_dataframe = cs2_regres
# adjust index numbers based on missing MonthlyIncome column or add column to competition set
# regresIdx = c(16,30,36,7,15,38,12)


# import data: CaseStudy2CompSet No Salary.csv from AWS S3 msdsds6306 bucket

# first column header is `ï..ID` instead of `ID` which I guess is a UTF-8 encoding issue 
# url = "https://msdsds6306.s3.us-east-2.amazonaws.com/CaseStudy2CompSet+No+Salary.csv"
# competition = read.table(textConnection(getURL(url)), sep = ",", header = TRUE, stringsAsFactors = TRUE)

# so I use read.csv and specify encoding = "UTF-8" and it imports correctly.
url = "https://msdsds6306.s3.us-east-2.amazonaws.com/CaseStudy2CompSet+No+Salary.csv"
competition = read.csv(url, header = TRUE, stringsAsFactors = TRUE, encoding = "UTF-8")

# save a copy of the competition unlabeled data
# write.csv(competition, file = "data/CaseStudy2CompSet No Salary.csv", row.names = FALSE)

# get a sense of the data
# str(competition)
# summary(competition)

# create squared variables, both to keep the indexes consistent
competition = competition %>%
  mutate(
    YearsInCurrentRole2 = YearsInCurrentRole^2,
    YearsWithCurrManager2 = YearsWithCurrManager^2)
# check the conversion
# str(competition)

# add the MonthlyIncome column between MaritalStatus and MonthlyRate 
competition = competition %>%
  mutate(MonthlyIncome = NA, .after = "MaritalStatus")
# str(competition)

# train the linear regression model on the full `cs2_regres` data set
fullset_LM_model = lm(model_formula, data = cs2_regres)

# predict the labels on the competition set
preds = predict(fullset_LM_model, competition)

# add the labels to the MonthlyIncome column
competition = competition %>% mutate(MonthlyIncome = as.integer(preds))
# str(competition)

# for curiousity get the summary of MonthlyIncome from both datasets
summary(cs2_regres$MonthlyIncome)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1081    2840    4946    6390    8182   19999 

summary(competition$MonthlyIncome)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1576    2340    6008    6242    7056   19117 

# make dataframe with just competition set ordered IDs and labels
competitionLabels = competition %>% select(ID, MonthlyIncome)
# str(competitionLabels)

# save to file
# write.csv(competitionLabels, file = "data/Case2PredictionsHenderson Salary.csv", row.names = FALSE)

# I decide to treat integer and non-integer categorical variables as categorical starting with the original dataset `cs2` since the ordinal categorical variables are in an integer class.

# make a copy of the original dataset after converting numerical ranking variables to factors
cs2_regres2 = cs2_conv

# check the data
head(cs2_regres2$BusinessTravel)

[1] Travel_Rarely     Travel_Rarely     Travel_Frequently Travel_Rarely     Travel_Frequently Travel_Frequently
Levels: Non-Travel Travel_Frequently Travel_Rarely

# reorder factor levels
cs2_regres2$BusinessTravel = factor(cs2_regres2$BusinessTravel, levels = c("Non-Travel", "Travel_Rarely", "Travel_Frequently"), labels = c("Non-Travel", "Travel_Rarely", "Travel_Frequently"))

# check the conversion
head(cs2_regres2$BusinessTravel)

[1] Travel_Rarely     Travel_Rarely     Travel_Frequently Travel_Rarely     Travel_Frequently Travel_Frequently
Levels: Non-Travel Travel_Rarely Travel_Frequently

# repeat for marital status
head(cs2_regres2$MaritalStatus)

[1] Divorced Single   Single   Married  Single   Divorced
Levels: Divorced Married Single

cs2_regres2$MaritalStatus = factor(cs2_regres2$MaritalStatus, levels = c("Single", "Married", "Divorced"), labels = c("Single", "Married", "Divorced"))
head(cs2_regres2$MaritalStatus)

[1] Divorced Single   Single   Married  Single   Divorced
Levels: Single Married Divorced

# remove Over18 - factor with 1 level
cs2_regres2 = cs2_regres2 %>% select(-Over18)
str(cs2_regres2)

'data.frame':   870 obs. of  35 variables:
 $ ID                      : int  1 2 3 4 5 6 7 8 9 10 ...
 $ Age                     : int  32 40 35 32 24 27 41 37 34 34 ...
 $ Attrition               : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ BusinessTravel          : Factor w/ 3 levels "Non-Travel","Travel_Rarely",..: 2 2 3 2 3 3 2 2 2 3 ...
 $ DailyRate               : int  117 1308 200 801 567 294 1283 309 1333 653 ...
 $ Department              : Factor w/ 3 levels "Human Resources",..: 3 2 2 3 2 2 2 3 3 2 ...
 $ DistanceFromHome        : int  13 14 18 1 2 10 5 10 10 10 ...
 $ Education               : Factor w/ 5 levels "1","2","3","4",..: 4 3 2 4 1 2 5 4 4 4 ...
 $ EducationField          : Factor w/ 6 levels "Human Resources",..: 2 4 2 3 6 2 4 2 2 6 ...
 $ EmployeeCount           : int  1 1 1 1 1 1 1 1 1 1 ...
 $ EmployeeNumber          : int  859 1128 1412 2016 1646 733 1448 1105 1055 1597 ...
 $ EnvironmentSatisfaction : Factor w/ 4 levels "1","2","3","4": 2 3 3 3 1 4 2 4 3 4 ...
 $ Gender                  : Factor w/ 2 levels "Female","Male": 2 2 2 1 1 2 2 1 1 2 ...
 $ HourlyRate              : int  73 44 60 48 32 32 90 88 87 92 ...
 $ JobInvolvement          : Factor w/ 4 levels "1","2","3","4": 3 2 3 3 3 3 4 2 3 2 ...
 $ JobLevel                : Factor w/ 5 levels "1","2","3","4",..: 2 5 3 3 1 3 1 2 1 2 ...
 $ JobRole                 : Factor w/ 9 levels "Sales Representative",..: 5 8 7 5 4 7 4 5 1 6 ...
 $ JobSatisfaction         : Factor w/ 4 levels "1","2","3","4": 4 3 4 4 4 1 3 4 3 3 ...
 $ MaritalStatus           : Factor w/ 3 levels "Single","Married",..: 3 1 1 2 1 3 2 3 2 2 ...
 $ MonthlyIncome           : int  4403 19626 9362 10422 3760 8793 2127 6694 2220 5063 ...
 $ MonthlyRate             : int  9250 17544 19944 24032 17218 4809 5561 24223 18410 15332 ...
 $ NumCompaniesWorked      : int  2 1 2 1 1 1 2 2 1 1 ...
 $ OverTime                : Factor w/ 2 levels "No","Yes": 1 1 1 1 2 1 2 2 2 1 ...
 $ PercentSalaryHike       : int  11 14 11 19 13 21 12 14 19 14 ...
 $ PerformanceRating       : Factor w/ 2 levels "3","4": 1 1 1 1 1 2 1 1 1 1 ...
 $ RelationshipSatisfaction: Factor w/ 4 levels "1","2","3","4": 3 1 3 3 3 3 1 3 4 2 ...
 $ StandardHours           : int  80 80 80 80 80 80 80 80 80 80 ...
 $ StockOptionLevel        : Factor w/ 4 levels "0","1","2","3": 2 1 1 3 1 3 1 4 2 2 ...
 $ TotalWorkingYears       : int  8 21 10 14 6 9 7 8 1 8 ...
 $ TrainingTimesLastYear   : int  3 2 2 3 2 4 5 5 2 3 ...
 $ WorkLifeBalance         : Factor w/ 4 levels "1","2","3","4": 2 4 3 3 3 2 2 3 3 2 ...
 $ YearsAtCompany          : int  5 20 2 14 6 9 4 1 1 8 ...
 $ YearsInCurrentRole      : int  2 7 2 10 3 7 2 0 1 2 ...
 $ YearsSinceLastPromotion : int  0 4 2 5 1 1 0 0 0 7 ...
 $ YearsWithCurrManager    : int  3 9 2 7 3 7 3 0 0 7 ...

# library(car)
# library(kableExtra)
#library(olsrr)

# Fit the model will all variables
fit = lm(MonthlyIncome ~ . - EmployeeCount - StandardHours, data = cs2_regres2) # removed aliased variables

# Calculate VIF
vif_values = vif(fit)
print(vif_values)

                                GVIF Df GVIF^(1/(2*Df))
ID                          1.096327  1        1.047057
Age                         2.042160  1        1.429042
Attrition                   1.533611  1        1.238391
BusinessTravel              1.162671  2        1.038399
DailyRate                   1.069008  1        1.033928
Department                120.636700  2        3.314132
DistanceFromHome            1.109161  1        1.053167
Education                   1.467884  4        1.049147
EducationField              3.375656  5        1.129369
EmployeeNumber              1.086228  1        1.042223
EnvironmentSatisfaction     1.236561  3        1.036023
Gender                      1.063360  1        1.031194
HourlyRate                  1.068540  1        1.033702
JobInvolvement              1.279705  3        1.041961
JobLevel                   23.519418  4        1.483981
JobRole                  1360.714690  8        1.569858
JobSatisfaction             1.255779  3        1.038689
MaritalStatus               3.173388  2        1.334691
MonthlyRate                 1.083265  1        1.040800
NumCompaniesWorked          1.439581  1        1.199825
OverTime                    1.169916  1        1.081626
PercentSalaryHike           2.698229  1        1.642629
PerformanceRating           2.672490  1        1.634775
RelationshipSatisfaction    1.234630  3        1.035753
StockOptionLevel            3.469022  3        1.230367
TotalWorkingYears           5.782735  1        2.404732
TrainingTimesLastYear       1.083486  1        1.040906
WorkLifeBalance             1.233537  3        1.035600
YearsAtCompany              5.449373  1        2.334389
YearsInCurrentRole          3.136986  1        1.771154
YearsSinceLastPromotion     1.945934  1        1.394968
YearsWithCurrManager        2.905212  1        1.704468

# Variable selection with significance level
fore1 = ols_step_forward_p(fit, p_val = 0.2, details = FALSE)
back1 = ols_step_backward_p(fit, p_val = 0.2, details = FALSE) # bigger p-remove, more variables in the model; smaller, fewer
step1 = ols_step_both_p(fit, p_enter = 0.2, p_remove = 0.2, details = FALSE) # stepwise selection
fore1


                                 Stepwise Summary                                  
---------------------------------------------------------------------------------
Step    Variable                AIC          SBC       SBIC      R2       Adj. R2 
---------------------------------------------------------------------------------
 0      Base Model           17145.913    17155.450      NA    0.00000    0.00000 
 1      JobLevel             14903.153    14931.764      NA    0.92476    0.92441 
 2      JobRole              14549.801    14616.560      NA    0.95079    0.95010 
 3      TotalWorkingYears    14516.912    14588.439      NA    0.95272    0.95200 
 4      BusinessTravel       14510.833    14591.897      NA    0.95327    0.95245 
 5      DailyRate            14508.366    14594.199      NA    0.95351    0.95263 
 6      ID                   14507.882    14598.483      NA    0.95364    0.95271 
 7      Education            14508.119    14617.794      NA    0.95405    0.95291 
 8      Department           14508.347    14627.559      NA    0.95425    0.95301 
---------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.977       RMSE                  982.850 
R-Squared                 0.954       MSE                993397.211 
Adj. R-Squared            0.953       Coef. Var              15.597 
Pred R-Squared            0.952       AIC                 14508.347 
MAE                     750.488       SBC                 14627.559 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17529210346.763         23    762139580.294    767.205    0.0000 
Residual        840414040.433        846       993397.211                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                 Parameter Estimates                                                   
----------------------------------------------------------------------------------------------------------------------
                           model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------
                     (Intercept)     2406.444       480.268                  5.011    0.000     1463.787     3349.101 
                       JobLevel2     1718.401       139.357        0.179    12.331    0.000     1444.875     1991.926 
                       JobLevel3     4969.685       186.184        0.388    26.692    0.000     4604.248     5335.122 
                       JobLevel4     8345.512       282.314        0.460    29.561    0.000     7791.394     8899.629 
                       JobLevel5    10956.672       332.389        0.481    32.963    0.000    10304.268    11609.075 
    JobRoleLaboratory Technician     -553.843       347.398       -0.046    -1.594    0.111    -1235.707      128.020 
          JobRoleHuman Resources     -160.035       488.393       -0.006    -0.328    0.743    -1118.639      798.568 
       JobRoleResearch Scientist     -355.408       346.876       -0.031    -1.025    0.306    -1036.246      325.430 
          JobRoleSales Executive     1223.232       199.731        0.112     6.124    0.000      831.205     1615.258 
JobRoleHealthcare Representative      654.111       377.637        0.040     1.732    0.084      -87.105     1395.326 
   JobRoleManufacturing Director      766.332       375.657        0.050     2.040    0.042       29.003     1503.662 
        JobRoleResearch Director     4193.228       407.197        0.214    10.298    0.000     3393.993     4992.462 
                  JobRoleManager     4284.007       336.139        0.219    12.745    0.000     3624.242     4943.772 
               TotalWorkingYears       44.199         7.766        0.072     5.692    0.000       28.956       59.441 
     BusinessTravelTravel_Rarely      344.502       111.437        0.034     3.091    0.002      125.776      563.229 
 BusinessTravelTravel_Frequently      205.236       131.572        0.017     1.560    0.119      -53.010      463.482 
                       DailyRate        0.179         0.085        0.016     2.100    0.036        0.012        0.345 
                              ID       -0.228         0.136       -0.012    -1.668    0.096       -0.495        0.040 
                      Education2      -37.724       126.274       -0.003    -0.299    0.765     -285.570      210.123 
                      Education3      -89.765       116.405       -0.009    -0.771    0.441     -318.242      138.713 
                      Education4       58.401       122.739        0.006     0.476    0.634     -182.507      299.309 
                      Education5     -457.613       226.221       -0.017    -2.023    0.043     -901.634      -13.593 
DepartmentResearch & Development      248.790       417.223        0.026     0.596    0.551     -570.123     1067.703 
                 DepartmentSales     -337.864       426.663       -0.034    -0.792    0.429    -1175.306      499.578 
----------------------------------------------------------------------------------------------------------------------

back1


                                     Stepwise Summary                                     
----------------------------------------------------------------------------------------
Step    Variable                       AIC          SBC       SBIC      R2       Adj. R2 
----------------------------------------------------------------------------------------
 0      Full Model                  14567.970    14882.690      NA    0.95541    0.95187 
 1      HourlyRate                  14565.970    14875.922      NA    0.95541    0.95193 
 2      Attrition                   14564.013    14869.196      NA    0.95541    0.95198 
 3      OverTime                    14562.084    14862.499      NA    0.95541    0.95204 
 4      Age                         14560.178    14855.824      NA    0.95540    0.95209 
 5      EnvironmentSatisfaction     14554.492    14835.833      NA    0.95538    0.95225 
 6      EducationField              14545.361    14802.860      NA    0.95534    0.95250 
 7      YearsAtCompany              14543.740    14796.470      NA    0.95532    0.95254 
 8      MaritalStatus               14540.603    14783.796      NA    0.95528    0.95260 
 9      StockOptionLevel            14536.170    14765.057      NA    0.95520    0.95269 
 10     JobInvolvement              14531.512    14746.094      NA    0.95513    0.95279 
 11     TrainingTimesLastYear       14530.114    14739.928      NA    0.95510    0.95281 
 12     JobSatisfaction             14525.876    14721.384      NA    0.95500    0.95289 
 13     NumCompaniesWorked          14524.487    14715.227      NA    0.95497    0.95291 
 14     RelationshipSatisfaction    14520.524    14696.958      NA    0.95487    0.95297 
 15     YearsInCurrentRole          14519.184    14690.850      NA    0.95483    0.95299 
 16     WorkLifeBalance             14515.161    14672.521      NA    0.95473    0.95306 
 17     YearsWithCurrManager        14513.771    14666.363      NA    0.95470    0.95308 
 18     MonthlyRate                 14512.431    14660.255      NA    0.95466    0.95310 
 19     YearsSinceLastPromotion     14511.385    14654.440      NA    0.95461    0.95310 
 20     DistanceFromHome            14510.453    14648.739      NA    0.95456    0.95310 
 21     EmployeeNumber              14509.712    14643.230      NA    0.95449    0.95309 
 22     Gender                      14509.157    14637.906      NA    0.95442    0.95307 
 23     PercentSalaryHike           14508.841    14632.822      NA    0.95433    0.95303 
 24     PerformanceRating           14508.347    14627.559      NA    0.95425    0.95301 
----------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.977       RMSE                  982.850 
R-Squared                 0.954       MSE                993397.211 
Adj. R-Squared            0.953       Coef. Var              15.597 
Pred R-Squared            0.952       AIC                 14508.347 
MAE                     750.488       SBC                 14627.559 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17529210346.763         23    762139580.294    767.205    0.0000 
Residual        840414040.433        846       993397.211                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                 Parameter Estimates                                                   
----------------------------------------------------------------------------------------------------------------------
                           model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------
                     (Intercept)     2406.444       480.268                  5.011    0.000     1463.787     3349.101 
                              ID       -0.228         0.136       -0.012    -1.668    0.096       -0.495        0.040 
     BusinessTravelTravel_Rarely      344.502       111.437        0.034     3.091    0.002      125.776      563.229 
 BusinessTravelTravel_Frequently      205.236       131.572        0.017     1.560    0.119      -53.010      463.482 
                       DailyRate        0.179         0.085        0.016     2.100    0.036        0.012        0.345 
DepartmentResearch & Development      248.790       417.223        0.026     0.596    0.551     -570.123     1067.703 
                 DepartmentSales     -337.864       426.663       -0.034    -0.792    0.429    -1175.306      499.578 
                      Education2      -37.724       126.274       -0.003    -0.299    0.765     -285.570      210.123 
                      Education3      -89.765       116.405       -0.009    -0.771    0.441     -318.242      138.713 
                      Education4       58.401       122.739        0.006     0.476    0.634     -182.507      299.309 
                      Education5     -457.613       226.221       -0.017    -2.023    0.043     -901.634      -13.593 
                       JobLevel2     1718.401       139.357        0.179    12.331    0.000     1444.875     1991.926 
                       JobLevel3     4969.685       186.184        0.388    26.692    0.000     4604.248     5335.122 
                       JobLevel4     8345.512       282.314        0.460    29.561    0.000     7791.394     8899.629 
                       JobLevel5    10956.672       332.389        0.481    32.963    0.000    10304.268    11609.075 
    JobRoleLaboratory Technician     -553.843       347.398       -0.046    -1.594    0.111    -1235.707      128.020 
          JobRoleHuman Resources     -160.035       488.393       -0.006    -0.328    0.743    -1118.639      798.568 
       JobRoleResearch Scientist     -355.408       346.876       -0.031    -1.025    0.306    -1036.246      325.430 
          JobRoleSales Executive     1223.232       199.731        0.112     6.124    0.000      831.205     1615.258 
JobRoleHealthcare Representative      654.111       377.637        0.040     1.732    0.084      -87.105     1395.326 
   JobRoleManufacturing Director      766.332       375.657        0.050     2.040    0.042       29.003     1503.662 
        JobRoleResearch Director     4193.228       407.197        0.214    10.298    0.000     3393.993     4992.462 
                  JobRoleManager     4284.007       336.139        0.219    12.745    0.000     3624.242     4943.772 
               TotalWorkingYears       44.199         7.766        0.072     5.692    0.000       28.956       59.441 
----------------------------------------------------------------------------------------------------------------------

step1


                                   Stepwise Summary                                    
-------------------------------------------------------------------------------------
Step    Variable                    AIC          SBC       SBIC      R2       Adj. R2 
-------------------------------------------------------------------------------------
 0      Base Model               17145.913    17155.450      NA    0.00000    0.00000 
 1      JobLevel (+)             14903.153    14931.764      NA    0.92476    0.92441 
 2      JobRole (+)              14549.801    14616.560      NA    0.95079    0.95010 
 3      TotalWorkingYears (+)    14516.912    14588.439      NA    0.95272    0.95200 
 4      BusinessTravel (+)       14510.833    14591.897      NA    0.95327    0.95245 
 5      DailyRate (+)            14508.366    14594.199      NA    0.95351    0.95263 
 6      ID (+)                   14507.882    14598.483      NA    0.95364    0.95271 
 7      Education (+)            14508.119    14617.794      NA    0.95405    0.95291 
 8      Department (+)           14508.347    14627.559      NA    0.95425    0.95301 
-------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.977       RMSE                  982.850 
R-Squared                 0.954       MSE                993397.211 
Adj. R-Squared            0.953       Coef. Var              15.597 
Pred R-Squared            0.952       AIC                 14508.347 
MAE                     750.488       SBC                 14627.559 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17529210346.763         23    762139580.294    767.205    0.0000 
Residual        840414040.433        846       993397.211                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                 Parameter Estimates                                                   
----------------------------------------------------------------------------------------------------------------------
                           model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------
                     (Intercept)     2406.444       480.268                  5.011    0.000     1463.787     3349.101 
                       JobLevel2     1718.401       139.357        0.179    12.331    0.000     1444.875     1991.926 
                       JobLevel3     4969.685       186.184        0.388    26.692    0.000     4604.248     5335.122 
                       JobLevel4     8345.512       282.314        0.460    29.561    0.000     7791.394     8899.629 
                       JobLevel5    10956.672       332.389        0.481    32.963    0.000    10304.268    11609.075 
    JobRoleLaboratory Technician     -553.843       347.398       -0.046    -1.594    0.111    -1235.707      128.020 
          JobRoleHuman Resources     -160.035       488.393       -0.006    -0.328    0.743    -1118.639      798.568 
       JobRoleResearch Scientist     -355.408       346.876       -0.031    -1.025    0.306    -1036.246      325.430 
          JobRoleSales Executive     1223.232       199.731        0.112     6.124    0.000      831.205     1615.258 
JobRoleHealthcare Representative      654.111       377.637        0.040     1.732    0.084      -87.105     1395.326 
   JobRoleManufacturing Director      766.332       375.657        0.050     2.040    0.042       29.003     1503.662 
        JobRoleResearch Director     4193.228       407.197        0.214    10.298    0.000     3393.993     4992.462 
                  JobRoleManager     4284.007       336.139        0.219    12.745    0.000     3624.242     4943.772 
               TotalWorkingYears       44.199         7.766        0.072     5.692    0.000       28.956       59.441 
     BusinessTravelTravel_Rarely      344.502       111.437        0.034     3.091    0.002      125.776      563.229 
 BusinessTravelTravel_Frequently      205.236       131.572        0.017     1.560    0.119      -53.010      463.482 
                       DailyRate        0.179         0.085        0.016     2.100    0.036        0.012        0.345 
                              ID       -0.228         0.136       -0.012    -1.668    0.096       -0.495        0.040 
                      Education2      -37.724       126.274       -0.003    -0.299    0.765     -285.570      210.123 
                      Education3      -89.765       116.405       -0.009    -0.771    0.441     -318.242      138.713 
                      Education4       58.401       122.739        0.006     0.476    0.634     -182.507      299.309 
                      Education5     -457.613       226.221       -0.017    -2.023    0.043     -901.634      -13.593 
DepartmentResearch & Development      248.790       417.223        0.026     0.596    0.551     -570.123     1067.703 
                 DepartmentSales     -337.864       426.663       -0.034    -0.792    0.429    -1175.306      499.578 
----------------------------------------------------------------------------------------------------------------------

# forward: JobLevel, JobRole, TotalWorkingYears, BusinessTravel, DailyRate, ID, Education, Department
# backward: ID, BusinessTravel, DailyRate, Department, Education, JobLevel, JobRole, TotalWorkingYears
# stepwise: JobLevel, JobRole, TotalWorkingYears, BusinessTravel, DailyRate, ID, Education, Department

# Variable selection with AIC
fore2 = ols_step_forward_aic(fit, details = FALSE)
back2 = ols_step_backward_aic(fit, details = FALSE)
step2 = ols_step_both_aic(fit, details = FALSE)
fore2


                                 Stepwise Summary                                  
---------------------------------------------------------------------------------
Step    Variable                AIC          SBC       SBIC      R2       Adj. R2 
---------------------------------------------------------------------------------
 0      Base Model           17145.913    17155.450      NA    0.00000    0.00000 
 1      JobLevel             14903.153    14931.764      NA    0.92476    0.92441 
 2      JobRole              14549.801    14616.560      NA    0.95079    0.95010 
 3      TotalWorkingYears    14516.912    14588.439      NA    0.95272    0.95200 
 4      BusinessTravel       14510.833    14591.897      NA    0.95327    0.95245 
 5      DailyRate            14508.366    14594.199      NA    0.95351    0.95263 
 6      ID                   14507.882    14598.483      NA    0.95364    0.95271 
---------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.977       RMSE                  989.387 
R-Squared                 0.954       MSE                999567.033 
Adj. R-Squared            0.953       Coef. Var              15.645 
Pred R-Squared            0.952       AIC                 14507.882 
MAE                     757.865       SBC                 14598.483 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                      ANOVA                                       
---------------------------------------------------------------------------------
                       Sum of                                                    
                      Squares         DF       Mean Square       F          Sig. 
---------------------------------------------------------------------------------
Regression    17517993274.884         17    1030470192.640    1030.917    0.0000 
Residual        851631112.311        852        999567.033                       
Total         18369624387.195        869                                         
---------------------------------------------------------------------------------

                                                 Parameter Estimates                                                   
----------------------------------------------------------------------------------------------------------------------
                           model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------
                     (Intercept)     2047.802       198.897                 10.296    0.000     1657.417     2438.188 
                       JobLevel2     1708.803       138.458        0.178    12.342    0.000     1437.044     1980.561 
                       JobLevel3     4941.408       186.075        0.386    26.556    0.000     4576.189     5306.627 
                       JobLevel4     8261.027       280.819        0.456    29.418    0.000     7709.849     8812.206 
                       JobLevel5    10937.256       330.773        0.480    33.066    0.000    10288.031    11586.481 
    JobRoleLaboratory Technician       20.887       162.666        0.002     0.128    0.898     -298.386      340.159 
          JobRoleHuman Resources      153.145       238.202        0.006     0.643    0.520     -314.386      620.677 
       JobRoleResearch Scientist      212.049       159.830        0.018     1.327    0.185     -101.658      525.757 
          JobRoleSales Executive     1226.701       199.750        0.112     6.141    0.000      834.641     1618.762 
JobRoleHealthcare Representative     1245.795       220.122        0.077     5.660    0.000      813.751     1677.840 
   JobRoleManufacturing Director     1353.309       216.300        0.088     6.257    0.000      928.766     1777.853 
        JobRoleResearch Director     4747.815       267.694        0.243    17.736    0.000     4222.398     5273.233 
                  JobRoleManager     4618.324       290.233        0.236    15.912    0.000     4048.668     5187.981 
               TotalWorkingYears       45.282         7.716        0.074     5.869    0.000       30.138       60.427 
     BusinessTravelTravel_Rarely      331.967       111.601        0.033     2.975    0.003      112.923      551.011 
 BusinessTravelTravel_Frequently      187.285       131.735        0.016     1.422    0.155      -71.278      445.848 
                       DailyRate        0.174         0.085        0.015     2.044    0.041        0.007        0.341 
                              ID       -0.213         0.136       -0.012    -1.561    0.119       -0.481        0.055 
----------------------------------------------------------------------------------------------------------------------

back2


                                       Stepwise Summary                                        
---------------------------------------------------------------------------------------------
Step    Variable                       AIC          SBC         SBIC         R2       Adj. R2 
---------------------------------------------------------------------------------------------
 0      Full Model                  14567.970    14882.690           NA    0.95541    0.95187 
 1      EducationField              14558.870    14849.748    12038.647    0.95537    0.95211 
 2      EnvironmentSatisfaction     14553.211    14829.784    12036.595    0.95535    0.95227 
 3      JobInvolvement              14548.857    14811.124    12035.865    0.95526    0.95236 
 4      StockOptionLevel            14544.370    14792.332    12035.021    0.95519    0.95245 
 5      RelationshipSatisfaction    14540.121    14773.777    12034.431    0.95510    0.95253 
 6      JobSatisfaction             14536.064    14755.414    12034.050    0.95499    0.95259 
 7      WorkLifeBalance             14532.198    14737.244    12033.878    0.95488    0.95265 
 8      MaritalStatus               14528.858    14724.366    12032.310    0.95485    0.95273 
 9      HourlyRate                  14526.858    14717.598    12030.154    0.95485    0.95279 
 10     Age                         14524.932    14710.903    12028.076    0.95485    0.95284 
 11     Attrition                   14523.015    14704.218    12026.013    0.95484    0.95289 
 12     OverTime                    14521.114    14697.548    12023.970    0.95484    0.95294 
 13     NumCompaniesWorked          14519.461    14691.127    12022.181    0.95482    0.95298 
 14     YearsWithCurrManager        14517.865    14684.762    12020.454    0.95480    0.95301 
 15     TrainingTimesLastYear       14516.385    14678.514    12018.848    0.95477    0.95304 
 16     MonthlyRate                 14515.205    14672.565    12017.547    0.95473    0.95305 
 17     YearsInCurrentRole          14513.998    14666.590    12016.225    0.95469    0.95307 
 18     YearsAtCompany              14512.431    14660.255    12014.547    0.95466    0.95310 
 19     YearsSinceLastPromotion     14511.385    14654.440    12013.395    0.95461    0.95310 
 20     Education                   14510.250    14634.231    12018.065    0.95425    0.95296 
 21     DistanceFromHome            14509.513    14628.725    12017.239    0.95419    0.95294 
 22     EmployeeNumber              14508.953    14623.397    12016.596    0.95411    0.95292 
 23     Gender                      14508.463    14618.139    12016.028    0.95403    0.95289 
 24     Department                  14508.418    14608.557    12017.888    0.95382    0.95279 
 25     PercentSalaryHike           14508.337    14603.707    12017.741    0.95372    0.95274 
 26     PerformanceRating           14507.882    14598.483    12017.223    0.95364    0.95271 
---------------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.977       RMSE                  989.387 
R-Squared                 0.954       MSE                999567.033 
Adj. R-Squared            0.953       Coef. Var              15.645 
Pred R-Squared            0.952       AIC                 14507.882 
MAE                     757.865       SBC                 14598.483 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                      ANOVA                                       
---------------------------------------------------------------------------------
                       Sum of                                                    
                      Squares         DF       Mean Square       F          Sig. 
---------------------------------------------------------------------------------
Regression    17517993274.884         17    1030470192.640    1030.917    0.0000 
Residual        851631112.311        852        999567.033                       
Total         18369624387.195        869                                         
---------------------------------------------------------------------------------

                                                 Parameter Estimates                                                   
----------------------------------------------------------------------------------------------------------------------
                           model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------
                     (Intercept)     2047.802       198.897                 10.296    0.000     1657.417     2438.188 
                              ID       -0.213         0.136       -0.012    -1.561    0.119       -0.481        0.055 
     BusinessTravelTravel_Rarely      331.967       111.601        0.033     2.975    0.003      112.923      551.011 
 BusinessTravelTravel_Frequently      187.285       131.735        0.016     1.422    0.155      -71.278      445.848 
                       DailyRate        0.174         0.085        0.015     2.044    0.041        0.007        0.341 
                       JobLevel2     1708.803       138.458        0.178    12.342    0.000     1437.044     1980.561 
                       JobLevel3     4941.408       186.075        0.386    26.556    0.000     4576.189     5306.627 
                       JobLevel4     8261.027       280.819        0.456    29.418    0.000     7709.849     8812.206 
                       JobLevel5    10937.256       330.773        0.480    33.066    0.000    10288.031    11586.481 
    JobRoleLaboratory Technician       20.887       162.666        0.002     0.128    0.898     -298.386      340.159 
          JobRoleHuman Resources      153.145       238.202        0.006     0.643    0.520     -314.386      620.677 
       JobRoleResearch Scientist      212.049       159.830        0.018     1.327    0.185     -101.658      525.757 
          JobRoleSales Executive     1226.701       199.750        0.112     6.141    0.000      834.641     1618.762 
JobRoleHealthcare Representative     1245.795       220.122        0.077     5.660    0.000      813.751     1677.840 
   JobRoleManufacturing Director     1353.309       216.300        0.088     6.257    0.000      928.766     1777.853 
        JobRoleResearch Director     4747.815       267.694        0.243    17.736    0.000     4222.398     5273.233 
                  JobRoleManager     4618.324       290.233        0.236    15.912    0.000     4048.668     5187.981 
               TotalWorkingYears       45.282         7.716        0.074     5.869    0.000       30.138       60.427 
----------------------------------------------------------------------------------------------------------------------

step2


                                   Stepwise Summary                                    
-------------------------------------------------------------------------------------
Step    Variable                    AIC          SBC       SBIC      R2       Adj. R2 
-------------------------------------------------------------------------------------
 0      Base Model               17145.913    17155.450      NA    0.00000    0.00000 
 1      JobLevel (+)             14903.153    14931.764      NA    0.92476    0.92441 
 2      JobRole (+)              14549.801    14616.560      NA    0.95079    0.95010 
 3      TotalWorkingYears (+)    14516.912    14588.439      NA    0.95272    0.95200 
 4      BusinessTravel (+)       14510.833    14591.897      NA    0.95327    0.95245 
 5      DailyRate (+)            14508.366    14594.199      NA    0.95351    0.95263 
 6      ID (+)                   14507.882    14598.483      NA    0.95364    0.95271 
-------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.977       RMSE                  989.387 
R-Squared                 0.954       MSE                999567.033 
Adj. R-Squared            0.953       Coef. Var              15.645 
Pred R-Squared            0.952       AIC                 14507.882 
MAE                     757.865       SBC                 14598.483 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                      ANOVA                                       
---------------------------------------------------------------------------------
                       Sum of                                                    
                      Squares         DF       Mean Square       F          Sig. 
---------------------------------------------------------------------------------
Regression    17517993274.884         17    1030470192.640    1030.917    0.0000 
Residual        851631112.311        852        999567.033                       
Total         18369624387.195        869                                         
---------------------------------------------------------------------------------

                                                 Parameter Estimates                                                   
----------------------------------------------------------------------------------------------------------------------
                           model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------
                     (Intercept)     2047.802       198.897                 10.296    0.000     1657.417     2438.188 
                       JobLevel2     1708.803       138.458        0.178    12.342    0.000     1437.044     1980.561 
                       JobLevel3     4941.408       186.075        0.386    26.556    0.000     4576.189     5306.627 
                       JobLevel4     8261.027       280.819        0.456    29.418    0.000     7709.849     8812.206 
                       JobLevel5    10937.256       330.773        0.480    33.066    0.000    10288.031    11586.481 
    JobRoleLaboratory Technician       20.887       162.666        0.002     0.128    0.898     -298.386      340.159 
          JobRoleHuman Resources      153.145       238.202        0.006     0.643    0.520     -314.386      620.677 
       JobRoleResearch Scientist      212.049       159.830        0.018     1.327    0.185     -101.658      525.757 
          JobRoleSales Executive     1226.701       199.750        0.112     6.141    0.000      834.641     1618.762 
JobRoleHealthcare Representative     1245.795       220.122        0.077     5.660    0.000      813.751     1677.840 
   JobRoleManufacturing Director     1353.309       216.300        0.088     6.257    0.000      928.766     1777.853 
        JobRoleResearch Director     4747.815       267.694        0.243    17.736    0.000     4222.398     5273.233 
                  JobRoleManager     4618.324       290.233        0.236    15.912    0.000     4048.668     5187.981 
               TotalWorkingYears       45.282         7.716        0.074     5.869    0.000       30.138       60.427 
     BusinessTravelTravel_Rarely      331.967       111.601        0.033     2.975    0.003      112.923      551.011 
 BusinessTravelTravel_Frequently      187.285       131.735        0.016     1.422    0.155      -71.278      445.848 
                       DailyRate        0.174         0.085        0.015     2.044    0.041        0.007        0.341 
                              ID       -0.213         0.136       -0.012    -1.561    0.119       -0.481        0.055 
----------------------------------------------------------------------------------------------------------------------

# forward: JobLevel, JobRole, TotalWorkingYears, BusinessTravel, DailyRate, ID
# backward: ID + BusinessTravel + DailyRate + JobLevel + JobRole + TotalWorkingYears
# stepwise: JobLevel, JobRole, TotalWorkingYears, BusinessTravel, DailyRate, ID


# Create 2-way interactions with the most important variables from the variable selection above and run variable selection including them
cs2_regresSmall = cs2_regres2 %>% 
  select(MonthlyIncome, ID, BusinessTravel, DailyRate, Department, Education, JobLevel, JobRole, TotalWorkingYears)
str(cs2_regresSmall)

'data.frame':   870 obs. of  9 variables:
 $ MonthlyIncome    : int  4403 19626 9362 10422 3760 8793 2127 6694 2220 5063 ...
 $ ID               : int  1 2 3 4 5 6 7 8 9 10 ...
 $ BusinessTravel   : Factor w/ 3 levels "Non-Travel","Travel_Rarely",..: 2 2 3 2 3 3 2 2 2 3 ...
 $ DailyRate        : int  117 1308 200 801 567 294 1283 309 1333 653 ...
 $ Department       : Factor w/ 3 levels "Human Resources",..: 3 2 2 3 2 2 2 3 3 2 ...
 $ Education        : Factor w/ 5 levels "1","2","3","4",..: 4 3 2 4 1 2 5 4 4 4 ...
 $ JobLevel         : Factor w/ 5 levels "1","2","3","4",..: 2 5 3 3 1 3 1 2 1 2 ...
 $ JobRole          : Factor w/ 9 levels "Sales Representative",..: 5 8 7 5 4 7 4 5 1 6 ...
 $ TotalWorkingYears: int  8 21 10 14 6 9 7 8 1 8 ...

fit2 = lm(MonthlyIncome ~ .^2, data = cs2_regresSmall)

fore3 = ols_step_forward_p(fit2, p_val = 0.2, details = FALSE)
back3 = ols_step_backward_p(fit2, p_val = 0.2, details = FALSE)
# step3 = ols_step_both_p(fit2, p_enter = 0.2, p_remove = 0.2, details = FALSE) # this gets an error
fore3


                                           Stepwise Summary                                            
-----------------------------------------------------------------------------------------------------
Step    Variable                               AIC          SBC         SBIC         R2       Adj. R2 
-----------------------------------------------------------------------------------------------------
 0      Base Model                          17145.913    17155.450    14673.060    0.00000    0.00000 
 1      JobLevel                            14903.153    14931.764    12423.882    0.92476    0.92441 
 2      JobRole                             14549.801    14616.560    12056.020    0.95079    0.95010 
 3      TotalWorkingYears                   14516.912    14588.439    12021.959    0.95272    0.95200 
 4      BusinessTravel                      14510.833    14591.897    12012.640    0.95327    0.95245 
 5      DailyRate                           14508.366    14594.199    12008.918    0.95351    0.95263 
 6      ID:TotalWorkingYears                14506.847    14597.449    12006.143    0.95369    0.95277 
 7      Department                          14506.644    14606.782    12002.695    0.95392    0.95289 
 8      Education                           14506.843    14626.055    11995.688    0.95433    0.95309 
 9      JobLevel:TotalWorkingYears          14502.096    14640.382    11983.797    0.95499    0.95355 
 10     JobRole:TotalWorkingYears           14481.506    14657.940    11948.342    0.95685    0.95504 
 11     ID                                  14483.504    14664.707    11949.117    0.95685    0.95498 
 12     BusinessTravel:TotalWorkingYears    14482.435    14673.175    11944.889    0.95710    0.95514 
 13     ID:DailyRate                        14482.652    14678.161    11943.911    0.95719    0.95517 
-----------------------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.978       RMSE                  950.795 
R-Squared                 0.957       MSE                947577.972 
Adj. R-Squared            0.955       Coef. Var              15.233 
Pred R-Squared            0.953       AIC                 14482.652 
MAE                     719.332       SBC                 14678.161 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17583134670.495         39    450849606.936    475.792    0.0000 
Residual        786489716.700        830       947577.972                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                          Parameter Estimates                                                            
----------------------------------------------------------------------------------------------------------------------------------------
                                             model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------------------------
                                       (Intercept)     2096.372       550.478                  3.808    0.000     1015.879     3176.866 
                                         JobLevel2     3454.874       375.618        0.361     9.198    0.000     2717.602     4192.146 
                                         JobLevel3     5910.328       426.433        0.461    13.860    0.000     5073.315     6747.341 
                                         JobLevel4    11466.881       803.739        0.632    14.267    0.000     9889.281    13044.482 
                                         JobLevel5    13660.280      1129.838        0.600    12.090    0.000    11442.604    15877.956 
                      JobRoleLaboratory Technician     -311.497       390.806       -0.026    -0.797    0.426    -1078.581      455.586 
                            JobRoleHuman Resources       32.530       638.927        0.001     0.051    0.959    -1221.574     1286.633 
                         JobRoleResearch Scientist     -436.485       388.177       -0.038    -1.124    0.261    -1198.409      325.440 
                            JobRoleSales Executive     -582.624       437.934       -0.053    -1.330    0.184    -1442.212      276.965 
                  JobRoleHealthcare Representative     -943.548       570.212       -0.058    -1.655    0.098    -2062.775      175.680 
                     JobRoleManufacturing Director    -1146.193       559.029       -0.075    -2.050    0.041    -2243.470      -48.916 
                          JobRoleResearch Director     2399.402       759.128        0.123     3.161    0.002      909.366     3889.438 
                                    JobRoleManager     2377.394       858.594        0.122     2.769    0.006      692.123     4062.665 
                                 TotalWorkingYears       86.402        33.537        0.141     2.576    0.010       20.574      152.230 
                       BusinessTravelTravel_Rarely      540.376       189.316        0.053     2.854    0.004      168.781      911.970 
                   BusinessTravelTravel_Frequently      579.880       222.998        0.049     2.600    0.009      142.174     1017.586 
                                         DailyRate       -0.005         0.173        0.000    -0.026    0.979       -0.344        0.335 
                  DepartmentResearch & Development      290.272       438.189        0.030     0.662    0.508     -569.816     1150.361 
                                   DepartmentSales     -295.333       446.250       -0.030    -0.662    0.508    -1171.245      580.578 
                                        Education2       32.039       125.270        0.003     0.256    0.798     -213.844      277.921 
                                        Education3      -32.169       115.093       -0.003    -0.280    0.780     -258.077      193.739 
                                        Education4       82.590       121.267        0.008     0.681    0.496     -155.435      320.616 
                                        Education5     -478.152       224.810       -0.018    -2.127    0.034     -919.416      -36.889 
                                                ID       -0.343         0.362       -0.019    -0.948    0.343       -1.053        0.367 
                              TotalWorkingYears:ID       -0.021         0.018       -0.021    -1.182    0.238       -0.056        0.014 
                       JobLevel2:TotalWorkingYears     -134.950        30.503       -0.162    -4.424    0.000     -194.823      -75.077 
                       JobLevel3:TotalWorkingYears      -75.976        31.922       -0.094    -2.380    0.018     -138.634      -13.318 
                       JobLevel4:TotalWorkingYears     -190.931        42.477       -0.275    -4.495    0.000     -274.306     -107.557 
                       JobLevel5:TotalWorkingYears     -173.090        53.061       -0.203    -3.262    0.001     -277.240      -68.940 
    JobRoleLaboratory Technician:TotalWorkingYears      -33.148        33.922       -0.027    -0.977    0.329      -99.731       33.435 
          JobRoleHuman Resources:TotalWorkingYears      -33.149        67.192       -0.009    -0.493    0.622     -165.035       98.738 
       JobRoleResearch Scientist:TotalWorkingYears       12.455        33.532        0.010     0.371    0.710      -53.362       78.272 
          JobRoleSales Executive:TotalWorkingYears      138.103        42.634        0.160     3.239    0.001       54.420      221.786 
JobRoleHealthcare Representative:TotalWorkingYears      119.088        44.019        0.115     2.705    0.007       32.686      205.490 
   JobRoleManufacturing Director:TotalWorkingYears      144.953        44.067        0.134     3.289    0.001       58.458      231.449 
        JobRoleResearch Director:TotalWorkingYears      130.684        50.106        0.149     2.608    0.009       32.335      229.034 
                  JobRoleManager:TotalWorkingYears      136.550        51.948        0.178     2.629    0.009       34.586      238.515 
     TotalWorkingYears:BusinessTravelTravel_Rarely      -23.891        15.581       -0.042    -1.533    0.126      -54.475        6.692 
 TotalWorkingYears:BusinessTravelTravel_Frequently      -39.701        17.497       -0.047    -2.269    0.024      -74.044       -5.359 
                                      DailyRate:ID        0.000         0.000        0.027     1.305    0.192        0.000        0.001 
----------------------------------------------------------------------------------------------------------------------------------------

back3


                                         Stepwise Summary                                          
-------------------------------------------------------------------------------------------------
Step    Variable                           AIC          SBC         SBIC         R2       Adj. R2 
-------------------------------------------------------------------------------------------------
 0      Full Model                      14731.980    15857.344    11825.552    0.96358    0.95345 
 1      Department:TotalWorkingYears    14728.015    15843.843    11824.666    0.96358    0.95352 
 2      BusinessTravel:JobRole          14699.356    15738.888    11826.964    0.96344    0.95435 
 3      BusinessTravel:DailyRate        14695.645    15725.640    11826.326    0.96342    0.95446 
 4      ID:Education                    14688.416    15699.336    11826.154    0.96339    0.95468 
 5      DailyRate:TotalWorkingYears     14686.893    15693.045    11825.700    0.96337    0.95472 
 6      DailyRate:Department            14683.908    15680.523    11825.768    0.96333    0.95480 
 7      ID:Department                   14680.761    15667.839    11825.680    0.96329    0.95488 
 8      Department:JobLevel             14665.621    15614.551    11825.602    0.96326    0.95503 
 9      Department:Education            14653.709    15564.491    11828.657    0.96308    0.95519 
 10     ID:BusinessTravel               14651.246    15552.491    11829.244    0.96302    0.95524 
 11     ID:JobRole                      14643.335    15506.432    11836.209    0.96267    0.95532 
 12     DailyRate:JobRole               14634.444    15459.393    11842.237    0.96237    0.95544 
 13     Education:JobRole               14605.207    15277.565    11875.269    0.96083    0.95551 
 14     DailyRate:JobLevel              14601.174    15254.458    11878.290    0.96065    0.95554 
 15     BusinessTravel:Department       14597.511    15231.720    11881.682    0.96046    0.95555 
 16     Education:JobLevel              14582.447    15140.361    11897.425    0.95968    0.95559 
 17     DailyRate:Education             14577.808    15116.647    11899.891    0.95952    0.95564 
 18     Department                      14577.808    15116.647    11899.891    0.95952    0.95564 
 19     Department:JobRole              14544.171    14997.177    11901.383    0.95941    0.95563 
 20     JobRole:TotalWorkingYears       14538.485    14953.344    11910.696    0.95893    0.95555 
 21     ID:TotalWorkingYears            14537.830    14947.921    11911.203    0.95887    0.95554 
 22     Education:TotalWorkingYears     14535.726    14926.742    11916.196    0.95859    0.95546 
-------------------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.979       RMSE                  935.119 
R-Squared                 0.959       MSE                941546.719 
Adj. R-Squared            0.955       Coef. Var              15.185 
Pred R-Squared             -Inf       AIC                 14535.726 
MAE                     700.747       SBC                 14926.742 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17608854637.839         61    288669748.161    306.591    0.0000 
Residual        760769749.356        808       941546.719                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                          Parameter Estimates                                                           
---------------------------------------------------------------------------------------------------------------------------------------
                                            model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
---------------------------------------------------------------------------------------------------------------------------------------
                                      (Intercept)     1931.368       436.692                  4.423    0.000     1074.183     2788.552 
                                               ID       -0.169         0.352       -0.009    -0.481    0.631       -0.859        0.521 
                      BusinessTravelTravel_Rarely      274.115       400.945        0.027     0.684    0.494     -512.901     1061.130 
                  BusinessTravelTravel_Frequently      663.288       461.583        0.056     1.437    0.151     -242.756     1569.332 
                                        DailyRate       -0.034         0.175       -0.003    -0.193    0.847       -0.378        0.310 
                                       Education2      213.046       407.188        0.019     0.523    0.601     -586.225     1012.317 
                                       Education3     -454.374       387.918       -0.048    -1.171    0.242    -1215.821      307.072 
                                       Education4      407.244       412.011        0.040     0.988    0.323     -401.494     1215.981 
                                       Education5     -278.193       801.607       -0.010    -0.347    0.729    -1851.669     1295.284 
                                        JobLevel2     1710.172       683.493        0.178     2.502    0.013      368.540     3051.804 
                                        JobLevel3     4372.304       975.583        0.341     4.482    0.000     2457.328     6287.279 
                                        JobLevel4    10004.610      1361.182        0.552     7.350    0.000     7332.740    12676.480 
                                        JobLevel5    10451.257      1774.960        0.459     5.888    0.000     6967.180    13935.333 
                     JobRoleLaboratory Technician      174.118       169.872        0.014     1.025    0.306     -159.324      507.560 
                           JobRoleHuman Resources       74.997       251.126        0.003     0.299    0.765     -417.940      567.934 
                        JobRoleResearch Scientist      194.985       167.254        0.017     1.166    0.244     -133.318      523.288 
                           JobRoleSales Executive      822.192       778.622        0.075     1.056    0.291     -706.169     2350.554 
                 JobRoleHealthcare Representative      218.821       806.431        0.013     0.271    0.786    -1364.126     1801.767 
                    JobRoleManufacturing Director     1129.165       580.726        0.074     1.944    0.052      -10.746     2269.075 
                         JobRoleResearch Director     3896.783       796.474        0.199     4.893    0.000     2333.381     5460.186 
                                   JobRoleManager     3947.259       718.521        0.202     5.494    0.000     2536.870     5357.648 
                                TotalWorkingYears      101.416        29.196        0.166     3.474    0.001       44.108      158.725 
                                     ID:DailyRate        0.000         0.000        0.027     1.276    0.202        0.000        0.001 
                                     ID:JobLevel2       -0.775         0.318       -0.043    -2.435    0.015       -1.399       -0.150 
                                     ID:JobLevel3       -0.467         0.407       -0.020    -1.147    0.252       -1.267        0.332 
                                     ID:JobLevel4       -0.174         0.586       -0.005    -0.296    0.767       -1.325        0.978 
                                     ID:JobLevel5       -0.293         0.680       -0.006    -0.431    0.667       -1.629        1.043 
           BusinessTravelTravel_Rarely:Education2      -75.294       433.711       -0.006    -0.174    0.862     -926.627      776.039 
       BusinessTravelTravel_Frequently:Education2     -682.001       498.347       -0.028    -1.369    0.172    -1660.208      296.207 
           BusinessTravelTravel_Rarely:Education3      507.250       410.350        0.049     1.236    0.217     -298.228     1312.727 
       BusinessTravelTravel_Frequently:Education3      268.878       465.528        0.015     0.578    0.564     -644.908     1182.665 
           BusinessTravelTravel_Rarely:Education4     -313.654       435.213       -0.027    -0.721    0.471    -1167.935      540.626 
       BusinessTravelTravel_Frequently:Education4     -462.340       499.286       -0.020    -0.926    0.355    -1442.390      517.710 
           BusinessTravelTravel_Rarely:Education5       -2.820       849.168        0.000    -0.003    0.997    -1669.655     1664.015 
       BusinessTravelTravel_Frequently:Education5     -661.275       931.682       -0.013    -0.710    0.478    -2490.078     1167.528 
            BusinessTravelTravel_Rarely:JobLevel2      814.678       325.847        0.076     2.500    0.013      175.072     1454.283 
        BusinessTravelTravel_Frequently:JobLevel2      670.612       370.711        0.036     1.809    0.071      -57.058     1398.281 
            BusinessTravelTravel_Rarely:JobLevel3      528.060       428.411        0.035     1.233    0.218     -312.870     1368.991 
        BusinessTravelTravel_Frequently:JobLevel3      967.560       496.072        0.036     1.950    0.051       -6.182     1941.301 
            BusinessTravelTravel_Rarely:JobLevel4      451.852       906.659        0.021     0.498    0.618    -1327.832     2231.537 
        BusinessTravelTravel_Frequently:JobLevel4      903.738       977.555        0.024     0.924    0.356    -1015.109     2822.585 
            BusinessTravelTravel_Rarely:JobLevel5     2219.553      1284.285        0.092     1.728    0.084     -301.376     4740.482 
        BusinessTravelTravel_Frequently:JobLevel5     1716.209      1425.501        0.022     1.204    0.229    -1081.912     4514.330 
    BusinessTravelTravel_Rarely:TotalWorkingYears      -50.722        27.893       -0.089    -1.818    0.069     -105.474        4.029 
BusinessTravelTravel_Frequently:TotalWorkingYears      -77.352        31.161       -0.091    -2.482    0.013     -138.517      -16.187 
           JobLevel2:JobRoleLaboratory Technician     -198.715       615.421       -0.008    -0.323    0.747    -1406.727     1009.297 
           JobLevel3:JobRoleLaboratory Technician    -4066.656      1057.198       -0.052    -3.847    0.000    -6141.834    -1991.478 
           JobLevel4:JobRoleLaboratory Technician           NA       945.287        0.000     0.359    0.720           NA           NA 
           JobLevel5:JobRoleLaboratory Technician           NA      1117.711        0.000     0.321    0.748           NA           NA 
                 JobLevel2:JobRoleHuman Resources      339.550       615.763        0.003     0.426    0.670    -1515.958     2195.057 
                 JobLevel3:JobRoleHuman Resources      359.095      1321.708       -0.004    -0.290    0.772    -1834.864     2553.054 
                 JobLevel4:JobRoleHuman Resources           NA       543.627        0.000     0.475    0.635           NA           NA 
                 JobLevel5:JobRoleHuman Resources           NA       628.512        0.000    -0.321    0.748           NA           NA 
              JobLevel2:JobRoleResearch Scientist      262.454       594.335        0.039     1.640    0.101     -946.230     1471.137 
              JobLevel3:JobRoleResearch Scientist     -382.783       669.702        0.002     0.354    0.724    -2977.169     2211.604 
              JobLevel4:JobRoleResearch Scientist           NA       649.737        0.000    -0.596    0.551           NA           NA 
              JobLevel5:JobRoleResearch Scientist           NA       604.821        0.000     0.392    0.695           NA           NA 
                 JobLevel2:JobRoleSales Executive      258.330       474.939        0.022     0.585    0.559     -808.758     1325.418 
                 JobLevel3:JobRoleSales Executive     -201.852        20.084       -0.001    -1.391    0.165    -1435.561     1031.857 
                 JobLevel4:JobRoleSales Executive           NA        21.342        0.001     2.920    0.004           NA           NA 
                 JobLevel5:JobRoleSales Executive           NA        27.605        0.000    -2.265    0.024           NA           NA 
       JobLevel2:JobRoleHealthcare Representative      974.696        36.601       -0.002    -0.857    0.392     -191.926     2141.318 
       JobLevel3:JobRoleHealthcare Representative      236.949            NA        0.000        NA       NA    -1077.611     1551.510 
       JobLevel4:JobRoleHealthcare Representative           NA            NA        0.005        NA       NA           NA           NA 
       JobLevel5:JobRoleHealthcare Representative           NA            NA        0.000        NA       NA           NA           NA 
          JobLevel2:JobRoleManufacturing Director           NA            NA        0.000        NA       NA           NA           NA 
          JobLevel3:JobRoleManufacturing Director     -387.127            NA        0.008        NA       NA    -1662.499      888.244 
          JobLevel4:JobRoleManufacturing Director           NA            NA       -0.009        NA       NA           NA           NA 
          JobLevel5:JobRoleManufacturing Director           NA            NA        0.000        NA       NA           NA           NA 
               JobLevel2:JobRoleResearch Director           NA            NA        0.000        NA       NA           NA           NA 
               JobLevel3:JobRoleResearch Director      237.018            NA        0.057        NA       NA     -950.188     1424.224 
               JobLevel4:JobRoleResearch Director      277.747            NA        0.124        NA       NA     -654.512     1210.007 
               JobLevel5:JobRoleResearch Director           NA            NA        0.283        NA       NA           NA           NA 
                         JobLevel2:JobRoleManager           NA            NA        0.000        NA       NA           NA           NA 
                         JobLevel3:JobRoleManager           NA            NA        0.003        NA       NA           NA           NA 
                         JobLevel4:JobRoleManager           NA            NA        0.003        NA       NA           NA           NA 
                         JobLevel5:JobRoleManager           NA            NA        0.007        NA       NA           NA           NA 
                      JobLevel2:TotalWorkingYears      -27.935            NA        0.990        NA       NA      -67.358       11.488 
                      JobLevel3:TotalWorkingYears       62.326            NA        0.271        NA       NA       20.434      104.218 
                      JobLevel4:TotalWorkingYears      -62.527            NA        1.627        NA       NA     -116.713       -8.341 
                      JobLevel5:TotalWorkingYears      -31.349            NA        4.575        NA       NA     -103.193       40.494 
---------------------------------------------------------------------------------------------------------------------------------------

# With Interaction Terms:
# Forward: JobLevel + JobRole + TotalWorkingYears + BusinessTravel + DailyRate + ID:TotalWorkingYears + Department + Education + JobLevel:TotalWorkingYears + JobRole:TotalWorkingYears + ID + BusinessTravel:TotalWorkingYears + ID:DailyRate 

# Backward: ID + BusinessTravel + DailyRate + Education + JobLevel + JobRole + TotalWorkingYears + ID:DailyRate + ID:JobLevel + BusinessTravel:Education + BusinessTravel:JobLevel + BusinessTravel:TotalWorkingYears + JobLevel:JobRole + JobLevel:TotalWorkingYears 

# Stepwise: MonthlyIncome ~ JobLevel + JobRole + TotalWorkingYears + BusinessTravel + DailyRate + ID:TotalWorkingYears + Department + Education + JobLevel:JobRole + Education:TotalWorkingYears


# Candidate models from the variable selection methods above
model8 = lm(MonthlyIncome ~ ID + BusinessTravel + DailyRate + Department + Education + JobLevel + JobRole + TotalWorkingYears, data = cs2_regresSmall)

model7a = lm(MonthlyIncome ~ ID + BusinessTravel + DailyRate + Department + JobLevel + JobRole + TotalWorkingYears, data = cs2_regresSmall)

# model7b = lm(MonthlyIncome ~ ID + BusinessTravel + DailyRate + Education + JobLevel + JobRole + TotalWorkingYears, data = cs2_regresSmall)

model6 = lm(MonthlyIncome ~ ID + BusinessTravel + DailyRate + JobLevel + JobRole + TotalWorkingYears, data = cs2_regresSmall)

model8intFull = lm(MonthlyIncome ~ ID + BusinessTravel + DailyRate + Department + Education + JobLevel + JobRole + TotalWorkingYears + ID:TotalWorkingYears + ID:DailyRate + ID:JobLevel + BusinessTravel:Education + BusinessTravel:JobLevel + BusinessTravel:TotalWorkingYears + Education:TotalWorkingYears + JobLevel:JobRole + JobLevel:TotalWorkingYears + JobRole:TotalWorkingYears, data = cs2_regresSmall)

model8int1 = lm(MonthlyIncome ~ ID + BusinessTravel + JobLevel + JobRole + TotalWorkingYears + DailyRate + Education + ID:DailyRate + BusinessTravel:TotalWorkingYears + Education:TotalWorkingYears + JobLevel:TotalWorkingYears + JobRole:TotalWorkingYears, data = cs2_regresSmall) 

model8int2 = lm(MonthlyIncome ~ ID + BusinessTravel + JobLevel + JobRole + TotalWorkingYears + ID:DailyRate + BusinessTravel:TotalWorkingYears + Education:TotalWorkingYears + JobLevel:TotalWorkingYears + JobRole:TotalWorkingYears, data = cs2_regresSmall)

# Using a restricted list of interaction variables, rerun variable selection with a smaller p-value or AIC
fore4 = ols_step_forward_p(model8intFull, p_val = 0.15, details = FALSE)
back4 = ols_step_backward_p(model8intFull, p_val = 0.15, details = FALSE)
step4 = ols_step_both_p(model8intFull, p_enter = 0.15, p_remove = 0.15, details = FALSE)
fore4


                                           Stepwise Summary                                            
-----------------------------------------------------------------------------------------------------
Step    Variable                               AIC          SBC         SBIC         R2       Adj. R2 
-----------------------------------------------------------------------------------------------------
 0      Base Model                          17145.913    17155.450    14673.364    0.00000    0.00000 
 1      JobLevel                            14903.153    14931.764    12427.846    0.92476    0.92441 
 2      JobRole                             14549.801    14616.560    12062.925    0.95079    0.95010 
 3      TotalWorkingYears                   14516.912    14588.439    12031.194    0.95272    0.95200 
 4      BusinessTravel                      14510.833    14591.897    12024.166    0.95327    0.95245 
 5      DailyRate                           14508.366    14594.199    12022.724    0.95351    0.95263 
 6      ID:TotalWorkingYears                14506.847    14597.449    12022.239    0.95369    0.95277 
 7      Department                          14506.644    14606.782    12021.111    0.95392    0.95289 
 8      Education                           14506.843    14626.055    12016.514    0.95433    0.95309 
 9      JobLevel:TotalWorkingYears          14502.096    14640.382    12007.181    0.95499    0.95355 
 10     JobRole:TotalWorkingYears           14481.506    14657.940    11974.949    0.95685    0.95504 
 11     ID                                  14483.504    14664.707    11978.139    0.95685    0.95498 
 12     BusinessTravel:TotalWorkingYears    14482.435    14673.175    11976.481    0.95710    0.95514 
-----------------------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.978       RMSE                  951.770 
R-Squared                 0.957       MSE                948379.019 
Adj. R-Squared            0.955       Coef. Var              15.240 
Pred R-Squared            0.953       AIC                 14482.435 
MAE                     720.268       SBC                 14673.175 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17581521422.397         38    462671616.379    487.855    0.0000 
Residual        788102964.798        831       948379.019                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                          Parameter Estimates                                                            
----------------------------------------------------------------------------------------------------------------------------------------
                                             model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------------------------
                                       (Intercept)     1963.375       541.188                  3.628    0.000      901.119     3025.631 
                                         JobLevel2     3436.166       375.502        0.359     9.151    0.000     2699.122     4173.211 
                                         JobLevel3     5904.527       426.590        0.461    13.841    0.000     5067.207     6741.847 
                                         JobLevel4    11448.283       803.952        0.631    14.240    0.000     9870.267    13026.299 
                                         JobLevel5    13621.607      1129.927        0.598    12.055    0.000    11403.761    15839.454 
                      JobRoleLaboratory Technician     -311.602       390.971       -0.026    -0.797    0.426    -1079.008      455.804 
                            JobRoleHuman Resources        7.248       638.903        0.000     0.011    0.991    -1246.806     1261.302 
                         JobRoleResearch Scientist     -423.518       388.214       -0.037    -1.091    0.276    -1185.513      338.477 
                            JobRoleSales Executive     -553.482       437.549       -0.051    -1.265    0.206    -1412.314      305.349 
                  JobRoleHealthcare Representative     -906.720       569.754       -0.056    -1.591    0.112    -2025.046      211.606 
                     JobRoleManufacturing Director    -1122.848       558.979       -0.073    -2.009    0.045    -2220.025      -25.672 
                          JobRoleResearch Director     2398.402       759.448        0.123     3.158    0.002      907.740     3889.064 
                                    JobRoleManager     2342.011       858.528        0.120     2.728    0.007      656.872     4027.151 
                                 TotalWorkingYears       86.378        33.551        0.141     2.575    0.010       20.523      152.234 
                       BusinessTravelTravel_Rarely      536.438       189.372        0.053     2.833    0.005      164.735      908.142 
                   BusinessTravelTravel_Frequently      576.349       223.076        0.048     2.584    0.010      138.491     1014.207 
                                         DailyRate        0.193         0.084        0.017     2.281    0.023        0.027        0.358 
                  DepartmentResearch & Development      259.067       437.721        0.027     0.592    0.554     -600.101     1118.235 
                                   DepartmentSales     -315.321       446.176       -0.032    -0.707    0.480    -1191.085      560.443 
                                        Education2       27.026       125.264        0.002     0.216    0.829     -218.844      272.897 
                                        Education3      -38.177       115.050       -0.004    -0.332    0.740     -263.999      187.645 
                                        Education4       82.580       121.318        0.008     0.681    0.496     -155.546      320.706 
                                        Education5     -481.239       224.893       -0.018    -2.140    0.033     -922.664      -39.814 
                                                ID        0.015         0.236        0.001     0.064    0.949       -0.448        0.478 
                              TotalWorkingYears:ID       -0.021         0.018       -0.021    -1.201    0.230       -0.056        0.014 
                       JobLevel2:TotalWorkingYears     -134.880        30.516       -0.162    -4.420    0.000     -194.778      -74.982 
                       JobLevel3:TotalWorkingYears      -76.451        31.934       -0.095    -2.394    0.017     -139.131      -13.771 
                       JobLevel4:TotalWorkingYears     -190.927        42.495       -0.275    -4.493    0.000     -274.337     -107.517 
                       JobLevel5:TotalWorkingYears     -172.386        53.081       -0.202    -3.248    0.001     -276.575      -68.198 
    JobRoleLaboratory Technician:TotalWorkingYears      -32.645        33.934       -0.026    -0.962    0.336      -99.252       33.962 
          JobRoleHuman Resources:TotalWorkingYears      -31.992        67.215       -0.008    -0.476    0.634     -163.922       99.938 
       JobRoleResearch Scientist:TotalWorkingYears       11.407        33.536        0.009     0.340    0.734      -54.419       77.233 
          JobRoleSales Executive:TotalWorkingYears      135.935        42.620        0.158     3.189    0.001       52.280      219.590 
JobRoleHealthcare Representative:TotalWorkingYears      117.977        44.030        0.114     2.680    0.008       31.555      204.399 
   JobRoleManufacturing Director:TotalWorkingYears      144.176        44.081        0.133     3.271    0.001       57.652      230.700 
        JobRoleResearch Director:TotalWorkingYears      131.060        50.126        0.149     2.615    0.009       32.670      229.449 
                  JobRoleManager:TotalWorkingYears      138.065        51.957        0.180     2.657    0.008       36.084      240.047 
     TotalWorkingYears:BusinessTravelTravel_Rarely      -22.856        15.568       -0.040    -1.468    0.142      -53.413        7.701 
 TotalWorkingYears:BusinessTravelTravel_Frequently      -38.305        17.471       -0.045    -2.192    0.029      -72.598       -4.012 
----------------------------------------------------------------------------------------------------------------------------------------

back4


                                         Stepwise Summary                                         
------------------------------------------------------------------------------------------------
Step    Variable                          AIC          SBC         SBIC         R2       Adj. R2 
------------------------------------------------------------------------------------------------
 0      Full Model                     14545.808    15008.351    11948.518    0.95952    0.95564 
 1      Department                     14544.171    14997.177    11947.325    0.95941    0.95563 
 2      JobRole:TotalWorkingYears      14538.485    14953.344    11953.622    0.95893    0.95555 
 3      ID:TotalWorkingYears           14537.830    14947.921    11951.538    0.95887    0.95554 
 4      Education:TotalWorkingYears    14535.726    14926.742    11953.776    0.95859    0.95546 
 5      ID:JobLevel                    14534.299    14906.242    11956.706    0.95827    0.95534 
 6      ID:DailyRate                   14533.764    14900.938    11954.806    0.95820    0.95532 
------------------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.979       RMSE                  939.449 
R-Squared                 0.958       MSE                944441.563 
Adj. R-Squared            0.955       Coef. Var              15.208 
Pred R-Squared             -Inf       AIC                 14533.764 
MAE                     706.002       SBC                 14900.938 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17601793396.304         56    314317739.220    332.808    0.0000 
Residual        767830990.892        813       944441.563                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                          Parameter Estimates                                                           
---------------------------------------------------------------------------------------------------------------------------------------
                                            model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
---------------------------------------------------------------------------------------------------------------------------------------
                                      (Intercept)     1981.230       404.054                  4.903    0.000     1188.119     2774.342 
                                               ID       -0.195         0.136       -0.011    -1.432    0.152       -0.463        0.072 
                      BusinessTravelTravel_Rarely      245.749       400.066        0.024     0.614    0.539     -539.536     1031.033 
                  BusinessTravelTravel_Frequently      609.476       459.392        0.051     1.327    0.185     -292.259     1511.211 
                                        DailyRate        0.169         0.085        0.015     1.997    0.046        0.003        0.336 
                                       Education2      185.582       406.205        0.016     0.457    0.648     -611.753      982.916 
                                       Education3     -478.757       385.165       -0.050    -1.243    0.214    -1234.791      277.278 
                                       Education4      371.525       410.084        0.036     0.906    0.365     -433.424     1176.473 
                                       Education5     -319.505       800.673       -0.012    -0.399    0.690    -1891.135     1252.126 
                                        JobLevel2     1423.051       675.164        0.149     2.108    0.035       97.781     2748.321 
                                        JobLevel3     4215.794       944.986        0.329     4.461    0.000     2360.894     6070.695 
                                        JobLevel4    10017.276      1336.176        0.552     7.497    0.000     7394.514    12640.038 
                                        JobLevel5    10298.692      1769.042        0.452     5.822    0.000     6826.263    13771.121 
                     JobRoleLaboratory Technician      169.838       170.014        0.014     0.999    0.318     -163.881      503.556 
                           JobRoleHuman Resources      112.469       251.010        0.004     0.448    0.654     -380.235      605.174 
                        JobRoleResearch Scientist      182.884       167.389        0.016     1.093    0.275     -145.681      511.450 
                           JobRoleSales Executive      741.559       778.979        0.068     0.952    0.341     -787.487     2270.605 
                 JobRoleHealthcare Representative      204.453       804.853        0.013     0.254    0.800    -1375.381     1784.287 
                    JobRoleManufacturing Director     1069.513       580.959        0.070     1.841    0.066      -70.843     2209.868 
                         JobRoleResearch Director     3812.860       792.844        0.195     4.809    0.000     2256.597     5369.123 
                                   JobRoleManager     3883.580       719.068        0.199     5.401    0.000     2472.132     5295.028 
                                TotalWorkingYears       98.748        29.203        0.161     3.381    0.001       41.427      156.069 
           BusinessTravelTravel_Rarely:Education2      -70.855       433.197       -0.005    -0.164    0.870     -921.172      779.461 
       BusinessTravelTravel_Frequently:Education2     -609.467       496.132       -0.025    -1.228    0.220    -1583.317      364.384 
           BusinessTravelTravel_Rarely:Education3      509.591       408.245        0.049     1.248    0.212     -291.747     1310.929 
       BusinessTravelTravel_Frequently:Education3      284.918       462.830        0.016     0.616    0.538     -623.564     1193.399 
           BusinessTravelTravel_Rarely:Education4     -282.088       433.841       -0.025    -0.650    0.516    -1133.669      569.493 
       BusinessTravelTravel_Frequently:Education4     -384.481       495.626       -0.017    -0.776    0.438    -1357.339      588.378 
           BusinessTravelTravel_Rarely:Education5       13.732       848.268        0.000     0.016    0.987    -1651.321     1678.785 
       BusinessTravelTravel_Frequently:Education5     -549.789       927.689       -0.011    -0.593    0.554    -2370.737     1271.158 
            BusinessTravelTravel_Rarely:JobLevel2      818.867       326.016        0.077     2.512    0.012      178.935     1458.799 
        BusinessTravelTravel_Frequently:JobLevel2      677.880       371.024        0.037     1.827    0.068      -50.399     1406.158 
            BusinessTravelTravel_Rarely:JobLevel3      506.615       428.760        0.034     1.182    0.238     -334.993     1348.223 
        BusinessTravelTravel_Frequently:JobLevel3      943.197       496.668        0.035     1.899    0.058      -31.705     1918.100 
            BusinessTravelTravel_Rarely:JobLevel4      391.607       906.680        0.018     0.432    0.666    -1388.103     2171.317 
        BusinessTravelTravel_Frequently:JobLevel4      875.223       978.446        0.023     0.895    0.371    -1045.355     2795.800 
            BusinessTravelTravel_Rarely:JobLevel5     2207.097      1284.825        0.092     1.718    0.086     -314.869     4729.062 
        BusinessTravelTravel_Frequently:JobLevel5     1768.993      1422.982        0.023     1.243    0.214    -1024.159     4562.144 
    BusinessTravelTravel_Rarely:TotalWorkingYears      -47.958        27.900       -0.084    -1.719    0.086     -102.723        6.806 
BusinessTravelTravel_Frequently:TotalWorkingYears      -75.124        31.186       -0.089    -2.409    0.016     -136.338      -13.910 
           JobLevel2:JobRoleLaboratory Technician     -314.561       614.068       -0.013    -0.512    0.609    -1519.907      890.785 
           JobLevel3:JobRoleLaboratory Technician    -4078.369      1054.039       -0.052    -3.869    0.000    -6147.327    -2009.410 
           JobLevel4:JobRoleLaboratory Technician           NA       943.066        0.000     0.173    0.863           NA           NA 
           JobLevel5:JobRoleLaboratory Technician           NA      1118.486        0.000     0.214    0.831           NA           NA 
                 JobLevel2:JobRoleHuman Resources      163.140       616.277        0.002     0.351    0.725    -1687.992     2014.271 
                 JobLevel3:JobRoleHuman Resources      239.102      1320.172       -0.004    -0.286    0.775    -1956.358     2434.563 
                 JobLevel4:JobRoleHuman Resources           NA       543.412        0.000     0.494    0.622           NA           NA 
                 JobLevel5:JobRoleHuman Resources           NA       620.366        0.000    -0.234    0.815           NA           NA 
              JobLevel2:JobRoleResearch Scientist      216.593       591.741        0.037     1.582    0.114     -993.088     1426.275 
              JobLevel3:JobRoleResearch Scientist     -378.175       666.125        0.002     0.332    0.740    -2969.523     2213.173 
              JobLevel4:JobRoleResearch Scientist           NA       645.096        0.000    -0.532    0.595           NA           NA 
              JobLevel5:JobRoleResearch Scientist           NA       594.881        0.000     0.482    0.630           NA           NA 
                 JobLevel2:JobRoleSales Executive      268.175       466.080        0.025     0.681    0.496     -798.481     1334.831 
                 JobLevel3:JobRoleSales Executive     -145.052        20.079       -0.001    -1.354    0.176    -1362.759     1072.655 
                 JobLevel4:JobRoleSales Executive           NA        21.327        0.001     2.897    0.004           NA           NA 
                 JobLevel5:JobRoleSales Executive           NA        27.634        0.000    -2.254    0.024           NA           NA 
       JobLevel2:JobRoleHealthcare Representative      936.244        36.428       -0.001    -0.758    0.449     -225.277     2097.764 
       JobLevel3:JobRoleHealthcare Representative      220.929            NA        0.000        NA       NA    -1086.598     1528.456 
       JobLevel4:JobRoleHealthcare Representative           NA            NA        0.004        NA       NA           NA           NA 
       JobLevel5:JobRoleHealthcare Representative           NA            NA        0.000        NA       NA           NA           NA 
          JobLevel2:JobRoleManufacturing Director           NA            NA        0.000        NA       NA           NA           NA 
          JobLevel3:JobRoleManufacturing Director     -343.474            NA        0.007        NA       NA    -1609.724      922.776 
          JobLevel4:JobRoleManufacturing Director           NA            NA       -0.009        NA       NA           NA           NA 
          JobLevel5:JobRoleManufacturing Director           NA            NA        0.000        NA       NA           NA           NA 
               JobLevel2:JobRoleResearch Director           NA            NA        0.000        NA       NA           NA           NA 
               JobLevel3:JobRoleResearch Director      286.575            NA        0.048        NA       NA     -881.109     1454.259 
               JobLevel4:JobRoleResearch Director      317.407            NA        0.119        NA       NA     -597.455     1232.268 
               JobLevel5:JobRoleResearch Director           NA            NA        0.284        NA       NA           NA           NA 
                         JobLevel2:JobRoleManager           NA            NA        0.000        NA       NA           NA           NA 
                         JobLevel3:JobRoleManager           NA            NA        0.003        NA       NA           NA           NA 
                         JobLevel4:JobRoleManager           NA            NA        0.004        NA       NA           NA           NA 
                         JobLevel5:JobRoleManager           NA            NA        0.006        NA       NA           NA           NA 
                      JobLevel2:TotalWorkingYears      -27.189            NA        0.893        NA       NA      -66.602       12.225 
                      JobLevel3:TotalWorkingYears       61.789            NA        0.253        NA       NA       19.927      103.651 
                      JobLevel4:TotalWorkingYears      -62.300            NA        1.541        NA       NA     -116.543       -8.057 
                      JobLevel5:TotalWorkingYears      -27.618            NA        4.476        NA       NA      -99.122       43.886 
---------------------------------------------------------------------------------------------------------------------------------------

step4


                                             Stepwise Summary                                              
---------------------------------------------------------------------------------------------------------
Step    Variable                                   AIC          SBC         SBIC         R2       Adj. R2 
---------------------------------------------------------------------------------------------------------
 0      Base Model                              17145.913    17155.450    14673.364    0.00000    0.00000 
 1      JobLevel (+)                            14903.153    14931.764    12427.846    0.92476    0.92441 
 2      JobRole (+)                             14549.801    14616.560    12062.925    0.95079    0.95010 
 3      TotalWorkingYears (+)                   14516.912    14588.439    12031.194    0.95272    0.95200 
 4      BusinessTravel (+)                      14510.833    14591.897    12024.166    0.95327    0.95245 
 5      DailyRate (+)                           14508.366    14594.199    12022.724    0.95351    0.95263 
 6      ID:TotalWorkingYears (+)                14506.847    14597.449    12022.239    0.95369    0.95277 
 7      Department (+)                          14506.644    14606.782    12021.111    0.95392    0.95289 
 8      Education (+)                           14506.843    14626.055    12016.514    0.95433    0.95309 
 9      JobLevel:TotalWorkingYears (+)          14502.096    14640.382    12007.181    0.95499    0.95355 
 10     ID:TotalWorkingYears (-)                14504.934    14638.452    12008.825    0.95474    0.95335 
 11     JobRole:TotalWorkingYears (+)           14484.047    14655.713    11976.153    0.95662    0.95485 
 12     Department (-)                          14483.286    14645.415    11976.124    0.95646    0.95479 
 13     ID (+)                                  14482.513    14649.410    11976.603    0.95660    0.95488 
 14     BusinessTravel:TotalWorkingYears (+)    14481.292    14657.726    11974.743    0.95686    0.95505 
---------------------------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.978       RMSE                  954.430 
R-Squared                 0.957       MSE                950257.644 
Adj. R-Squared            0.955       Coef. Var              15.255 
Pred R-Squared            0.953       AIC                 14481.292 
MAE                     724.659       SBC                 14657.726 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17577109512.207         35    502203128.920    528.492    0.0000 
Residual        792514874.989        834       950257.644                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                          Parameter Estimates                                                            
----------------------------------------------------------------------------------------------------------------------------------------
                                             model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------------------------
                                       (Intercept)     1747.552       279.575                  6.251    0.000     1198.799     2296.305 
                                         JobLevel2     3436.066       375.871        0.359     9.142    0.000     2698.302     4173.829 
                                         JobLevel3     5912.556       426.949        0.462    13.848    0.000     5074.536     6750.576 
                                         JobLevel4    11566.564       800.352        0.638    14.452    0.000     9995.623    13137.504 
                                         JobLevel5    13574.124      1103.538        0.596    12.301    0.000    11408.085    15740.162 
                      JobRoleLaboratory Technician      268.233       242.730        0.022     1.105    0.269     -208.200      744.666 
                            JobRoleHuman Resources      349.642       455.570        0.013     0.767    0.443     -544.557     1243.841 
                         JobRoleResearch Scientist      144.010       238.987        0.012     0.603    0.547     -325.077      613.096 
                            JobRoleSales Executive     -548.140       437.967       -0.050    -1.252    0.211    -1407.786      311.506 
                  JobRoleHealthcare Representative     -323.847       480.434       -0.020    -0.674    0.500    -1266.849      619.154 
                     JobRoleManufacturing Director     -552.344       469.202       -0.036    -1.177    0.239    -1473.299      368.611 
                          JobRoleResearch Director     2959.810       700.478        0.151     4.225    0.000     1584.904     4334.716 
                                    JobRoleManager     2802.084       817.122        0.143     3.429    0.001     1198.226     4405.941 
                                 TotalWorkingYears       77.841        32.375        0.127     2.404    0.016       14.295      141.387 
                       BusinessTravelTravel_Rarely      544.211       188.953        0.054     2.880    0.004      173.332      915.091 
                   BusinessTravelTravel_Frequently      576.252       223.237        0.048     2.581    0.010      138.080     1014.424 
                                         DailyRate        0.189         0.084        0.017     2.243    0.025        0.024        0.355 
                                        Education2       21.138       125.146        0.002     0.169    0.866     -224.499      266.775 
                                        Education3      -38.940       115.014       -0.004    -0.339    0.735     -264.691      186.811 
                                        Education4       77.448       121.140        0.008     0.639    0.523     -160.327      315.224 
                                        Education5     -495.972       224.972       -0.018    -2.205    0.028     -937.550      -54.395 
                                                ID       -0.212         0.135       -0.012    -1.575    0.116       -0.476        0.052 
                       JobLevel2:TotalWorkingYears     -134.894        30.545       -0.162    -4.416    0.000     -194.849      -74.939 
                       JobLevel3:TotalWorkingYears      -77.279        31.960       -0.096    -2.418    0.016     -140.011      -14.547 
                       JobLevel4:TotalWorkingYears     -195.431        42.402       -0.282    -4.609    0.000     -278.659     -112.203 
                       JobLevel5:TotalWorkingYears     -169.228        51.897       -0.199    -3.261    0.001     -271.093      -67.364 
    JobRoleLaboratory Technician:TotalWorkingYears      -32.588        33.966       -0.026    -0.959    0.338      -99.257       34.081 
          JobRoleHuman Resources:TotalWorkingYears      -34.418        67.254       -0.009    -0.512    0.609     -166.424       97.589 
       JobRoleResearch Scientist:TotalWorkingYears       12.675        33.559        0.010     0.378    0.706      -53.196       78.546 
          JobRoleSales Executive:TotalWorkingYears      136.024        42.661        0.158     3.188    0.001       52.288      219.759 
JobRoleHealthcare Representative:TotalWorkingYears      117.551        44.065        0.113     2.668    0.008       31.060      204.042 
   JobRoleManufacturing Director:TotalWorkingYears      145.199        44.121        0.134     3.291    0.001       58.599      231.800 
        JobRoleResearch Director:TotalWorkingYears      131.617        50.135        0.150     2.625    0.009       33.211      230.024 
                  JobRoleManager:TotalWorkingYears      132.610        51.754        0.173     2.562    0.011       31.027      234.192 
     TotalWorkingYears:BusinessTravelTravel_Rarely      -24.342        15.432       -0.043    -1.577    0.115      -54.632        5.948 
 TotalWorkingYears:BusinessTravelTravel_Frequently      -39.107        17.480       -0.046    -2.237    0.026      -73.418       -4.797 
----------------------------------------------------------------------------------------------------------------------------------------

# fore5 = ols_step_forward_aic(model8intFull, details = FALSE) # this errors
back5 = ols_step_backward_aic(model8intFull, details = FALSE)
# step5 = ols_step_both_aic(model8intFull, details = FALSE) # this errors
back5


                                       Stepwise Summary                                        
---------------------------------------------------------------------------------------------
Step    Variable                       AIC          SBC         SBIC         R2       Adj. R2 
---------------------------------------------------------------------------------------------
 0      Full Model                  14545.808    15008.351    11948.518    0.95952    0.95564 
 1      JobLevel:JobRole            14500.508    14810.460    11962.612    0.95864    0.95541 
 2      BusinessTravel:Education    14494.359    14766.163    11968.545    0.95817    0.95535 
 3      BusinessTravel:JobLevel     14488.144    14721.800    11974.495    0.95770    0.95528 
 4      Education                   14482.974    14697.556    11948.613    0.95756    0.95535 
 5      ID:JobLevel                 14480.949    14676.457    11952.924    0.95727    0.95526 
 6      DailyRate                   14478.950    14669.690    11989.703    0.95727    0.95531 
 7      ID:TotalWorkingYears        14478.467    14664.438    11989.986    0.95719    0.95529 
 8      Department                  14477.928    14654.362    11988.943    0.95702    0.95522 
---------------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.978       RMSE                  952.586 
R-Squared                 0.957       MSE                946590.233 
Adj. R-Squared            0.955       Coef. Var              15.225 
Pred R-Squared            0.953       AIC                 14477.928 
MAE                     721.605       SBC                 14654.362 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17580168132.874         35    502290518.082    530.631    0.0000 
Residual        789456254.321        834       946590.233                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                          Parameter Estimates                                                            
----------------------------------------------------------------------------------------------------------------------------------------
                                             model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------------------------
                                       (Intercept)     1911.484       255.632                  7.477    0.000     1409.727     2413.242 
                                                ID       -0.565         0.186       -0.031    -3.044    0.002       -0.929       -0.201 
                       BusinessTravelTravel_Rarely      538.693       188.969        0.053     2.851    0.004      167.782      909.604 
                   BusinessTravelTravel_Frequently      531.837       223.765        0.045     2.377    0.018       92.627      971.046 
                                         JobLevel2     3461.417       374.861        0.361     9.234    0.000     2725.635     4197.199 
                                         JobLevel3     5929.361       425.636        0.463    13.931    0.000     5093.917     6764.805 
                                         JobLevel4    11449.241       794.590        0.631    14.409    0.000     9889.610    13008.873 
                                         JobLevel5    13685.639      1107.375        0.601    12.359    0.000    11512.069    15859.208 
                      JobRoleLaboratory Technician      281.712       242.050        0.023     1.164    0.245     -193.388      756.812 
                            JobRoleHuman Resources      298.204       453.625        0.011     0.657    0.511     -592.176     1188.584 
                         JobRoleResearch Scientist      126.430       238.005        0.011     0.531    0.595     -340.730      593.590 
                            JobRoleSales Executive     -570.172       437.603       -0.052    -1.303    0.193    -1429.104      288.761 
                  JobRoleHealthcare Representative     -369.207       482.406       -0.023    -0.765    0.444    -1316.080      577.667 
                     JobRoleManufacturing Director     -572.028       468.678       -0.037    -1.221    0.223    -1491.956      347.900 
                          JobRoleResearch Director     2925.000       699.332        0.150     4.183    0.000     1552.344     4297.657 
                                    JobRoleManager     2883.003       817.734        0.147     3.526    0.000     1277.945     4488.061 
                                 TotalWorkingYears       81.752        32.962        0.134     2.480    0.013       17.055      146.450 
                                      ID:DailyRate        0.000         0.000        0.027     2.649    0.008        0.000        0.001 
     BusinessTravelTravel_Rarely:TotalWorkingYears      -24.157        15.501       -0.042    -1.558    0.120      -54.582        6.269 
 BusinessTravelTravel_Frequently:TotalWorkingYears      -35.185        17.660       -0.042    -1.992    0.047      -69.848       -0.521 
                      TotalWorkingYears:Education2       -0.945        10.751       -0.001    -0.088    0.930      -22.047       20.157 
                      TotalWorkingYears:Education3       -8.047         9.337       -0.013    -0.862    0.389      -26.374       10.280 
                      TotalWorkingYears:Education4       -2.523         9.517       -0.004    -0.265    0.791      -21.202       16.156 
                      TotalWorkingYears:Education5      -41.826        15.284       -0.025    -2.737    0.006      -71.825      -11.827 
                       JobLevel2:TotalWorkingYears     -135.855        30.530       -0.164    -4.450    0.000     -195.779      -75.931 
                       JobLevel3:TotalWorkingYears      -78.703        31.887       -0.097    -2.468    0.014     -141.291      -16.114 
                       JobLevel4:TotalWorkingYears     -190.720        42.216       -0.275    -4.518    0.000     -273.581     -107.859 
                       JobLevel5:TotalWorkingYears     -174.547        51.893       -0.205    -3.364    0.001     -276.404      -72.691 
    JobRoleLaboratory Technician:TotalWorkingYears      -33.854        33.873       -0.027    -0.999    0.318     -100.341       32.633 
          JobRoleHuman Resources:TotalWorkingYears      -29.605        66.990       -0.008    -0.442    0.659     -161.093      101.883 
       JobRoleResearch Scientist:TotalWorkingYears       15.313        33.535        0.013     0.457    0.648      -50.510       81.135 
          JobRoleSales Executive:TotalWorkingYears      138.168        42.698        0.160     3.236    0.001       54.360      221.977 
JobRoleHealthcare Representative:TotalWorkingYears      120.265        44.265        0.116     2.717    0.007       33.380      207.149 
   JobRoleManufacturing Director:TotalWorkingYears      146.706        44.164        0.136     3.322    0.001       60.020      233.391 
        JobRoleResearch Director:TotalWorkingYears      135.828        50.135        0.155     2.709    0.007       37.423      234.233 
                  JobRoleManager:TotalWorkingYears      130.320        51.791        0.170     2.516    0.012       28.664      231.976 
----------------------------------------------------------------------------------------------------------------------------------------

# Evaluate models above with internal cross-validation
# define training control
train_control = trainControl(method="LOOCV")

# train the model 
model8CV = train(MonthlyIncome ~ ID + BusinessTravel + DailyRate + Department + Education + JobLevel + JobRole + TotalWorkingYears, data = cs2_regresSmall, trControl = train_control, method = "lm")

model7aCV = train(MonthlyIncome ~ ID + BusinessTravel + DailyRate + Department + JobLevel + JobRole + TotalWorkingYears, data = cs2_regresSmall, trControl = train_control, method = "lm")

# model7bCV = train(MonthlyIncome ~ ID + BusinessTravel + DailyRate + Education + JobLevel + JobRole + TotalWorkingYears, data = cs2_regresSmall, trControl = train_control, method = "lm")

model6CV = train(MonthlyIncome ~ ID + BusinessTravel + DailyRate + JobLevel + JobRole + TotalWorkingYears, data = cs2_regresSmall, trControl = train_control, method = "lm")

model8intFullCV = train(MonthlyIncome ~ ID + BusinessTravel + DailyRate + Department + Education + JobLevel + JobRole + TotalWorkingYears + ID:TotalWorkingYears + ID:DailyRate + ID:JobLevel + BusinessTravel:Education + BusinessTravel:JobLevel + BusinessTravel:TotalWorkingYears + Education:TotalWorkingYears + JobLevel:JobRole + JobLevel:TotalWorkingYears + JobRole:TotalWorkingYears, data = cs2_regresSmall, trControl = train_control, method = "lm")

model8int1CV = train(MonthlyIncome ~ ID + BusinessTravel + JobLevel + JobRole + TotalWorkingYears + DailyRate + Education + ID:DailyRate + BusinessTravel:TotalWorkingYears + Education:TotalWorkingYears + JobLevel:TotalWorkingYears + JobRole:TotalWorkingYears, data = cs2_regresSmall, trControl = train_control, method = "lm")

model8int2CV = train(MonthlyIncome ~ ID + BusinessTravel + JobLevel + JobRole + TotalWorkingYears + ID:DailyRate + BusinessTravel:TotalWorkingYears + Education:TotalWorkingYears + JobLevel:TotalWorkingYears + JobRole:TotalWorkingYears, data = cs2_regresSmall, trControl = train_control, method = "lm")

model8CV

Linear Regression 

870 samples
  8 predictor

No pre-processing
Resampling: Leave-One-Out Cross-Validation 
Summary of sample sizes: 869, 869, 869, 869, 869, 869, ... 
Resampling results:

  RMSE      Rsquared  MAE     
  1007.978  0.951882  770.7709

Tuning parameter 'intercept' was held constant at a value of TRUE

model7aCV

Linear Regression 

870 samples
  7 predictor

No pre-processing
Resampling: Leave-One-Out Cross-Validation 
Summary of sample sizes: 869, 869, 869, 869, 869, 869, ... 
Resampling results:

  RMSE      Rsquared   MAE     
  1007.927  0.9518864  771.4089

Tuning parameter 'intercept' was held constant at a value of TRUE

# model7bCV
model6CV

Linear Regression 

870 samples
  6 predictor

No pre-processing
Resampling: Leave-One-Out Cross-Validation 
Summary of sample sizes: 869, 869, 869, 869, 869, 869, ... 
Resampling results:

  RMSE      Rsquared  MAE     
  1009.009  0.951783  773.4415

Tuning parameter 'intercept' was held constant at a value of TRUE

model8intFullCV

Linear Regression 

870 samples
  8 predictor

No pre-processing
Resampling: Leave-One-Out Cross-Validation 
Summary of sample sizes: 869, 869, 869, 869, 869, 869, ... 
Resampling results:

  RMSE      Rsquared   MAE     
  1012.851  0.9514514  763.7219

Tuning parameter 'intercept' was held constant at a value of TRUE

model8int1CV

Linear Regression 

870 samples
  7 predictor

No pre-processing
Resampling: Leave-One-Out Cross-Validation 
Summary of sample sizes: 869, 869, 869, 869, 869, 869, ... 
Resampling results:

  RMSE      Rsquared   MAE     
  994.6385  0.9531522  755.3346

Tuning parameter 'intercept' was held constant at a value of TRUE

model8int2CV

Linear Regression 

870 samples
  7 predictor

No pre-processing
Resampling: Leave-One-Out Cross-Validation 
Summary of sample sizes: 869, 869, 869, 869, 869, 869, ... 
Resampling results:

  RMSE     Rsquared   MAE     
  991.292  0.9534655  752.3138

Tuning parameter 'intercept' was held constant at a value of TRUE

# Examine residuals
plot(model8)

# Add squared and logged terms
str(cs2_regresSmall)

'data.frame':   870 obs. of  9 variables:
 $ MonthlyIncome    : int  4403 19626 9362 10422 3760 8793 2127 6694 2220 5063 ...
 $ ID               : int  1 2 3 4 5 6 7 8 9 10 ...
 $ BusinessTravel   : Factor w/ 3 levels "Non-Travel","Travel_Rarely",..: 2 2 3 2 3 3 2 2 2 3 ...
 $ DailyRate        : int  117 1308 200 801 567 294 1283 309 1333 653 ...
 $ Department       : Factor w/ 3 levels "Human Resources",..: 3 2 2 3 2 2 2 3 3 2 ...
 $ Education        : Factor w/ 5 levels "1","2","3","4",..: 4 3 2 4 1 2 5 4 4 4 ...
 $ JobLevel         : Factor w/ 5 levels "1","2","3","4",..: 2 5 3 3 1 3 1 2 1 2 ...
 $ JobRole          : Factor w/ 9 levels "Sales Representative",..: 5 8 7 5 4 7 4 5 1 6 ...
 $ TotalWorkingYears: int  8 21 10 14 6 9 7 8 1 8 ...

cs2_regresSmall2 = cs2_regresSmall %>% 
  mutate(logMonthlyIncome = log(MonthlyIncome),
         MonthlyIncome2 = MonthlyIncome^2,
         logID = log(ID),
         ID2 = ID^2,
         logDailyRate = log(DailyRate),
         DailyRate2 = DailyRate^2,
         logTotalWorkingYears = log(TotalWorkingYears),
         TotalWorkingYears2 = TotalWorkingYears^2)
str(cs2_regresSmall2)

'data.frame':   870 obs. of  17 variables:
 $ MonthlyIncome       : int  4403 19626 9362 10422 3760 8793 2127 6694 2220 5063 ...
 $ ID                  : int  1 2 3 4 5 6 7 8 9 10 ...
 $ BusinessTravel      : Factor w/ 3 levels "Non-Travel","Travel_Rarely",..: 2 2 3 2 3 3 2 2 2 3 ...
 $ DailyRate           : int  117 1308 200 801 567 294 1283 309 1333 653 ...
 $ Department          : Factor w/ 3 levels "Human Resources",..: 3 2 2 3 2 2 2 3 3 2 ...
 $ Education           : Factor w/ 5 levels "1","2","3","4",..: 4 3 2 4 1 2 5 4 4 4 ...
 $ JobLevel            : Factor w/ 5 levels "1","2","3","4",..: 2 5 3 3 1 3 1 2 1 2 ...
 $ JobRole             : Factor w/ 9 levels "Sales Representative",..: 5 8 7 5 4 7 4 5 1 6 ...
 $ TotalWorkingYears   : int  8 21 10 14 6 9 7 8 1 8 ...
 $ logMonthlyIncome    : num  8.39 9.88 9.14 9.25 8.23 ...
 $ MonthlyIncome2      : num  1.94e+07 3.85e+08 8.76e+07 1.09e+08 1.41e+07 ...
 $ logID               : num  0 0.693 1.099 1.386 1.609 ...
 $ ID2                 : num  1 4 9 16 25 36 49 64 81 100 ...
 $ logDailyRate        : num  4.76 7.18 5.3 6.69 6.34 ...
 $ DailyRate2          : num  13689 1710864 40000 641601 321489 ...
 $ logTotalWorkingYears: num  2.08 3.04 2.3 2.64 1.79 ...
 $ TotalWorkingYears2  : num  64 441 100 196 36 81 49 64 1 64 ...

sum(is.na(cs2_regresSmall2))

[1] 0

# Identify numeric columns
numeric_columns <- sapply(cs2_regresSmall2, is.numeric)

# Check for NaNs in numeric columns
nan_check <- sapply(cs2_regresSmall2[, numeric_columns], function(x) sum(is.nan(x)))
print(nan_check)

       MonthlyIncome                   ID            DailyRate    TotalWorkingYears     logMonthlyIncome       MonthlyIncome2 
                   0                    0                    0                    0                    0                    0 
               logID                  ID2         logDailyRate           DailyRate2 logTotalWorkingYears   TotalWorkingYears2 
                   0                    0                    0                    0                    0                    0 

# Check for Infs in numeric columns
inf_check <- sapply(cs2_regresSmall2[, numeric_columns], function(x) sum(is.infinite(x)))
print(inf_check)

       MonthlyIncome                   ID            DailyRate    TotalWorkingYears     logMonthlyIncome       MonthlyIncome2 
                   0                    0                    0                    0                    0                    0 
               logID                  ID2         logDailyRate           DailyRate2 logTotalWorkingYears   TotalWorkingYears2 
                   0                    0                    0                    0                    7                    0 

# Replace Infs with a large finite number
cs2_regresSmall2$logTotalWorkingYears[is.infinite(cs2_regresSmall2$logTotalWorkingYears)] <- max(cs2_regresSmall2$logTotalWorkingYears[!is.infinite(cs2_regresSmall2$logTotalWorkingYears)], na.rm = TRUE)

fit_trans1 = lm(MonthlyIncome ~ . -logMonthlyIncome -MonthlyIncome2, data = cs2_regresSmall2)
fit_trans2 = lm(logMonthlyIncome ~ . -MonthlyIncome -MonthlyIncome2, data = cs2_regresSmall2)
fit_trans3 = lm(MonthlyIncome2 ~ . -MonthlyIncome -logMonthlyIncome, data = cs2_regresSmall2)

fore6 = ols_step_forward_p(fit_trans1, p_val = 0.2, details = FALSE)
back6 = ols_step_backward_p(fit_trans1, p_val = 0.2, details = FALSE)
step6 = ols_step_both_p(fit_trans1, p_enter = 0.2, p_remove = 0.2, details = FALSE)
fore6


                                  Stepwise Summary                                  
----------------------------------------------------------------------------------
Step    Variable                 AIC          SBC       SBIC      R2       Adj. R2 
----------------------------------------------------------------------------------
 0      Base Model            17145.913    17155.450      NA    0.00000    0.00000 
 1      JobLevel              14903.153    14931.764      NA    0.92476    0.92441 
 2      JobRole               14549.801    14616.560      NA    0.95079    0.95010 
 3      TotalWorkingYears     14516.912    14588.439      NA    0.95272    0.95200 
 4      TotalWorkingYears2    14506.128    14582.424      NA    0.95341    0.95265 
 5      logID                 14502.757    14583.821      NA    0.95370    0.95289 
 6      logDailyRate          14499.937    14585.770      NA    0.95395    0.95309 
 7      BusinessTravel        14495.172    14590.542      NA    0.95442    0.95345 
 8      Education             14494.697    14609.141      NA    0.95486    0.95369 
 9      ID2                   14494.857    14614.069      NA    0.95495    0.95373 
----------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.977       RMSE                  975.259 
R-Squared                 0.955       MSE                978112.725 
Adj. R-Squared            0.954       Coef. Var              15.477 
Pred R-Squared            0.953       AIC                 14494.857 
MAE                     745.991       SBC                 14614.069 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17542141021.679         23    762701783.551    779.769    0.0000 
Residual        827483365.517        846       978112.725                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                 Parameter Estimates                                                   
----------------------------------------------------------------------------------------------------------------------
                           model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------
                     (Intercept)     1887.174       465.101                  4.058    0.000      974.288     2800.061 
                       JobLevel2     1617.409       142.062        0.169    11.385    0.000     1338.574     1896.244 
                       JobLevel3     4852.402       187.827        0.379    25.834    0.000     4483.740     5221.064 
                       JobLevel4     8460.641       281.981        0.467    30.004    0.000     7907.177     9014.105 
                       JobLevel5    11078.569       331.103        0.487    33.460    0.000    10428.689    11728.448 
    JobRoleLaboratory Technician      -30.756       162.669       -0.003    -0.189    0.850     -350.038      288.525 
          JobRoleHuman Resources      102.713       236.725        0.004     0.434    0.664     -361.925      567.351 
       JobRoleResearch Scientist      169.855       160.948        0.015     1.055    0.292     -146.050      485.760 
          JobRoleSales Executive     1171.799       198.885        0.107     5.892    0.000      781.433     1562.165 
JobRoleHealthcare Representative     1203.639       218.250        0.074     5.515    0.000      775.264     1632.014 
   JobRoleManufacturing Director     1292.773       215.144        0.084     6.009    0.000      870.494     1715.053 
        JobRoleResearch Director     4719.410       267.441        0.241    17.647    0.000     4194.484     5244.335 
                  JobRoleManager     4526.010       288.720        0.231    15.676    0.000     3959.318     5092.701 
               TotalWorkingYears       94.105        17.377        0.154     5.416    0.000       59.999      128.212 
              TotalWorkingYears2       -1.699         0.531       -0.090    -3.199    0.001       -2.741       -0.656 
                           logID     -133.840        52.583       -0.029    -2.545    0.011     -237.049      -30.631 
                    logDailyRate      124.977        52.668        0.018     2.373    0.018       21.601      228.353 
     BusinessTravelTravel_Rarely      307.896       110.985        0.030     2.774    0.006       90.057      525.735 
 BusinessTravelTravel_Frequently      181.586       130.747        0.015     1.389    0.165      -75.041      438.212 
                      Education2      -71.147       125.691       -0.006    -0.566    0.572     -317.850      175.557 
                      Education3      -96.332       115.631       -0.010    -0.833    0.405     -323.290      130.626 
                      Education4       39.610       122.008        0.004     0.325    0.746     -199.865      279.085 
                      Education5     -511.951       225.089       -0.019    -2.274    0.023     -953.750      -70.153 
                             ID2        0.000         0.000        0.015     1.339    0.181        0.000        0.001 
----------------------------------------------------------------------------------------------------------------------

back6


                                   Stepwise Summary                                   
------------------------------------------------------------------------------------
Step    Variable                   AIC          SBC       SBIC      R2       Adj. R2 
------------------------------------------------------------------------------------
 0      Full Model              14502.314    14650.137      NA    0.95519    0.95364 
 1      logTotalWorkingYears    14500.315    14643.370      NA    0.95519    0.95370 
 2      ID                      14498.321    14636.608      NA    0.95519    0.95375 
 3      DailyRate2              14496.773    14630.291      NA    0.95516    0.95378 
 4      DailyRate               14495.744    14624.493      NA    0.95511    0.95379 
 5      Department              14494.857    14614.069      NA    0.95495    0.95373 
------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.977       RMSE                  975.259 
R-Squared                 0.955       MSE                978112.725 
Adj. R-Squared            0.954       Coef. Var              15.477 
Pred R-Squared            0.953       AIC                 14494.857 
MAE                     745.991       SBC                 14614.069 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17542141021.679         23    762701783.551    779.769    0.0000 
Residual        827483365.517        846       978112.725                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                 Parameter Estimates                                                   
----------------------------------------------------------------------------------------------------------------------
                           model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------
                     (Intercept)     1887.174       465.101                  4.058    0.000      974.288     2800.061 
     BusinessTravelTravel_Rarely      307.896       110.985        0.030     2.774    0.006       90.057      525.735 
 BusinessTravelTravel_Frequently      181.586       130.747        0.015     1.389    0.165      -75.041      438.212 
                      Education2      -71.147       125.691       -0.006    -0.566    0.572     -317.850      175.557 
                      Education3      -96.332       115.631       -0.010    -0.833    0.405     -323.290      130.626 
                      Education4       39.610       122.008        0.004     0.325    0.746     -199.865      279.085 
                      Education5     -511.951       225.089       -0.019    -2.274    0.023     -953.750      -70.153 
                       JobLevel2     1617.409       142.062        0.169    11.385    0.000     1338.574     1896.244 
                       JobLevel3     4852.402       187.827        0.379    25.834    0.000     4483.740     5221.064 
                       JobLevel4     8460.641       281.981        0.467    30.004    0.000     7907.177     9014.105 
                       JobLevel5    11078.569       331.103        0.487    33.460    0.000    10428.689    11728.448 
    JobRoleLaboratory Technician      -30.756       162.669       -0.003    -0.189    0.850     -350.038      288.525 
          JobRoleHuman Resources      102.713       236.725        0.004     0.434    0.664     -361.925      567.351 
       JobRoleResearch Scientist      169.855       160.948        0.015     1.055    0.292     -146.050      485.760 
          JobRoleSales Executive     1171.799       198.885        0.107     5.892    0.000      781.433     1562.165 
JobRoleHealthcare Representative     1203.639       218.250        0.074     5.515    0.000      775.264     1632.014 
   JobRoleManufacturing Director     1292.773       215.144        0.084     6.009    0.000      870.494     1715.053 
        JobRoleResearch Director     4719.410       267.441        0.241    17.647    0.000     4194.484     5244.335 
                  JobRoleManager     4526.010       288.720        0.231    15.676    0.000     3959.318     5092.701 
               TotalWorkingYears       94.105        17.377        0.154     5.416    0.000       59.999      128.212 
                           logID     -133.840        52.583       -0.029    -2.545    0.011     -237.049      -30.631 
                             ID2        0.000         0.000        0.015     1.339    0.181        0.000        0.001 
                    logDailyRate      124.977        52.668        0.018     2.373    0.018       21.601      228.353 
              TotalWorkingYears2       -1.699         0.531       -0.090    -3.199    0.001       -2.741       -0.656 
----------------------------------------------------------------------------------------------------------------------

step6


                                    Stepwise Summary                                    
--------------------------------------------------------------------------------------
Step    Variable                     AIC          SBC       SBIC      R2       Adj. R2 
--------------------------------------------------------------------------------------
 0      Base Model                17145.913    17155.450      NA    0.00000    0.00000 
 1      JobLevel (+)              14903.153    14931.764      NA    0.92476    0.92441 
 2      JobRole (+)               14549.801    14616.560      NA    0.95079    0.95010 
 3      TotalWorkingYears (+)     14516.912    14588.439      NA    0.95272    0.95200 
 4      TotalWorkingYears2 (+)    14506.128    14582.424      NA    0.95341    0.95265 
 5      logID (+)                 14502.757    14583.821      NA    0.95370    0.95289 
 6      logDailyRate (+)          14499.937    14585.770      NA    0.95395    0.95309 
 7      BusinessTravel (+)        14495.172    14590.542      NA    0.95442    0.95345 
 8      Education (+)             14494.697    14609.141      NA    0.95486    0.95369 
 9      ID2 (+)                   14494.857    14614.069      NA    0.95495    0.95373 
--------------------------------------------------------------------------------------

Final Model Output 
------------------

                           Model Summary                             
--------------------------------------------------------------------
R                         0.977       RMSE                  975.259 
R-Squared                 0.955       MSE                978112.725 
Adj. R-Squared            0.954       Coef. Var              15.477 
Pred R-Squared            0.953       AIC                 14494.857 
MAE                     745.991       SBC                 14614.069 
--------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                      
-------------------------------------------------------------------------------
                       Sum of                                                  
                      Squares         DF      Mean Square       F         Sig. 
-------------------------------------------------------------------------------
Regression    17542141021.679         23    762701783.551    779.769    0.0000 
Residual        827483365.517        846       978112.725                      
Total         18369624387.195        869                                       
-------------------------------------------------------------------------------

                                                 Parameter Estimates                                                   
----------------------------------------------------------------------------------------------------------------------
                           model         Beta    Std. Error    Std. Beta      t        Sig         lower        upper 
----------------------------------------------------------------------------------------------------------------------
                     (Intercept)     1887.174       465.101                  4.058    0.000      974.288     2800.061 
                       JobLevel2     1617.409       142.062        0.169    11.385    0.000     1338.574     1896.244 
                       JobLevel3     4852.402       187.827        0.379    25.834    0.000     4483.740     5221.064 
                       JobLevel4     8460.641       281.981        0.467    30.004    0.000     7907.177     9014.105 
                       JobLevel5    11078.569       331.103        0.487    33.460    0.000    10428.689    11728.448 
    JobRoleLaboratory Technician      -30.756       162.669       -0.003    -0.189    0.850     -350.038      288.525 
          JobRoleHuman Resources      102.713       236.725        0.004     0.434    0.664     -361.925      567.351 
       JobRoleResearch Scientist      169.855       160.948        0.015     1.055    0.292     -146.050      485.760 
          JobRoleSales Executive     1171.799       198.885        0.107     5.892    0.000      781.433     1562.165 
JobRoleHealthcare Representative     1203.639       218.250        0.074     5.515    0.000      775.264     1632.014 
   JobRoleManufacturing Director     1292.773       215.144        0.084     6.009    0.000      870.494     1715.053 
        JobRoleResearch Director     4719.410       267.441        0.241    17.647    0.000     4194.484     5244.335 
                  JobRoleManager     4526.010       288.720        0.231    15.676    0.000     3959.318     5092.701 
               TotalWorkingYears       94.105        17.377        0.154     5.416    0.000       59.999      128.212 
              TotalWorkingYears2       -1.699         0.531       -0.090    -3.199    0.001       -2.741       -0.656 
                           logID     -133.840        52.583       -0.029    -2.545    0.011     -237.049      -30.631 
                    logDailyRate      124.977        52.668        0.018     2.373    0.018       21.601      228.353 
     BusinessTravelTravel_Rarely      307.896       110.985        0.030     2.774    0.006       90.057      525.735 
 BusinessTravelTravel_Frequently      181.586       130.747        0.015     1.389    0.165      -75.041      438.212 
                      Education2      -71.147       125.691       -0.006    -0.566    0.572     -317.850      175.557 
                      Education3      -96.332       115.631       -0.010    -0.833    0.405     -323.290      130.626 
                      Education4       39.610       122.008        0.004     0.325    0.746     -199.865      279.085 
                      Education5     -511.951       225.089       -0.019    -2.274    0.023     -953.750      -70.153 
                             ID2        0.000         0.000        0.015     1.339    0.181        0.000        0.001 
----------------------------------------------------------------------------------------------------------------------

fore7 = ols_step_forward_p(fit_trans2, p_val = 0.2, details = FALSE)
back7 = ols_step_backward_p(fit_trans2, p_val = 0.2, details = FALSE)
step7 = ols_step_both_p(fit_trans2, p_enter = 0.2, p_remove = 0.2, details = FALSE)
fore7


                                  Stepwise Summary                                  
----------------------------------------------------------------------------------
Step    Variable                  AIC         SBC       SBIC      R2       Adj. R2 
----------------------------------------------------------------------------------
 0      Base Model              1752.980    1762.517      NA    0.00000    0.00000 
 1      JobLevel                 -47.889     -19.278      NA    0.87496    0.87439 
 2      logTotalWorkingYears     -79.546     -46.166      NA    0.87971    0.87901 
 3      JobRole                 -190.641    -119.114      NA    0.89606    0.89448 
 4      BusinessTravel          -199.676    -118.612      NA    0.89760    0.89581 
 5      logDailyRate            -202.689    -116.856      NA    0.89819    0.89628 
 6      TotalWorkingYears       -203.815    -113.214      NA    0.89856    0.89653 
 7      TotalWorkingYears2      -221.167    -125.797      NA    0.90079    0.89869 
 8      Education               -220.928    -106.484      NA    0.90167    0.89912 
----------------------------------------------------------------------------------

Final Model Output 
------------------

                         Model Summary                           
----------------------------------------------------------------
R                       0.950       RMSE                  0.207 
R-Squared               0.902       MSE                   0.044 
Adj. R-Squared          0.899       Coef. Var             2.461 
Pred R-Squared          0.896       AIC                -220.928 
MAE                     0.154       SBC                -106.484 
----------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                ANOVA                                 
---------------------------------------------------------------------
               Sum of                                                
              Squares         DF    Mean Square       F         Sig. 
---------------------------------------------------------------------
Regression    342.898         22         15.586    353.042    0.0000 
Residual       37.394        847          0.044                      
Total         380.291        869                                     
---------------------------------------------------------------------

                                            Parameter Estimates                                              
------------------------------------------------------------------------------------------------------------
                           model      Beta    Std. Error    Std. Beta      t        Sig      lower    upper 
------------------------------------------------------------------------------------------------------------
                     (Intercept)     7.508         0.085                 88.064    0.000     7.341    7.675 
                       JobLevel2     0.451         0.030        0.327    14.950    0.000     0.392    0.510 
                       JobLevel3     0.902         0.040        0.489    22.631    0.000     0.824    0.980 
                       JobLevel4     1.193         0.060        0.457    19.897    0.000     1.075    1.310 
                       JobLevel5     1.315         0.070        0.401    18.717    0.000     1.177    1.453 
            logTotalWorkingYears     0.015         0.020        0.018     0.723    0.470    -0.025    0.054 
    JobRoleLaboratory Technician     0.018         0.035        0.010     0.509    0.611    -0.050    0.085 
          JobRoleHuman Resources     0.049         0.050        0.013     0.983    0.326    -0.049    0.148 
       JobRoleResearch Scientist     0.068         0.034        0.041     1.990    0.047     0.001    0.135 
          JobRoleSales Executive     0.263         0.042        0.167     6.222    0.000     0.180    0.346 
JobRoleHealthcare Representative     0.272         0.046        0.116     5.859    0.000     0.181    0.363 
   JobRoleManufacturing Director     0.280         0.046        0.127     6.126    0.000     0.190    0.370 
        JobRoleResearch Director     0.558         0.057        0.198     9.818    0.000     0.446    0.669 
                  JobRoleManager     0.533         0.061        0.189     8.685    0.000     0.412    0.653 
     BusinessTravelTravel_Rarely     0.072         0.024        0.049     3.034    0.002     0.025    0.118 
 BusinessTravelTravel_Frequently     0.049         0.028        0.029     1.775    0.076    -0.005    0.104 
                    logDailyRate     0.022         0.011        0.021     1.947    0.052     0.000    0.044 
               TotalWorkingYears     0.025         0.005        0.284     4.657    0.000     0.014    0.036 
              TotalWorkingYears2    -0.001         0.000       -0.210    -4.379    0.000    -0.001    0.000 
                      Education2    -0.006         0.027       -0.004    -0.223    0.824    -0.058    0.046 
                      Education3    -0.026         0.025       -0.019    -1.072    0.284    -0.075    0.022 
                      Education4     0.016         0.026        0.011     0.601    0.548    -0.035    0.066 
                      Education5    -0.069         0.048       -0.018    -1.453    0.147    -0.163    0.024 
------------------------------------------------------------------------------------------------------------

back7


                                  Stepwise Summary                                  
----------------------------------------------------------------------------------
Step    Variable                  AIC         SBC       SBIC      R2       Adj. R2 
----------------------------------------------------------------------------------
 0      Full Model              -211.392     -63.569      NA    0.90217    0.89880 
 1      ID2                     -213.386     -70.331      NA    0.90217    0.89892 
 2      Department              -216.911     -83.393      NA    0.90212    0.89910 
 3      logTotalWorkingYears    -218.365     -89.616      NA    0.90206    0.89916 
 4      DailyRate2              -219.778     -95.798      NA    0.90199    0.89921 
 5      DailyRate               -220.496    -101.284      NA    0.90185    0.89918 
 6      ID                      -221.191    -106.747      NA    0.90170    0.89915 
 7      logID                   -222.391    -112.716      NA    0.90161    0.89917 
----------------------------------------------------------------------------------

Final Model Output 
------------------

                         Model Summary                           
----------------------------------------------------------------
R                       0.950       RMSE                  0.207 
R-Squared               0.902       MSE                   0.044 
Adj. R-Squared          0.899       Coef. Var             2.460 
Pred R-Squared          0.897       AIC                -222.391 
MAE                     0.154       SBC                -112.716 
----------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                ANOVA                                 
---------------------------------------------------------------------
               Sum of                                                
              Squares         DF    Mean Square       F         Sig. 
---------------------------------------------------------------------
Regression    342.875         21         16.327    370.037    0.0000 
Residual       37.417        848          0.044                      
Total         380.291        869                                     
---------------------------------------------------------------------

                                            Parameter Estimates                                              
------------------------------------------------------------------------------------------------------------
                           model      Beta    Std. Error    Std. Beta      t        Sig      lower    upper 
------------------------------------------------------------------------------------------------------------
                     (Intercept)     7.518         0.084                 89.378    0.000     7.353    7.683 
     BusinessTravelTravel_Rarely     0.071         0.024        0.048     2.992    0.003     0.024    0.117 
 BusinessTravelTravel_Frequently     0.049         0.028        0.028     1.748    0.081    -0.006    0.103 
                      Education2    -0.006         0.027       -0.004    -0.217    0.828    -0.058    0.047 
                      Education3    -0.026         0.025       -0.019    -1.062    0.288    -0.074    0.022 
                      Education4     0.016         0.026        0.011     0.614    0.539    -0.035    0.067 
                      Education5    -0.069         0.048       -0.018    -1.444    0.149    -0.163    0.025 
                       JobLevel2     0.451         0.030        0.327    14.965    0.000     0.392    0.511 
                       JobLevel3     0.901         0.040        0.489    22.628    0.000     0.823    0.980 
                       JobLevel4     1.191         0.060        0.457    19.890    0.000     1.074    1.309 
                       JobLevel5     1.314         0.070        0.401    18.710    0.000     1.176    1.451 
    JobRoleLaboratory Technician     0.018         0.035        0.011     0.528    0.597    -0.050    0.086 
          JobRoleHuman Resources     0.049         0.050        0.013     0.986    0.324    -0.049    0.148 
       JobRoleResearch Scientist     0.068         0.034        0.041     1.999    0.046     0.001    0.135 
          JobRoleSales Executive     0.264         0.042        0.168     6.254    0.000     0.181    0.347 
JobRoleHealthcare Representative     0.273         0.046        0.116     5.883    0.000     0.182    0.364 
   JobRoleManufacturing Director     0.281         0.046        0.128     6.157    0.000     0.191    0.371 
        JobRoleResearch Director     0.558         0.057        0.198     9.833    0.000     0.447    0.670 
                  JobRoleManager     0.533         0.061        0.190     8.697    0.000     0.413    0.654 
               TotalWorkingYears     0.028         0.004        0.316     7.543    0.000     0.021    0.035 
                    logDailyRate     0.022         0.011        0.021     1.940    0.053     0.000    0.044 
              TotalWorkingYears2    -0.001         0.000       -0.227    -5.501    0.000    -0.001    0.000 
------------------------------------------------------------------------------------------------------------

step7


                                    Stepwise Summary                                    
--------------------------------------------------------------------------------------
Step    Variable                      AIC         SBC       SBIC      R2       Adj. R2 
--------------------------------------------------------------------------------------
 0      Base Model                  1752.980    1762.517      NA    0.00000    0.00000 
 1      JobLevel (+)                 -47.889     -19.278      NA    0.87496    0.87439 
 2      logTotalWorkingYears (+)     -79.546     -46.166      NA    0.87971    0.87901 
 3      JobRole (+)                 -190.641    -119.114      NA    0.89606    0.89448 
 4      BusinessTravel (+)          -199.676    -118.612      NA    0.89760    0.89581 
 5      logDailyRate (+)            -202.689    -116.856      NA    0.89819    0.89628 
 6      TotalWorkingYears (+)       -203.815    -113.214      NA    0.89856    0.89653 
 7      TotalWorkingYears2 (+)      -221.167    -125.797      NA    0.90079    0.89869 
 8      logTotalWorkingYears (-)    -222.639    -132.037      NA    0.90073    0.89875 
 9      Education (+)               -222.391    -112.716      NA    0.90161    0.89917 
--------------------------------------------------------------------------------------

Final Model Output 
------------------

                         Model Summary                           
----------------------------------------------------------------
R                       0.950       RMSE                  0.207 
R-Squared               0.902       MSE                   0.044 
Adj. R-Squared          0.899       Coef. Var             2.460 
Pred R-Squared          0.897       AIC                -222.391 
MAE                     0.154       SBC                -112.716 
----------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                ANOVA                                 
---------------------------------------------------------------------
               Sum of                                                
              Squares         DF    Mean Square       F         Sig. 
---------------------------------------------------------------------
Regression    342.875         21         16.327    370.037    0.0000 
Residual       37.417        848          0.044                      
Total         380.291        869                                     
---------------------------------------------------------------------

                                            Parameter Estimates                                              
------------------------------------------------------------------------------------------------------------
                           model      Beta    Std. Error    Std. Beta      t        Sig      lower    upper 
------------------------------------------------------------------------------------------------------------
                     (Intercept)     7.518         0.084                 89.378    0.000     7.353    7.683 
                       JobLevel2     0.451         0.030        0.327    14.965    0.000     0.392    0.511 
                       JobLevel3     0.901         0.040        0.489    22.628    0.000     0.823    0.980 
                       JobLevel4     1.191         0.060        0.457    19.890    0.000     1.074    1.309 
                       JobLevel5     1.314         0.070        0.401    18.710    0.000     1.176    1.451 
    JobRoleLaboratory Technician     0.018         0.035        0.011     0.528    0.597    -0.050    0.086 
          JobRoleHuman Resources     0.049         0.050        0.013     0.986    0.324    -0.049    0.148 
       JobRoleResearch Scientist     0.068         0.034        0.041     1.999    0.046     0.001    0.135 
          JobRoleSales Executive     0.264         0.042        0.168     6.254    0.000     0.181    0.347 
JobRoleHealthcare Representative     0.273         0.046        0.116     5.883    0.000     0.182    0.364 
   JobRoleManufacturing Director     0.281         0.046        0.128     6.157    0.000     0.191    0.371 
        JobRoleResearch Director     0.558         0.057        0.198     9.833    0.000     0.447    0.670 
                  JobRoleManager     0.533         0.061        0.190     8.697    0.000     0.413    0.654 
     BusinessTravelTravel_Rarely     0.071         0.024        0.048     2.992    0.003     0.024    0.117 
 BusinessTravelTravel_Frequently     0.049         0.028        0.028     1.748    0.081    -0.006    0.103 
                    logDailyRate     0.022         0.011        0.021     1.940    0.053     0.000    0.044 
               TotalWorkingYears     0.028         0.004        0.316     7.543    0.000     0.021    0.035 
              TotalWorkingYears2    -0.001         0.000       -0.227    -5.501    0.000    -0.001    0.000 
                      Education2    -0.006         0.027       -0.004    -0.217    0.828    -0.058    0.047 
                      Education3    -0.026         0.025       -0.019    -1.062    0.288    -0.074    0.022 
                      Education4     0.016         0.026        0.011     0.614    0.539    -0.035    0.067 
                      Education5    -0.069         0.048       -0.018    -1.444    0.149    -0.163    0.025 
------------------------------------------------------------------------------------------------------------

# Candidate models with transformed variables
modelTrans1 = lm(MonthlyIncome ~ BusinessTravel + Education + JobLevel + JobRole + TotalWorkingYears + logID + logDailyRate + TotalWorkingYears2, data = cs2_regresSmall2) 

modelTrans2 = lm(logMonthlyIncome ~ JobLevel + JobRole + BusinessTravel + logDailyRate + TotalWorkingYears + TotalWorkingYears2 + Education, data = cs2_regresSmall2)

modelTrans1CV = train(MonthlyIncome ~ BusinessTravel + Education + JobLevel + JobRole + TotalWorkingYears + logID + logDailyRate + TotalWorkingYears2, data = cs2_regresSmall2, trControl = train_control, method = "lm")
modelTrans1CV

Linear Regression 

870 samples
  8 predictor

No pre-processing
Resampling: Leave-One-Out Cross-Validation 
Summary of sample sizes: 869, 869, 869, 869, 869, 869, ... 
Resampling results:

  RMSE      Rsquared   MAE   
  1001.033  0.9525427  766.95

Tuning parameter 'intercept' was held constant at a value of TRUE

# All candidate models
summary(model8)


Call:
lm(formula = MonthlyIncome ~ ID + BusinessTravel + DailyRate + 
    Department + Education + JobLevel + JobRole + TotalWorkingYears, 
    data = cs2_regresSmall)

Residuals:
    Min      1Q  Median      3Q     Max 
-3175.4  -617.2   -56.0   588.6  4195.1 

Coefficients:
                                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)                       2.406e+03  4.803e+02   5.011 6.61e-07 ***
ID                               -2.276e-01  1.365e-01  -1.668  0.09569 .  
BusinessTravelTravel_Rarely       3.445e+02  1.114e+02   3.091  0.00206 ** 
BusinessTravelTravel_Frequently   2.052e+02  1.316e+02   1.560  0.11916    
DailyRate                         1.785e-01  8.502e-02   2.100  0.03604 *  
DepartmentResearch & Development  2.488e+02  4.172e+02   0.596  0.55113    
DepartmentSales                  -3.379e+02  4.267e+02  -0.792  0.42866    
Education2                       -3.772e+01  1.263e+02  -0.299  0.76521    
Education3                       -8.976e+01  1.164e+02  -0.771  0.44084    
Education4                        5.840e+01  1.227e+02   0.476  0.63433    
Education5                       -4.576e+02  2.262e+02  -2.023  0.04340 *  
JobLevel2                         1.718e+03  1.394e+02  12.331  < 2e-16 ***
JobLevel3                         4.970e+03  1.862e+02  26.692  < 2e-16 ***
JobLevel4                         8.346e+03  2.823e+02  29.561  < 2e-16 ***
JobLevel5                         1.096e+04  3.324e+02  32.963  < 2e-16 ***
JobRoleLaboratory Technician     -5.538e+02  3.474e+02  -1.594  0.11125    
JobRoleHuman Resources           -1.600e+02  4.884e+02  -0.328  0.74324    
JobRoleResearch Scientist        -3.554e+02  3.469e+02  -1.025  0.30585    
JobRoleSales Executive            1.223e+03  1.997e+02   6.124 1.39e-09 ***
JobRoleHealthcare Representative  6.541e+02  3.776e+02   1.732  0.08362 .  
JobRoleManufacturing Director     7.663e+02  3.757e+02   2.040  0.04166 *  
JobRoleResearch Director          4.193e+03  4.072e+02  10.298  < 2e-16 ***
JobRoleManager                    4.284e+03  3.361e+02  12.745  < 2e-16 ***
TotalWorkingYears                 4.420e+01  7.766e+00   5.692 1.74e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 996.7 on 846 degrees of freedom
Multiple R-squared:  0.9542,    Adjusted R-squared:  0.953 
F-statistic: 767.2 on 23 and 846 DF,  p-value: < 2.2e-16

summary(model7a)


Call:
lm(formula = MonthlyIncome ~ ID + BusinessTravel + DailyRate + 
    Department + JobLevel + JobRole + TotalWorkingYears, data = cs2_regresSmall)

Residuals:
    Min      1Q  Median      3Q     Max 
-3213.3  -608.7   -65.9   615.7  4188.0 

Coefficients:
                                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)                       2.401e+03  4.717e+02   5.089 4.42e-07 ***
ID                               -2.248e-01  1.365e-01  -1.647  0.09985 .  
BusinessTravelTravel_Rarely       3.397e+02  1.116e+02   3.044  0.00241 ** 
BusinessTravelTravel_Frequently   1.872e+02  1.316e+02   1.423  0.15524    
DailyRate                         1.764e-01  8.512e-02   2.072  0.03855 *  
DepartmentResearch & Development  2.335e+02  4.179e+02   0.559  0.57638    
DepartmentSales                  -3.572e+02  4.272e+02  -0.836  0.40337    
JobLevel2                         1.706e+03  1.384e+02  12.329  < 2e-16 ***
JobLevel3                         4.934e+03  1.860e+02  26.532  < 2e-16 ***
JobLevel4                         8.255e+03  2.807e+02  29.407  < 2e-16 ***
JobLevel5                         1.091e+04  3.325e+02  32.812  < 2e-16 ***
JobRoleLaboratory Technician     -5.718e+02  3.480e+02  -1.643  0.10078    
JobRoleHuman Resources           -2.049e+02  4.889e+02  -0.419  0.67531    
JobRoleResearch Scientist        -3.816e+02  3.472e+02  -1.099  0.27198    
JobRoleSales Executive            1.225e+03  1.996e+02   6.141 1.26e-09 ***
JobRoleHealthcare Representative  6.528e+02  3.784e+02   1.725  0.08483 .  
JobRoleManufacturing Director     7.603e+02  3.761e+02   2.021  0.04357 *  
JobRoleResearch Director          4.158e+03  4.073e+02  10.209  < 2e-16 ***
JobRoleManager                    4.296e+03  3.366e+02  12.762  < 2e-16 ***
TotalWorkingYears                 4.595e+01  7.726e+00   5.948 3.97e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 998.8 on 850 degrees of freedom
Multiple R-squared:  0.9538,    Adjusted R-squared:  0.9528 
F-statistic: 924.5 on 19 and 850 DF,  p-value: < 2.2e-16

summary(model6)


Call:
lm(formula = MonthlyIncome ~ ID + BusinessTravel + DailyRate + 
    JobLevel + JobRole + TotalWorkingYears, data = cs2_regresSmall)

Residuals:
    Min      1Q  Median      3Q     Max 
-3212.2  -618.9   -74.1   620.3  4184.9 

Coefficients:
                                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)                       2.048e+03  1.989e+02  10.296  < 2e-16 ***
ID                               -2.130e-01  1.364e-01  -1.561  0.11888    
BusinessTravelTravel_Rarely       3.320e+02  1.116e+02   2.975  0.00302 ** 
BusinessTravelTravel_Frequently   1.873e+02  1.317e+02   1.422  0.15549    
DailyRate                         1.741e-01  8.519e-02   2.044  0.04129 *  
JobLevel2                         1.709e+03  1.385e+02  12.342  < 2e-16 ***
JobLevel3                         4.941e+03  1.861e+02  26.556  < 2e-16 ***
JobLevel4                         8.261e+03  2.808e+02  29.418  < 2e-16 ***
JobLevel5                         1.094e+04  3.308e+02  33.066  < 2e-16 ***
JobRoleLaboratory Technician      2.089e+01  1.627e+02   0.128  0.89786    
JobRoleHuman Resources            1.531e+02  2.382e+02   0.643  0.52045    
JobRoleResearch Scientist         2.120e+02  1.598e+02   1.327  0.18496    
JobRoleSales Executive            1.227e+03  1.998e+02   6.141 1.26e-09 ***
JobRoleHealthcare Representative  1.246e+03  2.201e+02   5.660 2.07e-08 ***
JobRoleManufacturing Director     1.353e+03  2.163e+02   6.257 6.22e-10 ***
JobRoleResearch Director          4.748e+03  2.677e+02  17.736  < 2e-16 ***
JobRoleManager                    4.618e+03  2.902e+02  15.912  < 2e-16 ***
TotalWorkingYears                 4.528e+01  7.716e+00   5.869 6.29e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 999.8 on 852 degrees of freedom
Multiple R-squared:  0.9536,    Adjusted R-squared:  0.9527 
F-statistic:  1031 on 17 and 852 DF,  p-value: < 2.2e-16

summary(model8intFull)


Call:
lm(formula = MonthlyIncome ~ ID + BusinessTravel + DailyRate + 
    Department + Education + JobLevel + JobRole + TotalWorkingYears + 
    ID:TotalWorkingYears + ID:DailyRate + ID:JobLevel + BusinessTravel:Education + 
    BusinessTravel:JobLevel + BusinessTravel:TotalWorkingYears + 
    Education:TotalWorkingYears + JobLevel:JobRole + JobLevel:TotalWorkingYears + 
    JobRole:TotalWorkingYears, data = cs2_regresSmall)

Residuals:
    Min      1Q  Median      3Q     Max 
-3101.8  -545.3   -69.4   500.6  4137.5 

Coefficients: (19 not defined because of singularities)
                                                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                         2.139e+03  6.634e+02   3.224 0.001316 ** 
ID                                                  3.161e-02  3.937e-01   0.080 0.936023    
BusinessTravelTravel_Rarely                         2.830e+02  4.033e+02   0.702 0.483032    
BusinessTravelTravel_Frequently                     6.602e+02  4.626e+02   1.427 0.153902    
DailyRate                                          -2.970e-02  1.772e-01  -0.168 0.866936    
DepartmentResearch & Development                    2.705e+01  4.763e+02   0.057 0.954719    
DepartmentSales                                    -4.347e+02  4.774e+02  -0.911 0.362756    
Education2                                          1.827e+02  4.454e+02   0.410 0.681845    
Education3                                         -2.417e+02  4.243e+02  -0.570 0.568960    
Education4                                          5.969e+02  4.519e+02   1.321 0.186942    
Education5                                          3.903e+02  8.784e+02   0.444 0.656962    
JobLevel2                                           2.564e+03  8.275e+02   3.098 0.002016 ** 
JobLevel3                                           5.099e+03  1.424e+03   3.582 0.000362 ***
JobLevel4                                           1.038e+04  1.709e+03   6.072 1.95e-09 ***
JobLevel5                                           1.118e+04  2.216e+03   5.045 5.63e-07 ***
JobRoleLaboratory Technician                       -3.130e+02  4.142e+02  -0.756 0.450115    
JobRoleHuman Resources                             -1.182e+02  6.736e+02  -0.175 0.860749    
JobRoleResearch Scientist                          -2.104e+02  4.131e+02  -0.509 0.610668    
JobRoleSales Executive                             -2.093e+02  1.110e+03  -0.189 0.850435    
JobRoleHealthcare Representative                   -1.073e+03  1.242e+03  -0.864 0.388034    
JobRoleManufacturing Director                      -5.185e+02  9.032e+02  -0.574 0.566036    
JobRoleResearch Director                            2.363e+03  1.556e+03   1.519 0.129239    
JobRoleManager                                      2.717e+03  1.761e+03   1.543 0.123135    
TotalWorkingYears                                   1.367e+02  4.680e+01   2.921 0.003583 ** 
ID:TotalWorkingYears                               -3.850e-02  3.150e-02  -1.222 0.221989    
ID:DailyRate                                        4.695e-04  3.459e-04   1.358 0.174975    
ID:JobLevel2                                       -5.882e-01  3.487e-01  -1.687 0.092013 .  
ID:JobLevel3                                       -1.657e-01  4.873e-01  -0.340 0.733866    
ID:JobLevel4                                        3.925e-01  8.956e-01   0.438 0.661324    
ID:JobLevel5                                        5.722e-01  9.704e-01   0.590 0.555583    
BusinessTravelTravel_Rarely:Education2             -7.849e+01  4.371e+02  -0.180 0.857533    
BusinessTravelTravel_Frequently:Education2         -6.715e+02  4.997e+02  -1.344 0.179362    
BusinessTravelTravel_Rarely:Education3              4.364e+02  4.122e+02   1.059 0.290129    
BusinessTravelTravel_Frequently:Education3          1.936e+02  4.670e+02   0.415 0.678536    
BusinessTravelTravel_Rarely:Education4             -2.965e+02  4.383e+02  -0.676 0.498968    
BusinessTravelTravel_Frequently:Education4         -4.691e+02  5.008e+02  -0.937 0.349224    
BusinessTravelTravel_Rarely:Education5             -3.475e+01  8.552e+02  -0.041 0.967597    
BusinessTravelTravel_Frequently:Education5         -5.343e+02  9.689e+02  -0.551 0.581488    
BusinessTravelTravel_Rarely:JobLevel2               7.949e+02  3.295e+02   2.412 0.016077 *  
BusinessTravelTravel_Frequently:JobLevel2           6.952e+02  3.752e+02   1.853 0.064255 .  
BusinessTravelTravel_Rarely:JobLevel3               5.681e+02  4.325e+02   1.314 0.189339    
BusinessTravelTravel_Frequently:JobLevel3           9.998e+02  5.055e+02   1.978 0.048299 *  
BusinessTravelTravel_Rarely:JobLevel4               5.333e+02  9.416e+02   0.566 0.571294    
BusinessTravelTravel_Frequently:JobLevel4           1.101e+03  1.016e+03   1.084 0.278712    
BusinessTravelTravel_Rarely:JobLevel5               2.195e+03  1.331e+03   1.649 0.099548 .  
BusinessTravelTravel_Frequently:JobLevel5           1.649e+03  1.462e+03   1.128 0.259662    
BusinessTravelTravel_Rarely:TotalWorkingYears      -5.009e+01  2.854e+01  -1.755 0.079682 .  
BusinessTravelTravel_Frequently:TotalWorkingYears  -7.560e+01  3.177e+01  -2.379 0.017577 *  
Education2:TotalWorkingYears                        5.725e+00  1.897e+01   0.302 0.762899    
Education3:TotalWorkingYears                       -1.330e+01  1.563e+01  -0.851 0.395157    
Education4:TotalWorkingYears                       -1.798e+01  1.646e+01  -1.092 0.275036    
Education5:TotalWorkingYears                       -5.308e+01  3.402e+01  -1.560 0.119110    
JobLevel2:JobRoleLaboratory Technician             -1.898e+02  6.717e+02  -0.283 0.777597    
JobLevel3:JobRoleLaboratory Technician             -2.694e+03  1.487e+03  -1.812 0.070315 .  
JobLevel4:JobRoleLaboratory Technician                     NA         NA      NA       NA    
JobLevel5:JobRoleLaboratory Technician                     NA         NA      NA       NA    
JobLevel2:JobRoleHuman Resources                    4.278e+02  1.026e+03   0.417 0.676821    
JobLevel3:JobRoleHuman Resources                    5.298e+02  1.441e+03   0.368 0.713208    
JobLevel4:JobRoleHuman Resources                           NA         NA      NA       NA    
JobLevel5:JobRoleHuman Resources                           NA         NA      NA       NA    
JobLevel2:JobRoleResearch Scientist                 4.862e+02  6.737e+02   0.722 0.470727    
JobLevel3:JobRoleResearch Scientist                 1.429e+03  1.667e+03   0.857 0.391698    
JobLevel4:JobRoleResearch Scientist                        NA         NA      NA       NA    
JobLevel5:JobRoleResearch Scientist                        NA         NA      NA       NA    
JobLevel2:JobRoleSales Executive                    1.678e+02  7.054e+02   0.238 0.812043    
JobLevel3:JobRoleSales Executive                   -1.434e+02  9.882e+02  -0.145 0.884658    
JobLevel4:JobRoleSales Executive                           NA         NA      NA       NA    
JobLevel5:JobRoleSales Executive                           NA         NA      NA       NA    
JobLevel2:JobRoleHealthcare Representative          7.217e+02  7.786e+02   0.927 0.354259    
JobLevel3:JobRoleHealthcare Representative          1.955e+02  1.071e+03   0.183 0.855132    
JobLevel4:JobRoleHealthcare Representative                 NA         NA      NA       NA    
JobLevel5:JobRoleHealthcare Representative                 NA         NA      NA       NA    
JobLevel2:JobRoleManufacturing Director                    NA         NA      NA       NA    
JobLevel3:JobRoleManufacturing Director            -2.668e+02  1.013e+03  -0.263 0.792260    
JobLevel4:JobRoleManufacturing Director                    NA         NA      NA       NA    
JobLevel5:JobRoleManufacturing Director                    NA         NA      NA       NA    
JobLevel2:JobRoleResearch Director                         NA         NA      NA       NA    
JobLevel3:JobRoleResearch Director                  2.951e+02  8.921e+02   0.331 0.740922    
JobLevel4:JobRoleResearch Director                  3.010e+02  4.850e+02   0.621 0.534996    
JobLevel5:JobRoleResearch Director                         NA         NA      NA       NA    
JobLevel2:JobRoleManager                                   NA         NA      NA       NA    
JobLevel3:JobRoleManager                                   NA         NA      NA       NA    
JobLevel4:JobRoleManager                                   NA         NA      NA       NA    
JobLevel5:JobRoleManager                                   NA         NA      NA       NA    
JobLevel2:TotalWorkingYears                        -1.124e+02  3.648e+01  -3.080 0.002138 ** 
JobLevel3:TotalWorkingYears                        -3.676e+01  4.334e+01  -0.848 0.396601    
JobLevel4:TotalWorkingYears                        -1.546e+02  5.625e+01  -2.748 0.006128 ** 
JobLevel5:TotalWorkingYears                        -1.386e+02  7.068e+01  -1.962 0.050169 .  
JobRoleLaboratory Technician:TotalWorkingYears     -4.057e+00  3.815e+01  -0.106 0.915332    
JobRoleHuman Resources:TotalWorkingYears           -5.320e+01  7.699e+01  -0.691 0.489781    
JobRoleResearch Scientist:TotalWorkingYears        -1.741e+01  3.756e+01  -0.464 0.643044    
JobRoleSales Executive:TotalWorkingYears            9.611e+01  5.100e+01   1.885 0.059857 .  
JobRoleHealthcare Representative:TotalWorkingYears  8.930e+01  5.393e+01   1.656 0.098181 .  
JobRoleManufacturing Director:TotalWorkingYears     1.026e+02  5.388e+01   1.905 0.057202 .  
JobRoleResearch Director:TotalWorkingYears          9.983e+01  6.689e+01   1.493 0.135949    
JobRoleManager:TotalWorkingYears                    9.369e+01  7.569e+01   1.238 0.216191    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 968.3 on 793 degrees of freedom
Multiple R-squared:  0.9595,    Adjusted R-squared:  0.9556 
F-statistic: 247.3 on 76 and 793 DF,  p-value: < 2.2e-16

summary(model8int1)


Call:
lm(formula = MonthlyIncome ~ ID + BusinessTravel + JobLevel + 
    JobRole + TotalWorkingYears + DailyRate + Education + ID:DailyRate + 
    BusinessTravel:TotalWorkingYears + Education:TotalWorkingYears + 
    JobLevel:TotalWorkingYears + JobRole:TotalWorkingYears, data = cs2_regresSmall)

Residuals:
    Min      1Q  Median      3Q     Max 
-2981.2  -590.4   -81.3   541.8  4225.4 

Coefficients:
                                                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                         1.833e+03  3.151e+02   5.818 8.52e-09 ***
ID                                                 -5.671e-01  3.030e-01  -1.871 0.061634 .  
BusinessTravelTravel_Rarely                         5.268e+02  1.894e+02   2.781 0.005543 ** 
BusinessTravelTravel_Frequently                     5.260e+02  2.252e+02   2.336 0.019744 *  
JobLevel2                                           3.436e+03  3.782e+02   9.085  < 2e-16 ***
JobLevel3                                           5.898e+03  4.276e+02  13.792  < 2e-16 ***
JobLevel4                                           1.144e+04  8.086e+02  14.152  < 2e-16 ***
JobLevel5                                           1.356e+04  1.116e+03  12.148  < 2e-16 ***
JobRoleLaboratory Technician                        2.624e+02  2.432e+02   1.079 0.280914    
JobRoleHuman Resources                              2.915e+02  4.581e+02   0.636 0.524744    
JobRoleResearch Scientist                           9.341e+01  2.407e+02   0.388 0.698104    
JobRoleSales Executive                             -6.153e+02  4.406e+02  -1.397 0.162896    
JobRoleHealthcare Representative                   -4.064e+02  4.841e+02  -0.840 0.401412    
JobRoleManufacturing Director                      -5.997e+02  4.712e+02  -1.273 0.203496    
JobRoleResearch Director                            2.880e+03  7.016e+02   4.104 4.46e-05 ***
JobRoleManager                                      2.754e+03  8.249e+02   3.339 0.000878 ***
TotalWorkingYears                                   8.404e+01  3.382e+01   2.485 0.013149 *  
DailyRate                                          -7.276e-03  1.732e-01  -0.042 0.966497    
Education2                                          6.307e+01  2.122e+02   0.297 0.766395    
Education3                                          1.140e+02  1.861e+02   0.613 0.540097    
Education4                                          2.955e+02  2.040e+02   1.448 0.147869    
Education5                                          1.648e+02  4.596e+02   0.359 0.719968    
ID:DailyRate                                        4.527e-04  3.377e-04   1.341 0.180370    
BusinessTravelTravel_Rarely:TotalWorkingYears      -2.251e+01  1.557e+01  -1.446 0.148664    
BusinessTravelTravel_Frequently:TotalWorkingYears  -3.394e+01  1.787e+01  -1.899 0.057888 .  
TotalWorkingYears:Education2                       -3.694e+00  1.839e+01  -0.201 0.840811    
TotalWorkingYears:Education3                       -1.509e+01  1.509e+01  -1.000 0.317738    
TotalWorkingYears:Education4                       -2.067e+01  1.590e+01  -1.299 0.194151    
TotalWorkingYears:Education5                       -5.160e+01  3.057e+01  -1.688 0.091837 .  
JobLevel2:TotalWorkingYears                        -1.339e+02  3.078e+01  -4.352 1.52e-05 ***
JobLevel3:TotalWorkingYears                        -7.634e+01  3.205e+01  -2.382 0.017444 *  
JobLevel4:TotalWorkingYears                        -1.903e+02  4.267e+01  -4.459 9.35e-06 ***
JobLevel5:TotalWorkingYears                        -1.692e+02  5.216e+01  -3.243 0.001228 ** 
JobRoleLaboratory Technician:TotalWorkingYears     -3.229e+01  3.397e+01  -0.950 0.342215    
JobRoleHuman Resources:TotalWorkingYears           -2.865e+01  6.753e+01  -0.424 0.671455    
JobRoleResearch Scientist:TotalWorkingYears         1.825e+01  3.368e+01   0.542 0.588022    
JobRoleSales Executive:TotalWorkingYears            1.420e+02  4.289e+01   3.311 0.000970 ***
JobRoleHealthcare Representative:TotalWorkingYears  1.239e+02  4.446e+01   2.786 0.005453 ** 
JobRoleManufacturing Director:TotalWorkingYears     1.503e+02  4.434e+01   3.390 0.000733 ***
JobRoleResearch Director:TotalWorkingYears          1.403e+02  5.032e+01   2.788 0.005417 ** 
JobRoleManager:TotalWorkingYears                    1.384e+02  5.218e+01   2.653 0.008128 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 974.3 on 829 degrees of freedom
Multiple R-squared:  0.9572,    Adjusted R-squared:  0.9551 
F-statistic:   463 on 40 and 829 DF,  p-value: < 2.2e-16

summary(model8int2)


Call:
lm(formula = MonthlyIncome ~ ID + BusinessTravel + JobLevel + 
    JobRole + TotalWorkingYears + ID:DailyRate + BusinessTravel:TotalWorkingYears + 
    Education:TotalWorkingYears + JobLevel:TotalWorkingYears + 
    JobRole:TotalWorkingYears, data = cs2_regresSmall)

Residuals:
    Min      1Q  Median      3Q     Max 
-2948.3  -588.1   -75.3   553.5  4209.4 

Coefficients:
                                                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                         1.911e+03  2.556e+02   7.477 1.92e-13 ***
ID                                                 -5.649e-01  1.855e-01  -3.044 0.002405 ** 
BusinessTravelTravel_Rarely                         5.387e+02  1.890e+02   2.851 0.004470 ** 
BusinessTravelTravel_Frequently                     5.318e+02  2.238e+02   2.377 0.017690 *  
JobLevel2                                           3.461e+03  3.749e+02   9.234  < 2e-16 ***
JobLevel3                                           5.929e+03  4.256e+02  13.931  < 2e-16 ***
JobLevel4                                           1.145e+04  7.946e+02  14.409  < 2e-16 ***
JobLevel5                                           1.369e+04  1.107e+03  12.359  < 2e-16 ***
JobRoleLaboratory Technician                        2.817e+02  2.421e+02   1.164 0.244815    
JobRoleHuman Resources                              2.982e+02  4.536e+02   0.657 0.511118    
JobRoleResearch Scientist                           1.264e+02  2.380e+02   0.531 0.595417    
JobRoleSales Executive                             -5.702e+02  4.376e+02  -1.303 0.192954    
JobRoleHealthcare Representative                   -3.692e+02  4.824e+02  -0.765 0.444283    
JobRoleManufacturing Director                      -5.720e+02  4.687e+02  -1.221 0.222616    
JobRoleResearch Director                            2.925e+03  6.993e+02   4.183 3.19e-05 ***
JobRoleManager                                      2.883e+03  8.177e+02   3.526 0.000446 ***
TotalWorkingYears                                   8.175e+01  3.296e+01   2.480 0.013327 *  
ID:DailyRate                                        4.340e-04  1.638e-04   2.649 0.008231 ** 
BusinessTravelTravel_Rarely:TotalWorkingYears      -2.416e+01  1.550e+01  -1.558 0.119520    
BusinessTravelTravel_Frequently:TotalWorkingYears  -3.518e+01  1.766e+01  -1.992 0.046661 *  
TotalWorkingYears:Education2                       -9.450e-01  1.075e+01  -0.088 0.929977    
TotalWorkingYears:Education3                       -8.047e+00  9.337e+00  -0.862 0.389043    
TotalWorkingYears:Education4                       -2.523e+00  9.517e+00  -0.265 0.790996    
TotalWorkingYears:Education5                       -4.183e+01  1.528e+01  -2.737 0.006339 ** 
JobLevel2:TotalWorkingYears                        -1.359e+02  3.053e+01  -4.450 9.75e-06 ***
JobLevel3:TotalWorkingYears                        -7.870e+01  3.189e+01  -2.468 0.013780 *  
JobLevel4:TotalWorkingYears                        -1.907e+02  4.222e+01  -4.518 7.15e-06 ***
JobLevel5:TotalWorkingYears                        -1.745e+02  5.189e+01  -3.364 0.000804 ***
JobRoleLaboratory Technician:TotalWorkingYears     -3.385e+01  3.387e+01  -0.999 0.317881    
JobRoleHuman Resources:TotalWorkingYears           -2.960e+01  6.699e+01  -0.442 0.658655    
JobRoleResearch Scientist:TotalWorkingYears         1.531e+01  3.353e+01   0.457 0.648062    
JobRoleSales Executive:TotalWorkingYears            1.382e+02  4.270e+01   3.236 0.001260 ** 
JobRoleHealthcare Representative:TotalWorkingYears  1.203e+02  4.427e+01   2.717 0.006726 ** 
JobRoleManufacturing Director:TotalWorkingYears     1.467e+02  4.416e+01   3.322 0.000933 ***
JobRoleResearch Director:TotalWorkingYears          1.358e+02  5.013e+01   2.709 0.006881 ** 
JobRoleManager:TotalWorkingYears                    1.303e+02  5.179e+01   2.516 0.012048 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 972.9 on 834 degrees of freedom
Multiple R-squared:  0.957, Adjusted R-squared:  0.9552 
F-statistic: 530.6 on 35 and 834 DF,  p-value: < 2.2e-16

summary(modelTrans1)


Call:
lm(formula = MonthlyIncome ~ BusinessTravel + Education + JobLevel + 
    JobRole + TotalWorkingYears + logID + logDailyRate + TotalWorkingYears2, 
    data = cs2_regresSmall2)

Residuals:
    Min      1Q  Median      3Q     Max 
-3051.1  -627.8   -51.2   598.7  4295.6 

Coefficients:
                                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)                       1704.4179   444.8155   3.832 0.000137 ***
BusinessTravelTravel_Rarely        303.7757   110.9945   2.737 0.006333 ** 
BusinessTravelTravel_Frequently    176.7867   130.7591   1.352 0.176735    
Education2                         -71.0251   125.7500  -0.565 0.572351    
Education3                         -99.2908   115.6643  -0.858 0.390892    
Education4                          35.0545   122.0180   0.287 0.773961    
Education5                        -516.8402   225.1648  -2.295 0.021955 *  
JobLevel2                         1618.7382   142.1249  11.390  < 2e-16 ***
JobLevel3                         4864.7427   187.6885  25.919  < 2e-16 ***
JobLevel4                         8461.0962   282.1123  29.992  < 2e-16 ***
JobLevel5                        11095.2055   331.0240  33.518  < 2e-16 ***
JobRoleLaboratory Technician       -24.8392   162.6847  -0.153 0.878684    
JobRoleHuman Resources             120.1665   236.4764   0.508 0.611477    
JobRoleResearch Scientist          164.2496   160.9690   1.020 0.307840    
JobRoleSales Executive            1176.0951   198.9519   5.911 4.91e-09 ***
JobRoleHealthcare Representative  1209.6435   218.3057   5.541 4.02e-08 ***
JobRoleManufacturing Director     1299.1118   215.1928   6.037 2.35e-09 ***
JobRoleResearch Director          4712.7444   267.5194  17.616  < 2e-16 ***
JobRoleManager                    4527.4683   288.8527  15.674  < 2e-16 ***
TotalWorkingYears                   93.0054    17.3653   5.356 1.10e-07 ***
logID                              -80.7336    34.5241  -2.338 0.019595 *  
logDailyRate                       119.2873    52.5208   2.271 0.023383 *  
TotalWorkingYears2                  -1.6759     0.5311  -3.156 0.001658 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 989.5 on 847 degrees of freedom
Multiple R-squared:  0.9549,    Adjusted R-squared:  0.9537 
F-statistic: 814.4 on 22 and 847 DF,  p-value: < 2.2e-16

summary(modelTrans2)


Call:
lm(formula = logMonthlyIncome ~ JobLevel + JobRole + BusinessTravel + 
    logDailyRate + TotalWorkingYears + TotalWorkingYears2 + Education, 
    data = cs2_regresSmall2)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.8594 -0.1120 -0.0001  0.1084  0.5952 

Coefficients:
                                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)                       7.5179743  0.0841147  89.378  < 2e-16 ***
JobLevel2                         0.4513147  0.0301582  14.965  < 2e-16 ***
JobLevel3                         0.9013450  0.0398339  22.628  < 2e-16 ***
JobLevel4                         1.1911995  0.0598908  19.890  < 2e-16 ***
JobLevel5                         1.3135032  0.0702037  18.710  < 2e-16 ***
JobRoleLaboratory Technician      0.0182445  0.0345243   0.528  0.59732    
JobRoleHuman Resources            0.0494673  0.0501587   0.986  0.32431    
JobRoleResearch Scientist         0.0683055  0.0341728   1.999  0.04595 *  
JobRoleSales Executive            0.2640869  0.0422254   6.254 6.33e-10 ***
JobRoleHealthcare Representative  0.2726471  0.0463449   5.883 5.80e-09 ***
JobRoleManufacturing Director     0.2810423  0.0456486   6.157 1.15e-09 ***
JobRoleResearch Director          0.5582316  0.0567741   9.833  < 2e-16 ***
JobRoleManager                    0.5333385  0.0613214   8.697  < 2e-16 ***
BusinessTravelTravel_Rarely       0.0705120  0.0235635   2.992  0.00285 ** 
BusinessTravelTravel_Frequently   0.0485274  0.0277578   1.748  0.08078 .  
logDailyRate                      0.0216274  0.0111497   1.940  0.05274 .  
TotalWorkingYears                 0.0278028  0.0036859   7.543 1.18e-13 ***
TotalWorkingYears2               -0.0006200  0.0001127  -5.501 4.99e-08 ***
Education2                       -0.0057960  0.0266956  -0.217  0.82817    
Education3                       -0.0260772  0.0245503  -1.062  0.28845    
Education4                        0.0159078  0.0258986   0.614  0.53922    
Education5                       -0.0689578  0.0477590  -1.444  0.14914    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2101 on 848 degrees of freedom
Multiple R-squared:  0.9016,    Adjusted R-squared:  0.8992 
F-statistic:   370 on 21 and 848 DF,  p-value: < 2.2e-16

# # AIC of candidate models
# AIC(model8)
# AIC(model7a)
# AIC(model6)
# AIC(model8intFull)
# AIC(model8int1)
# AIC(model8int2)
# AIC(modelTrans1)
# AIC(modelTrans2)


# Evaluation of candidate models and comparison with Version1 model
# Load necessary packages
# library(car)
# library(caret)

# List of models
old_model = lm(MonthlyIncome ~ JobLevel + TotalWorkingYears + YearsWithCurrManager + YearsWithCurrManager^2 + DistanceFromHome + JobInvolvement + EnvironmentSatisfaction, data = cs2_regres2)

# List of models and corresponding datasets
models <- list(model8, model7a, model6, model8intFull, model8int1, model8int2, modelTrans1, modelTrans2, old_model)
model_names <- c("model8", "model7a", "model6", "model8intFull", "model8int1", "model8int2", "modelTrans1", "modelTrans2", "old_model")
datasets <- c("cs2_regres2", "cs2_regres2", "cs2_regres2", "cs2_regres2", "cs2_regres2", "cs2_regres2", "cs2_regresSmall2", "cs2_regresSmall2", "cs2_regres2")

# Initialize an empty data frame to store results
results_df <- data.frame(Model = character(),
                         Adj_R_Squared = numeric(),
                         AIC = numeric(),
                         BIC = numeric(),
                         RMSE_Train = numeric(),
                         CVPRESS = numeric(),
                         RMSE_Test = numeric(),
                         stringsAsFactors = FALSE)

# Function to calculate CVPRESS
cvpress <- function(model, data) {
  residuals <- residuals(model)
  h <- hatvalues(model)
  cvpress_value <- sum((residuals / (1 - h))^2)
  return(cvpress_value)
}

# Function to evaluate a single model
evaluate_single_model <- function(model, train_data, test_data, response_var) {
  if (!inherits(model, "lm")) {
    stop("The model provided is not a valid linear model.")
  }
  
  # Model summary
  summary_stats <- summary(model)
  adj_r_squared <- summary_stats$adj.r.squared
  
  # AIC and BIC
  aic_value <- AIC(model)
  bic_value <- BIC(model)
  
  # RMSE on training data
  rmse_train <- sqrt(mean(residuals(model)^2))
  
  # CVPRESS
  cvpress_value <- cvpress(model, train_data)
  
  # Prediction accuracy (RMSE) on test data
  predictions <- predict(model, newdata=test_data)
  rmse_test <- sqrt(mean((predictions - test_data[[response_var]])^2))
  
  # Results
  results <- list(
    Adj_R_Squared = adj_r_squared,
    AIC = aic_value,
    BIC = bic_value,
    RMSE_Train = rmse_train,
    CVPRESS = cvpress_value,
    RMSE_Test = rmse_test
  )
  
  return(results)
}

# Create training and testing datasets based on cs2_regres2
set.seed(123)
trainIndex_cs2_regres2 <- createDataPartition(cs2_regres2$MonthlyIncome, p=0.8, list=FALSE)
trainData_cs2_regres2 <- cs2_regres2[trainIndex_cs2_regres2,]
testData_cs2_regres2 <- cs2_regres2[-trainIndex_cs2_regres2,]

# Create training and testing datasets based on cs2_regresSmall2
set.seed(123)
trainIndex_cs2_regresSmall2 <- createDataPartition(cs2_regresSmall2$MonthlyIncome, p=0.8, list=FALSE)
trainData_cs2_regresSmall2 <- cs2_regresSmall2[trainIndex_cs2_regresSmall2,]
testData_cs2_regresSmall2 <- cs2_regresSmall2[-trainIndex_cs2_regresSmall2,]

# Evaluate each model and store the results
for (i in seq_along(models)) {
  model <- models[[i]]
  model_name <- model_names[i]
  dataset_name <- datasets[i]
  
  if (dataset_name == "cs2_regres2") {
    trainData <- trainData_cs2_regres2
    testData <- testData_cs2_regres2
  } else if (dataset_name == "cs2_regresSmall2") {
    trainData <- trainData_cs2_regresSmall2
    testData <- testData_cs2_regresSmall2
  }
  
  results <- evaluate_single_model(model, trainData, testData, "MonthlyIncome")
  
  # Add the results to the data frame
  results_df <- rbind(results_df, 
                      data.frame(Model = model_name,
                                 Adj_R_Squared = results$Adj_R_Squared,
                                 AIC = results$AIC,
                                 BIC = results$BIC,
                                 RMSE_Train = results$RMSE_Train,
                                 CVPRESS = results$CVPRESS,
                                 RMSE_Test = results$RMSE_Test,
                                 stringsAsFactors = FALSE))
}

# Print the results table
print(results_df)

          Model Adj_R_Squared        AIC        BIC   RMSE_Train      CVPRESS RMSE_Test
1        model8     0.9530060 14508.3465 14627.5588  982.8495052 8.839379e+08  1025.989
2       model7a     0.9528093 14508.0845 14608.2228  987.2300657 8.838469e+08  1019.338
3        model6     0.9527141 14507.8817 14598.4830  989.3868485 8.857464e+08  1023.496
4 model8intFull     0.9556436 14507.8077 14879.7501  924.4757189          Inf  1004.716
5    model8int1     0.9550913 14485.1980 14685.4747  951.0931906 8.606960e+08  1021.842
6    model8int2     0.9552203 14477.9278 14654.3620  952.5864696 8.549141e+08  1016.073
7   modelTrans1     0.9536858 14494.6970 14609.1409  976.2912116 8.717977e+08  1014.849
8   modelTrans2     0.8991735  -222.3909  -112.7155    0.2073834 3.913144e+01  7769.196
9     old_model     0.9258193 14895.7109 14967.2383 1242.1182815 1.390087e+09  1306.783

# model8int2 = lm(MonthlyIncome ~ ID + BusinessTravel + JobLevel + JobRole + TotalWorkingYears + ID:DailyRate + BusinessTravel:TotalWorkingYears + Education:TotalWorkingYears + JobLevel:TotalWorkingYears + JobRole:TotalWorkingYears, data = cs2_regresSmall)

# another good performing model:
# model8int1 = lm(MonthlyIncome ~ ID + BusinessTravel + JobLevel + JobRole + TotalWorkingYears + DailyRate + Education + ID:DailyRate + BusinessTravel:TotalWorkingYears + Education:TotalWorkingYears + JobLevel:TotalWorkingYears + JobRole:TotalWorkingYears, data = cs2_regresSmall)

model_formula = as.formula("MonthlyIncome ~ ID + BusinessTravel + JobLevel + JobRole + TotalWorkingYears + ID:DailyRate + BusinessTravel:TotalWorkingYears + Education:TotalWorkingYears + JobLevel:TotalWorkingYears + JobRole:TotalWorkingYears")

# number of train/test splits
iters = 100

# split percentage
splitPerc = 0.7

# initialize vector to store squared error from each train/test split loop for training and validation sets
cv_error_train = numeric(iters)
cv_error_test = numeric(iters)
  
# external cross-validation loop
for (i in 1:iters) {
  
  set.seed(i)

  # generate the test train split
  trainIdx = sample(1:nrow(cs2_regresSmall), round(splitPerc * nrow(cs2_regresSmall)))
  IncomeTrn = cs2_regresSmall[trainIdx, ]
  IncomeTst = cs2_regresSmall[-trainIdx, ]
    
  # fit the model with train_data
  model = lm(model_formula, data = IncomeTrn)
    
  # predict on the training set (same data used to make model)
  predTrn = predict(model, newdata = IncomeTrn)
  
  # calculate the mean squared error of training pred
  cv_error_train[i] = mean((IncomeTrn$MonthlyIncome - predTrn)^2)
  
  # predict on the training set (same data used to make model)
  predTst = predict(model, newdata = IncomeTst)
    
  # calculate the mean squared error of training pred
  cv_error_test[i] = mean((IncomeTst$MonthlyIncome - predTst)^2)
}
  
# calculate the root mean squared error (RMSE) for the training set
RMSE_trn = sqrt(mean(cv_error_train)) # root of avg of error from each iteration 
  
# calculate the root mean squared error (RMSE) for the validation set
RMSE_tst = sqrt(mean(cv_error_test))
  
# print the results
cat("\nRMSE of training set: ", RMSE_trn, "\n")


RMSE of training set:  946.0464 

cat("\nRMSE of validation set: ", RMSE_tst, "\n")


RMSE of validation set:  998.5428 

# make predictions with linear regression model

# variables used: ID`, `BusinessTravel`, `JobLevel`, `JobRole`, `TotalWorkingYears`, `ID:DailyRate`, `BusinessTravel:TotalWorkingYears`, `Education:TotalWorkingYears`, `JobLevel:TotalWorkingYears`, `JobRole:TotalWorkingYears`


# import data: CaseStudy2CompSet No Salary.csv from AWS S3 msdsds6306 bucket

# first column header is `ï..ID` instead of `ID` which I guess is a UTF-8 encoding issue 
# url = "https://msdsds6306.s3.us-east-2.amazonaws.com/CaseStudy2CompSet+No+Salary.csv"
# competition = read.table(textConnection(getURL(url)), sep = ",", header = TRUE, stringsAsFactors = TRUE)

# so I use read.csv and specify encoding = "UTF-8" and it imports correctly.
url = "https://msdsds6306.s3.us-east-2.amazonaws.com/CaseStudy2CompSet+No+Salary.csv"
competition = read.csv(url, header = TRUE, stringsAsFactors = TRUE, encoding = "UTF-8")

# save a copy of the competition unlabeled data
# write.csv(competition, file = "data/CaseStudy2CompSet No Salary.csv", row.names = FALSE)

# get a sense of the data
# str(competition)
# summary(competition)

# add the MonthlyIncome column between MaritalStatus and MonthlyRate 
competition = competition %>%
  mutate(MonthlyIncome = NA, .after = "MaritalStatus")
str(competition)

'data.frame':   300 obs. of  36 variables:
 $ ID                      : int  871 872 873 874 875 876 877 878 879 880 ...
 $ Age                     : int  43 33 55 36 27 39 33 21 30 51 ...
 $ Attrition               : Factor w/ 2 levels "No","Yes": 1 1 2 1 1 2 1 2 1 1 ...
 $ BusinessTravel          : Factor w/ 3 levels "Non-Travel","Travel_Frequently",..: 2 3 3 1 3 3 1 2 2 3 ...
 $ DailyRate               : int  1422 461 267 1351 1302 895 750 251 1312 1405 ...
 $ Department              : Factor w/ 3 levels "Human Resources",..: 3 2 3 2 2 3 3 2 2 2 ...
 $ DistanceFromHome        : int  2 13 13 9 19 5 22 10 23 11 ...
 $ Education               : int  4 1 4 4 3 3 2 2 3 2 ...
 $ EducationField          : Factor w/ 6 levels "Human Resources",..: 2 2 3 2 5 6 3 2 2 6 ...
 $ EmployeeCount           : int  1 1 1 1 1 1 1 1 1 1 ...
 $ EmployeeNumber          : int  1849 995 1372 1949 1619 42 160 1279 159 1367 ...
 $ EnvironmentSatisfaction : int  1 2 1 1 4 4 3 1 1 4 ...
 $ Gender                  : Factor w/ 2 levels "Female","Male": 2 1 2 2 2 2 2 1 2 1 ...
 $ HourlyRate              : int  92 53 85 66 67 56 95 45 96 82 ...
 $ JobInvolvement          : int  3 3 4 4 2 3 3 2 1 2 ...
 $ JobLevel                : int  2 1 4 1 1 2 2 1 1 4 ...
 $ JobRole                 : Factor w/ 9 levels "Healthcare Representative",..: 8 7 8 3 3 9 8 3 7 5 ...
 $ JobSatisfaction         : int  4 4 3 2 1 4 2 3 3 2 ...
 $ MaritalStatus           : Factor w/ 3 levels "Divorced","Married",..: 2 3 3 2 1 2 2 3 1 3 ...
 $ MonthlyIncome           : logi  NA NA NA NA NA NA ...
 $ MonthlyRate             : int  19246 17241 9277 9238 16290 3335 15480 25308 22310 24439 ...
 $ NumCompaniesWorked      : int  1 3 6 1 1 3 0 1 1 3 ...
 $ Over18                  : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
 $ OverTime                : Factor w/ 2 levels "No","Yes": 1 1 2 1 1 1 1 1 1 1 ...
 $ PercentSalaryHike       : int  20 18 17 22 11 14 13 20 25 16 ...
 $ PerformanceRating       : int  4 3 3 4 3 3 3 4 4 3 ...
 $ RelationshipSatisfaction: int  3 1 3 2 1 3 1 3 3 2 ...
 $ StandardHours           : int  80 80 80 80 80 80 80 80 80 80 ...
 $ StockOptionLevel        : int  1 0 0 0 2 1 1 0 3 0 ...
 $ TotalWorkingYears       : int  7 5 24 5 7 19 8 2 10 29 ...
 $ TrainingTimesLastYear   : int  5 4 2 3 3 6 2 2 2 1 ...
 $ WorkLifeBalance         : int  3 3 2 3 3 4 4 1 2 2 ...
 $ YearsAtCompany          : int  7 3 19 5 7 1 7 2 10 5 ...
 $ YearsInCurrentRole      : int  7 2 7 4 7 0 7 2 7 2 ...
 $ YearsSinceLastPromotion : int  7 0 3 0 0 0 0 2 0 0 ...
 $ YearsWithCurrManager    : int  7 2 8 2 7 0 7 2 9 3 ...

# convert numerical ranking variables to factors
numVars_to_fact = c("Education", "EnvironmentSatisfaction",
                    "JobInvolvement", "JobLevel", "JobSatisfaction",
                    "PerformanceRating", "RelationshipSatisfaction",
                    "StockOptionLevel", "WorkLifeBalance")
competition = competition %>%
  mutate(across(all_of(numVars_to_fact), as.factor))
# check the conversion
str(competition)

'data.frame':   300 obs. of  36 variables:
 $ ID                      : int  871 872 873 874 875 876 877 878 879 880 ...
 $ Age                     : int  43 33 55 36 27 39 33 21 30 51 ...
 $ Attrition               : Factor w/ 2 levels "No","Yes": 1 1 2 1 1 2 1 2 1 1 ...
 $ BusinessTravel          : Factor w/ 3 levels "Non-Travel","Travel_Frequently",..: 2 3 3 1 3 3 1 2 2 3 ...
 $ DailyRate               : int  1422 461 267 1351 1302 895 750 251 1312 1405 ...
 $ Department              : Factor w/ 3 levels "Human Resources",..: 3 2 3 2 2 3 3 2 2 2 ...
 $ DistanceFromHome        : int  2 13 13 9 19 5 22 10 23 11 ...
 $ Education               : Factor w/ 5 levels "1","2","3","4",..: 4 1 4 4 3 3 2 2 3 2 ...
 $ EducationField          : Factor w/ 6 levels "Human Resources",..: 2 2 3 2 5 6 3 2 2 6 ...
 $ EmployeeCount           : int  1 1 1 1 1 1 1 1 1 1 ...
 $ EmployeeNumber          : int  1849 995 1372 1949 1619 42 160 1279 159 1367 ...
 $ EnvironmentSatisfaction : Factor w/ 4 levels "1","2","3","4": 1 2 1 1 4 4 3 1 1 4 ...
 $ Gender                  : Factor w/ 2 levels "Female","Male": 2 1 2 2 2 2 2 1 2 1 ...
 $ HourlyRate              : int  92 53 85 66 67 56 95 45 96 82 ...
 $ JobInvolvement          : Factor w/ 4 levels "1","2","3","4": 3 3 4 4 2 3 3 2 1 2 ...
 $ JobLevel                : Factor w/ 5 levels "1","2","3","4",..: 2 1 4 1 1 2 2 1 1 4 ...
 $ JobRole                 : Factor w/ 9 levels "Healthcare Representative",..: 8 7 8 3 3 9 8 3 7 5 ...
 $ JobSatisfaction         : Factor w/ 4 levels "1","2","3","4": 4 4 3 2 1 4 2 3 3 2 ...
 $ MaritalStatus           : Factor w/ 3 levels "Divorced","Married",..: 2 3 3 2 1 2 2 3 1 3 ...
 $ MonthlyIncome           : logi  NA NA NA NA NA NA ...
 $ MonthlyRate             : int  19246 17241 9277 9238 16290 3335 15480 25308 22310 24439 ...
 $ NumCompaniesWorked      : int  1 3 6 1 1 3 0 1 1 3 ...
 $ Over18                  : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
 $ OverTime                : Factor w/ 2 levels "No","Yes": 1 1 2 1 1 1 1 1 1 1 ...
 $ PercentSalaryHike       : int  20 18 17 22 11 14 13 20 25 16 ...
 $ PerformanceRating       : Factor w/ 2 levels "3","4": 2 1 1 2 1 1 1 2 2 1 ...
 $ RelationshipSatisfaction: Factor w/ 4 levels "1","2","3","4": 3 1 3 2 1 3 1 3 3 2 ...
 $ StandardHours           : int  80 80 80 80 80 80 80 80 80 80 ...
 $ StockOptionLevel        : Factor w/ 4 levels "0","1","2","3": 2 1 1 1 3 2 2 1 4 1 ...
 $ TotalWorkingYears       : int  7 5 24 5 7 19 8 2 10 29 ...
 $ TrainingTimesLastYear   : int  5 4 2 3 3 6 2 2 2 1 ...
 $ WorkLifeBalance         : Factor w/ 4 levels "1","2","3","4": 3 3 2 3 3 4 4 1 2 2 ...
 $ YearsAtCompany          : int  7 3 19 5 7 1 7 2 10 5 ...
 $ YearsInCurrentRole      : int  7 2 7 4 7 0 7 2 7 2 ...
 $ YearsSinceLastPromotion : int  7 0 3 0 0 0 0 2 0 0 ...
 $ YearsWithCurrManager    : int  7 2 8 2 7 0 7 2 9 3 ...

# train the linear regression model on the full `cs2_conv` data set
fullset_LM_model = lm(model_formula, data = cs2_conv)
summary(fullset_LM_model)


Call:
lm(formula = model_formula, data = cs2_conv)

Residuals:
    Min      1Q  Median      3Q     Max 
-2948.3  -588.1   -75.3   553.5  4209.4 

Coefficients:
                                                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                         1.911e+03  2.556e+02   7.477 1.92e-13 ***
ID                                                 -5.649e-01  1.855e-01  -3.044 0.002405 ** 
BusinessTravelTravel_Frequently                     5.318e+02  2.238e+02   2.377 0.017690 *  
BusinessTravelTravel_Rarely                         5.387e+02  1.890e+02   2.851 0.004470 ** 
JobLevel2                                           3.461e+03  3.749e+02   9.234  < 2e-16 ***
JobLevel3                                           5.929e+03  4.256e+02  13.931  < 2e-16 ***
JobLevel4                                           1.145e+04  7.946e+02  14.409  < 2e-16 ***
JobLevel5                                           1.369e+04  1.107e+03  12.359  < 2e-16 ***
JobRoleLaboratory Technician                        2.817e+02  2.421e+02   1.164 0.244815    
JobRoleHuman Resources                              2.982e+02  4.536e+02   0.657 0.511118    
JobRoleResearch Scientist                           1.264e+02  2.380e+02   0.531 0.595417    
JobRoleSales Executive                             -5.702e+02  4.376e+02  -1.303 0.192954    
JobRoleHealthcare Representative                   -3.692e+02  4.824e+02  -0.765 0.444283    
JobRoleManufacturing Director                      -5.720e+02  4.687e+02  -1.221 0.222616    
JobRoleResearch Director                            2.925e+03  6.993e+02   4.183 3.19e-05 ***
JobRoleManager                                      2.883e+03  8.177e+02   3.526 0.000446 ***
TotalWorkingYears                                   8.175e+01  3.296e+01   2.480 0.013327 *  
ID:DailyRate                                        4.340e-04  1.638e-04   2.649 0.008231 ** 
BusinessTravelTravel_Frequently:TotalWorkingYears  -3.518e+01  1.766e+01  -1.992 0.046661 *  
BusinessTravelTravel_Rarely:TotalWorkingYears      -2.416e+01  1.550e+01  -1.558 0.119520    
TotalWorkingYears:Education2                       -9.450e-01  1.075e+01  -0.088 0.929977    
TotalWorkingYears:Education3                       -8.047e+00  9.337e+00  -0.862 0.389043    
TotalWorkingYears:Education4                       -2.523e+00  9.517e+00  -0.265 0.790996    
TotalWorkingYears:Education5                       -4.183e+01  1.528e+01  -2.737 0.006339 ** 
JobLevel2:TotalWorkingYears                        -1.359e+02  3.053e+01  -4.450 9.75e-06 ***
JobLevel3:TotalWorkingYears                        -7.870e+01  3.189e+01  -2.468 0.013780 *  
JobLevel4:TotalWorkingYears                        -1.907e+02  4.222e+01  -4.518 7.15e-06 ***
JobLevel5:TotalWorkingYears                        -1.745e+02  5.189e+01  -3.364 0.000804 ***
JobRoleLaboratory Technician:TotalWorkingYears     -3.385e+01  3.387e+01  -0.999 0.317881    
JobRoleHuman Resources:TotalWorkingYears           -2.960e+01  6.699e+01  -0.442 0.658655    
JobRoleResearch Scientist:TotalWorkingYears         1.531e+01  3.353e+01   0.457 0.648062    
JobRoleSales Executive:TotalWorkingYears            1.382e+02  4.270e+01   3.236 0.001260 ** 
JobRoleHealthcare Representative:TotalWorkingYears  1.203e+02  4.427e+01   2.717 0.006726 ** 
JobRoleManufacturing Director:TotalWorkingYears     1.467e+02  4.416e+01   3.322 0.000933 ***
JobRoleResearch Director:TotalWorkingYears          1.358e+02  5.013e+01   2.709 0.006881 ** 
JobRoleManager:TotalWorkingYears                    1.303e+02  5.179e+01   2.516 0.012048 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 972.9 on 834 degrees of freedom
Multiple R-squared:  0.957, Adjusted R-squared:  0.9552 
F-statistic: 530.6 on 35 and 834 DF,  p-value: < 2.2e-16

# predict the labels on the competition set
preds = predict(fullset_LM_model, competition)

# add the labels to the MonthlyIncome column
competition = competition %>% mutate(MonthlyIncome = as.integer(preds))
str(competition)

'data.frame':   300 obs. of  36 variables:
 $ ID                      : int  871 872 873 874 875 876 877 878 879 880 ...
 $ Age                     : int  43 33 55 36 27 39 33 21 30 51 ...
 $ Attrition               : Factor w/ 2 levels "No","Yes": 1 1 2 1 1 2 1 2 1 1 ...
 $ BusinessTravel          : Factor w/ 3 levels "Non-Travel","Travel_Frequently",..: 2 3 3 1 3 3 1 2 2 3 ...
 $ DailyRate               : int  1422 461 267 1351 1302 895 750 251 1312 1405 ...
 $ Department              : Factor w/ 3 levels "Human Resources",..: 3 2 3 2 2 3 3 2 2 2 ...
 $ DistanceFromHome        : int  2 13 13 9 19 5 22 10 23 11 ...
 $ Education               : Factor w/ 5 levels "1","2","3","4",..: 4 1 4 4 3 3 2 2 3 2 ...
 $ EducationField          : Factor w/ 6 levels "Human Resources",..: 2 2 3 2 5 6 3 2 2 6 ...
 $ EmployeeCount           : int  1 1 1 1 1 1 1 1 1 1 ...
 $ EmployeeNumber          : int  1849 995 1372 1949 1619 42 160 1279 159 1367 ...
 $ EnvironmentSatisfaction : Factor w/ 4 levels "1","2","3","4": 1 2 1 1 4 4 3 1 1 4 ...
 $ Gender                  : Factor w/ 2 levels "Female","Male": 2 1 2 2 2 2 2 1 2 1 ...
 $ HourlyRate              : int  92 53 85 66 67 56 95 45 96 82 ...
 $ JobInvolvement          : Factor w/ 4 levels "1","2","3","4": 3 3 4 4 2 3 3 2 1 2 ...
 $ JobLevel                : Factor w/ 5 levels "1","2","3","4",..: 2 1 4 1 1 2 2 1 1 4 ...
 $ JobRole                 : Factor w/ 9 levels "Healthcare Representative",..: 8 7 8 3 3 9 8 3 7 5 ...
 $ JobSatisfaction         : Factor w/ 4 levels "1","2","3","4": 4 4 3 2 1 4 2 3 3 2 ...
 $ MaritalStatus           : Factor w/ 3 levels "Divorced","Married",..: 2 3 3 2 1 2 2 3 1 3 ...
 $ MonthlyIncome           : int  5704 2623 12997 2438 2841 4117 5257 2348 3112 13733 ...
 $ MonthlyRate             : int  19246 17241 9277 9238 16290 3335 15480 25308 22310 24439 ...
 $ NumCompaniesWorked      : int  1 3 6 1 1 3 0 1 1 3 ...
 $ Over18                  : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
 $ OverTime                : Factor w/ 2 levels "No","Yes": 1 1 2 1 1 1 1 1 1 1 ...
 $ PercentSalaryHike       : int  20 18 17 22 11 14 13 20 25 16 ...
 $ PerformanceRating       : Factor w/ 2 levels "3","4": 2 1 1 2 1 1 1 2 2 1 ...
 $ RelationshipSatisfaction: Factor w/ 4 levels "1","2","3","4": 3 1 3 2 1 3 1 3 3 2 ...
 $ StandardHours           : int  80 80 80 80 80 80 80 80 80 80 ...
 $ StockOptionLevel        : Factor w/ 4 levels "0","1","2","3": 2 1 1 1 3 2 2 1 4 1 ...
 $ TotalWorkingYears       : int  7 5 24 5 7 19 8 2 10 29 ...
 $ TrainingTimesLastYear   : int  5 4 2 3 3 6 2 2 2 1 ...
 $ WorkLifeBalance         : Factor w/ 4 levels "1","2","3","4": 3 3 2 3 3 4 4 1 2 2 ...
 $ YearsAtCompany          : int  7 3 19 5 7 1 7 2 10 5 ...
 $ YearsInCurrentRole      : int  7 2 7 4 7 0 7 2 7 2 ...
 $ YearsSinceLastPromotion : int  7 0 3 0 0 0 0 2 0 0 ...
 $ YearsWithCurrManager    : int  7 2 8 2 7 0 7 2 9 3 ...

# for curiousity get the summary of MonthlyIncome from both datasets
summary(cs2_conv$MonthlyIncome)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1081    2840    4946    6390    8182   19999 

summary(competition$MonthlyIncome)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1588    2719    5239    6067    6533   19449 

# make dataframe with just competition set ordered IDs and labels
competitionLabels = competition %>% dplyr::select(ID, MonthlyIncome)
# str(competitionLabels)

# save to file
# write.csv(competitionLabels, file = "data/Case2PredictionsHenderson2 Salary.csv", row.names = FALSE)

devtools::session_info()

─ Session info ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
 setting  value
 version  R version 4.3.2 (2023-10-31)
 os       macOS Monterey 12.7.5
 system   x86_64, darwin20
 ui       RStudio
 language (EN)
 collate  en_US.UTF-8
 ctype    en_US.UTF-8
 tz       America/New_York
 date     2024-08-24
 rstudio  2023.12.1+402 Ocean Storm (desktop)
 pandoc   3.1.1 @ /Applications/RStudio.app/Contents/Resources/app/quarto/bin/tools/ (via rmarkdown)

─ Packages ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
 package      * version    date (UTC) lib source
 abind          1.4-5      2016-07-21 [1] CRAN (R 4.3.0)
 backports      1.4.1      2021-12-13 [1] CRAN (R 4.3.0)
 base64enc      0.1-3      2015-07-28 [1] CRAN (R 4.3.0)
 bitops         1.0-7      2021-04-24 [1] CRAN (R 4.3.0)
 cachem         1.1.0      2024-05-16 [1] CRAN (R 4.3.3)
 car          * 3.1-2      2023-03-30 [1] CRAN (R 4.3.0)
 carData      * 3.0-5      2022-01-06 [1] CRAN (R 4.3.0)
 caret        * 6.0-94     2023-03-21 [1] CRAN (R 4.3.0)
 checkmate      2.3.1      2023-12-04 [1] CRAN (R 4.3.0)
 class        * 7.3-22     2023-05-03 [1] CRAN (R 4.3.2)
 cli            3.6.2      2023-12-11 [1] CRAN (R 4.3.0)
 cluster        2.1.4      2022-08-22 [1] CRAN (R 4.3.2)
 codetools      0.2-19     2023-02-01 [1] CRAN (R 4.3.2)
 colorspace     2.1-0      2023-01-23 [1] CRAN (R 4.3.0)
 combinat     * 0.0-8      2012-10-29 [1] CRAN (R 4.3.0)
 corrplot     * 0.92       2021-11-18 [1] CRAN (R 4.3.0)
 data.table     1.14.10    2023-12-08 [1] CRAN (R 4.3.0)
 DataExplorer * 0.8.3      2024-01-24 [1] CRAN (R 4.3.2)
 devtools       2.4.5      2022-10-11 [1] CRAN (R 4.3.0)
 digest         0.6.33     2023-07-07 [1] CRAN (R 4.3.0)
 dplyr        * 1.1.4      2023-11-17 [1] CRAN (R 4.3.0)
 e1071        * 1.7-14     2023-12-06 [1] CRAN (R 4.3.0)
 ellipsis       0.3.2      2021-04-29 [1] CRAN (R 4.3.0)
 evaluate       0.23       2023-11-01 [1] CRAN (R 4.3.0)
 fansi          1.0.6      2023-12-08 [1] CRAN (R 4.3.0)
 farver         2.1.1      2022-07-06 [1] CRAN (R 4.3.0)
 fastmap        1.2.0      2024-05-15 [1] CRAN (R 4.3.3)
 forcats      * 1.0.0      2023-01-29 [1] CRAN (R 4.3.0)
 foreach        1.5.2      2022-02-02 [1] CRAN (R 4.3.0)
 foreign        0.8-85     2023-09-09 [1] CRAN (R 4.3.2)
 Formula        1.2-5      2023-02-24 [1] CRAN (R 4.3.0)
 fs             1.6.3      2023-07-20 [1] CRAN (R 4.3.0)
 future         1.33.1     2023-12-22 [1] CRAN (R 4.3.0)
 future.apply   1.11.1     2023-12-21 [1] CRAN (R 4.3.0)
 generics       0.1.3      2022-07-05 [1] CRAN (R 4.3.0)
 GGally       * 2.2.1      2024-02-14 [1] CRAN (R 4.3.2)
 ggplot2      * 3.5.1      2024-04-23 [1] CRAN (R 4.3.2)
 ggstats        0.5.1      2023-11-21 [1] CRAN (R 4.3.0)
 globals        0.16.2     2022-11-21 [1] CRAN (R 4.3.0)
 glue           1.7.0      2024-01-09 [1] CRAN (R 4.3.0)
 goftest        1.2-3      2021-10-07 [1] CRAN (R 4.3.0)
 gower          1.0.1      2022-12-22 [1] CRAN (R 4.3.0)
 gridExtra    * 2.3        2017-09-09 [1] CRAN (R 4.3.0)
 gtable         0.3.4      2023-08-21 [1] CRAN (R 4.3.0)
 hardhat        1.3.1      2024-02-02 [1] CRAN (R 4.3.2)
 highr          0.10       2022-12-22 [1] CRAN (R 4.3.0)
 Hmisc        * 5.1-2      2024-03-11 [1] CRAN (R 4.3.2)
 hms            1.1.3      2023-03-21 [1] CRAN (R 4.3.0)
 htmlTable      2.4.2      2023-10-29 [1] CRAN (R 4.3.0)
 htmltools      0.5.7      2023-11-03 [1] CRAN (R 4.3.0)
 htmlwidgets    1.6.4      2023-12-06 [1] CRAN (R 4.3.0)
 httpuv         1.6.13     2023-12-06 [1] CRAN (R 4.3.0)
 igraph         1.6.0      2023-12-11 [1] CRAN (R 4.3.0)
 ipred          0.9-14     2023-03-09 [1] CRAN (R 4.3.0)
 iterators      1.0.14     2022-02-05 [1] CRAN (R 4.3.0)
 kableExtra   * 1.4.0      2024-01-24 [1] CRAN (R 4.3.2)
 knitr          1.45       2023-10-30 [1] CRAN (R 4.3.0)
 labeling       0.4.3      2023-08-29 [1] CRAN (R 4.3.0)
 later          1.3.2      2023-12-06 [1] CRAN (R 4.3.0)
 lattice      * 0.21-9     2023-10-01 [1] CRAN (R 4.3.2)
 lava           1.7.3      2023-11-04 [1] CRAN (R 4.3.0)
 lifecycle      1.0.4      2023-11-07 [1] CRAN (R 4.3.0)
 listenv        0.9.0      2022-12-16 [1] CRAN (R 4.3.0)
 lubridate    * 1.9.3      2023-09-27 [1] CRAN (R 4.3.0)
 magrittr       2.0.3      2022-03-30 [1] CRAN (R 4.3.0)
 MASS           7.3-60     2023-05-04 [1] CRAN (R 4.3.2)
 Matrix         1.6-1.1    2023-09-18 [1] CRAN (R 4.3.2)
 memoise        2.0.1      2021-11-26 [1] CRAN (R 4.3.0)
 mgcv           1.9-0      2023-07-11 [1] CRAN (R 4.3.2)
 mime           0.12       2021-09-28 [1] CRAN (R 4.3.0)
 miniUI         0.1.1.1    2018-05-18 [1] CRAN (R 4.3.0)
 ModelMetrics   1.2.2.2    2020-03-17 [1] CRAN (R 4.3.0)
 munsell        0.5.0      2018-06-12 [1] CRAN (R 4.3.0)
 networkD3      0.4        2017-03-18 [1] CRAN (R 4.3.0)
 nlme           3.1-163    2023-08-09 [1] CRAN (R 4.3.2)
 nnet           7.3-19     2023-05-03 [1] CRAN (R 4.3.2)
 nortest        1.0-4      2015-07-30 [1] CRAN (R 4.3.0)
 olsrr        * 0.6.0      2024-02-12 [1] CRAN (R 4.3.2)
 pander       * 0.6.5      2022-03-18 [1] CRAN (R 4.3.0)
 parallelly     1.36.0     2023-05-26 [1] CRAN (R 4.3.0)
 patchwork    * 1.2.0      2024-01-08 [1] CRAN (R 4.3.0)
 pillar         1.9.0      2023-03-22 [1] CRAN (R 4.3.0)
 pkgbuild       1.4.3      2023-12-10 [1] CRAN (R 4.3.0)
 pkgconfig      2.0.3      2019-09-22 [1] CRAN (R 4.3.0)
 pkgload        1.3.3      2023-09-22 [1] CRAN (R 4.3.0)
 plyr           1.8.9      2023-10-02 [1] CRAN (R 4.3.0)
 pROC           1.18.5     2023-11-01 [1] CRAN (R 4.3.0)
 prodlim        2023.08.28 2023-08-28 [1] CRAN (R 4.3.0)
 profvis        0.3.8      2023-05-02 [1] CRAN (R 4.3.0)
 promises       1.2.1      2023-08-10 [1] CRAN (R 4.3.0)
 proxy          0.4-27     2022-06-09 [1] CRAN (R 4.3.0)
 purrr        * 1.0.2      2023-08-10 [1] CRAN (R 4.3.0)
 R6             2.5.1      2021-08-19 [1] CRAN (R 4.3.0)
 RColorBrewer * 1.1-3      2022-04-03 [1] CRAN (R 4.3.0)
 Rcpp           1.0.12     2024-01-09 [1] CRAN (R 4.3.0)
 RCurl        * 1.98-1.14  2024-01-09 [1] CRAN (R 4.3.0)
 readr        * 2.1.4      2023-02-10 [1] CRAN (R 4.3.0)
 recipes        1.0.9      2023-12-13 [1] CRAN (R 4.3.0)
 remotes        2.4.2.1    2023-07-18 [1] CRAN (R 4.3.0)
 reshape2       1.4.4      2020-04-09 [1] CRAN (R 4.3.0)
 rlang          1.1.3      2024-01-10 [1] CRAN (R 4.3.0)
 rmarkdown      2.25       2023-09-18 [1] CRAN (R 4.3.0)
 rpart          4.1.21     2023-10-09 [1] CRAN (R 4.3.2)
 rsconnect      1.2.1      2024-01-31 [1] CRAN (R 4.3.2)
 rstudioapi     0.15.0     2023-07-07 [1] CRAN (R 4.3.0)
 scales         1.3.0      2023-11-28 [1] CRAN (R 4.3.0)
 sessioninfo    1.2.2      2021-12-06 [1] CRAN (R 4.3.0)
 shiny          1.9.1      2024-08-01 [1] CRAN (R 4.3.3)
 stringi        1.8.3      2023-12-11 [1] CRAN (R 4.3.0)
 stringr      * 1.5.1      2023-11-14 [1] CRAN (R 4.3.0)
 survival       3.5-7      2023-08-14 [1] CRAN (R 4.3.2)
 svglite        2.1.3      2023-12-08 [1] CRAN (R 4.3.0)
 systemfonts    1.0.5      2023-10-09 [1] CRAN (R 4.3.0)
 tibble       * 3.2.1      2023-03-20 [1] CRAN (R 4.3.0)
 tidyr        * 1.3.0      2023-01-24 [1] CRAN (R 4.3.0)
 tidyselect     1.2.0      2022-10-10 [1] CRAN (R 4.3.0)
 tidyverse    * 2.0.0      2023-02-22 [1] CRAN (R 4.3.0)
 timechange     0.2.0      2023-01-11 [1] CRAN (R 4.3.0)
 timeDate       4032.109   2023-12-14 [1] CRAN (R 4.3.0)
 tzdb           0.4.0      2023-05-12 [1] CRAN (R 4.3.0)
 urlchecker     1.0.1      2021-11-30 [1] CRAN (R 4.3.0)
 usethis        2.2.2      2023-07-06 [1] CRAN (R 4.3.0)
 utf8           1.2.4      2023-10-22 [1] CRAN (R 4.3.0)
 vctrs          0.6.5      2023-12-01 [1] CRAN (R 4.3.0)
 viridisLite    0.4.2      2023-05-02 [1] CRAN (R 4.3.0)
 withr          2.5.2      2023-10-30 [1] CRAN (R 4.3.0)
 xfun           0.41       2023-11-01 [1] CRAN (R 4.3.0)
 xml2           1.3.6      2023-12-04 [1] CRAN (R 4.3.0)
 xtable         1.8-4      2019-04-21 [1] CRAN (R 4.3.0)
 yaml           2.3.8      2023-12-11 [1] CRAN (R 4.3.0)

 [1] /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/library

───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────

# rmarkdown::render("Analysis_of_Employee_Attrition_and_Income_V2.Rmd", "md_document")