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Case Study 2
Christian
# Project Presentation
https://smu.zoom.us/rec/share/_PzRRtfdhT2ePWzXH0Lx2sIZMq8GwgeKTA2HAVasKvkCtHDZZRhChZdbOfmoVHVZ.ew57SCDdjbvTRiCs?startTime=1702429652000 Passcode: rdV076=w
CDCastr0.github.io/pro
Preparing the Environment and Loading the Data
This is loading the necessary libraries like readr, dplyr, tidyr, ggplot2, caret, e1071, and class.
# Load libraries
library(rmarkdown)
library(readr)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(tidyr)
library(caret)## Warning: package 'caret' was built under R version 4.3.2## Loading required package: ggplot2## Loading required package: latticelibrary(e1071)## Warning: package 'e1071' was built under R version 4.3.2library(class)
library(ggplot2)
# Load data
data <- read.csv(choose.files())# Convert categorical variables to factors
data$Attrition <- factor(data$Attrition, levels = c("No", "Yes"), labels = c(0, 1))
data$BusinessTravel <- factor(data$BusinessTravel)
data$Department <- factor(data$Department)
data$EducationField <- factor(data$EducationField)
data$Gender <- factor(data$Gender)
data$JobRole <- factor(data$JobRole)
data$MaritalStatus <- factor(data$MaritalStatus)
data$Over18 <- factor(data$Over18)
data$OverTime <- factor(data$OverTime)# Convert factors to numeric for correlation analysis
data_numeric <- data %>%
mutate(across(where(is.factor), as.numeric))
# Remove constant variables
data_numeric <- data_numeric %>% select_if(~sd(.) != 0)# Exploratory Data Analysis
To begin, we started by analyzing the correlation between all variables. This produced a correlation matrix used to reference different variables in the selection process.
# Perform correlation analysis
correlation <- cor(data_numeric, use = "complete.obs")
# Sort the correlation with Attrition and find the top factors
sorted_correlation <- sort(correlation['Attrition',], decreasing = TRUE)
# Display the top factors (excluding Attrition itself)
sorted_correlation[sorted_correlation != 1][1:3]## OverTime MaritalStatus JobRole
## 0.2720366 0.1970150 0.0905386We next plotted different graphs in order to understand how the variables related to each other.
ggplot(data, aes(x = JobRole, fill = Attrition)) +
geom_bar(position = "dodge") +
labs(title = "Job Role vs Attrition", x = "Job Role", y = "Count") +
theme_minimal()
ggplot(data, aes(x = OverTime, fill = Attrition)) +
geom_bar(position = "dodge") +
labs(title = "Overtime vs Attrition", x = "Overtime", y = "Count") +
theme_minimal()
ggplot(data, aes(x = MaritalStatus, fill = Attrition)) +
geom_bar(position = "dodge") +
labs(title = "Marital Status vs Attrition", x = "Marital Status", y = "Count") +
theme_minimal()
# Visualizing correlations
#correlation_plot <- cor(data %>% select_if(is.numeric))
#ggplot(data = as.data.frame(correlation_plot), aes(x = Var1, y = Var2, fill = value)) +
geom_tile()## geom_tile: linejoin = mitre, na.rm = FALSE
## stat_identity: na.rm = FALSE
## position_identity# Identifying top factors for attrition
#attrition_factors <- data %>%
# group_by(attrition) %>%
# summarise_all(funs(mean(., na.rm = TRUE)))
#Analyzing the distribution of attrition across different departments
#ggplot(data, aes(x = Department, fill = Attrition)) +
# geom_bar(position = "fill") +
# labs(title = "Attrition Distribution Across Departments", x = "Department", y = "Proportion")
# Exploring the relationship between job satisfaction and attrition
#ggplot(data, aes(x = JobSatisfaction, fill = Attrition)) +
# geom_bar(position = "fill") +
# labs(title = "Job Satisfaction vs Attrition", x = "Job Satisfaction Level", y = "Proportion")
# Relationship between total working years and attrition
#ggplot(data, aes(x = TotalWorkingYears, y = after_stat(count), fill = Attrition)) +
# geom_histogram(binwidth = 1, position = "dodge") +
# labs(title = "Total Working Years vs Attrition", x = "Total Working Years", y = "Count")
# Plotting histogram of a variable (example: Age)
#ggplot(data, aes(x = Age)) + geom_histogram(bins = 30) + theme_minimal()
# Exploring relationship between two variables (example: Age and Attrition)
#ggplot(data, aes(x = Age, fill = Attrition)) + geom_histogram(bins = 30) + theme_minimal()
# Analyzing the distribution of attrition across different departments
#ggplot(data, aes(x = Department, fill = Attrition)) +
# geom_bar(position = "fill") +
# labs(title = "Attrition Distribution Across Departments", x = "Department", y = "Proportion")
# Exploring the relationship between job satisfaction and attrition
#ggplot(data, aes(x = JobSatisfaction, fill = Attrition)) +
# geom_bar(position = "fill") +
# labs(title = "Job Satisfaction vs Attrition", x = "Job Satisfaction Level", y = "Proportion")
# Relationship between total working years and attrition
#ggplot(data, aes(x = TotalWorkingYears, y = after_stat(count), fill = Attrition)) +
# geom_histogram(binwidth = 1, position = "dodge") +
# labs(title = "Total Working Years vs Attrition", x = "Total Working Years", y = "Count")
# Analyzing job role specific trends in job satisfaction
#ggplot(data, aes(x = JobRole, y = JobSatisfaction)) +
# geom_boxplot() +
# labs(title = "Job Satisfaction Across Different Job Roles", x = "Job Role", y = "Job Satisfaction Level") +
# theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Job role specific attrition trends
#ggplot(data, aes(x = JobRole, fill = Attrition)) +
# geom_bar(position = "fill") +
# labs(title = "Attrition Rates Across Different Job Roles", x = "Job Role", y = "Proportion") +
# theme(axis.text.x = element_text(angle = 45, hjust = 1))
# Age distribution with respect to attrition
#ggplot(data, aes(x = Age, fill = Attrition)) +
# geom_histogram(binwidth = 1, position = "dodge") +
# labs(title = "Age Distribution vs Attrition", x = "Age", y = "Count")
# Exploring the impact of marital status on attrition
#ggplot(data, aes(x = MaritalStatus, fill = Attrition)) +
# geom_bar(position = "fill") +
# labs(title = "Marital Status vs Attrition", x = "Marital Status", y = "Proportion")Parts of the above EDA were generated by AI and were useful in coming up with creative graphs.
# Analysis of Important Variables
Given the most highly correlated variables, we decided to proceed with a model that includes them in order to test it’s accuracy.
data$Attrition## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1
## [38] 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0
## [75] 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## [112] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0
## [149] 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0
## [186] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
## [223] 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
## [260] 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
## [297] 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
## [334] 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0
## [371] 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
## [408] 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0
## [445] 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0
## [482] 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0
## [519] 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [556] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1
## [593] 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
## [630] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
## [667] 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0
## [704] 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0
## [741] 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
## [778] 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
## [815] 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1
## [852] 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0
## Levels: 0 1# Load the data
data <- read.csv(choose.files())
# Check the unique values in Attrition column
unique(data$Attrition)## [1] "No" "Yes"# Ensure Attrition is converted to a factor with correct levels
#data$Attrition <- factor(data$Attrition, levels = c("No", "Yes"))
# Convert other variables to factors
#data$OverTime <- factor(data$OverTime)
#data$JobRole <- factor(data$JobRole)
#data$MaritalStatus <- factor(data$MaritalStatus)
# Function to calculate attrition rates
#calculate_attrition_rate <- function(data, column_name) {
# data %>%
# group_by(!!sym(column_name)) %>%
# summarise(Attrition_Count = sum(Attrition == "Yes", na.rm = TRUE),
# Total_Count = n(),
# Attrition_Rate = Attrition_Count / Total_Count) %>%
# arrange(desc(Attrition_Rate))
#}
# Calculate attrition rates for Job Role, Overtime, and Marital Status
#job_role_attrition <- calculate_attrition_rate(data, "JobRole")
#overtime_attrition <- calculate_attrition_rate(data, "OverTime")
#marital_status_attrition <- calculate_attrition_rate(data, "MaritalStatus")
# Display the results
#job_role_attrition
#overtime_attrition
#marital_status_attritionThis did not yield a reliable or accurate model, so we began to search elsewhere for better variables.
# T-tests and Variables
# Load the data
data <- read.csv(choose.files())
# Ensure data$Attrition is a factor and check its levels
data$Attrition <- as.factor(data$Attrition)
print(levels(data$Attrition)) # Should output something like '0' and '1' or 'Yes' and 'No'## [1] "No" "Yes"# Identify numeric variables
numeric_vars <- sapply(data, is.numeric)
numeric_vars_names <- names(data)[numeric_vars]
# Initialize an empty data frame to store t-test results
t_test_results <- data.frame(Variable = character(),
p_value = numeric(),
mean_diff = numeric(),
stringsAsFactors = FALSE)
# Corrected code for handling variables with little or no variance within groups
for (var in numeric_vars_names) {
# Perform t-test if the variable has more than one unique value in both groups
if (length(unique(data[data$Attrition == levels(data$Attrition)[1], var])) > 1 &&
length(unique(data[data$Attrition == levels(data$Attrition)[2], var])) > 1) {
# Perform t-test
t_test <- t.test(data[[var]] ~ data$Attrition)
# Calculate mean difference
mean_diff <- abs(diff(tapply(data[[var]], data$Attrition, mean, na.rm=TRUE)))
# Append results to the data frame
t_test_results <- rbind(t_test_results,
data.frame(Variable = var,
p_value = t_test$p.value,
mean_diff = mean_diff))
}
}
# Order results by p-value
t_test_results <- t_test_results[order(t_test_results$p_value),]
# Display the results
print(t_test_results)## Variable p_value mean_diff
## Yes11 MonthlyIncome 2.412488e-07 1.937214e+03
## Yes9 JobLevel 4.041851e-07 4.807241e-01
## Yes18 TotalWorkingYears 6.595682e-07 3.417025e+00
## Yes22 YearsInCurrentRole 1.522152e-06 1.546282e+00
## Yes8 JobInvolvement 1.997298e-06 3.593933e-01
## Yes24 YearsWithCurrManager 5.084229e-06 1.427006e+00
## Yes17 StockOptionLevel 3.860043e-05 3.468689e-01
## Yes1 Age 5.049764e-05 3.626614e+00
## Yes21 YearsAtCompany 2.563021e-04 2.108513e+00
## Yes10 JobSatisfaction 1.497265e-03 3.259295e-01
## Yes3 DistanceFromHome 1.640519e-02 1.928376e+00
## Yes20 WorkLifeBalance 1.900885e-02 1.738748e-01
## Yes6 EnvironmentSatisfaction 3.397271e-02 2.312133e-01
## Yes19 TrainingTimesLastYear 5.948323e-02 2.171233e-01
## Yes13 NumCompaniesWorked 9.788235e-02 4.182975e-01
## Yes4 Education 1.421319e-01 1.375734e-01
## Yes ID 1.636497e-01 3.230577e+01
## Yes12 MonthlyRate 1.980950e-01 8.358376e+02
## Yes16 RelationshipSatisfaction 2.639669e-01 1.188845e-01
## Yes7 HourlyRate 2.744798e-01 2.001076e+00
## Yes2 DailyRate 3.188749e-01 3.686742e+01
## Yes5 EmployeeNumber 4.978776e-01 3.749432e+01
## Yes15 PerformanceRating 6.610278e-01 1.497065e-02
## Yes14 PercentSalaryHike 6.692297e-01 1.532290e-01
## Yes23 YearsSinceLastPromotion 8.983165e-01 3.962818e-02Given these results, we began to proceed with the new model.
# Load the data
train_data <- read.csv(choose.files())
test_data <- read.csv(choose.files())
str(train_data)## '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 : chr "No" "No" "No" "No" ...
## $ BusinessTravel : chr "Travel_Rarely" "Travel_Rarely" "Travel_Frequently" "Travel_Rarely" ...
## $ DailyRate : int 117 1308 200 801 567 294 1283 309 1333 653 ...
## $ Department : chr "Sales" "Research & Development" "Research & Development" "Sales" ...
## $ 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 : chr "Life Sciences" "Medical" "Life Sciences" "Marketing" ...
## $ 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 : chr "Male" "Male" "Male" "Female" ...
## $ 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 : chr "Sales Executive" "Research Director" "Manufacturing Director" "Sales Executive" ...
## $ JobSatisfaction : int 4 3 4 4 4 1 3 4 3 3 ...
## $ MaritalStatus : chr "Divorced" "Single" "Single" "Married" ...
## $ 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 : chr "Y" "Y" "Y" "Y" ...
## $ OverTime : chr "No" "No" "No" "No" ...
## $ 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 ...# Select relevant columns and convert factors (modify as per your top factors)
#train_data <- train_data %>%
# select(Attrition, OverTime, JobRole, MaritalStatus) %>%
# mutate(OverTime = factor(OverTime),
# Attrition = factor(Attrition, levels = c("No", "Yes")))
# Select relevant columns and convert factors (modify as per your top factors)
#train_data <- train_data %>%
# select(Attrition, MonthlyIncome, JobLevel, TotalWorkingYears) %>%
# mutate(MonthlyIncome = factor(MonthlyIncome),
# Attrition = factor(Attrition, levels = c("No", "Yes")))
# Assuming MonthlyIncome is already loaded in your data frame
# First, check the range of MonthlyIncome
range(train_data$MonthlyIncome)## [1] 1081 19999# Now, create the breaks for the intervals
min_income <- min(train_data$MonthlyIncome, na.rm = TRUE)
max_income <- max(train_data$MonthlyIncome, na.rm = TRUE)
breaks <- seq(from = min_income, to = max_income, by = 100)
# Use cut function to create a new factor variable
train_data$IncomeGroup <- cut(train_data$MonthlyIncome, breaks = breaks, include.lowest = TRUE, right = FALSE)
# Display the structure to see the changes
str(train_data$IncomeGroup)## Factor w/ 189 levels "[1.08e+03,1.18e+03)",..: 34 186 83 94 27 78 11 57 12 40 ...# Optional: Convert IncomeGroup to a numeric code if needed
train_data$IncomeGroupCode <- as.numeric(train_data$IncomeGroup)
# Display the first few rows of the dataset to verify
head(train_data)## ID Age Attrition BusinessTravel DailyRate Department
## 1 1 32 No Travel_Rarely 117 Sales
## 2 2 40 No Travel_Rarely 1308 Research & Development
## 3 3 35 No Travel_Frequently 200 Research & Development
## 4 4 32 No Travel_Rarely 801 Sales
## 5 5 24 No Travel_Frequently 567 Research & Development
## 6 6 27 No Travel_Frequently 294 Research & Development
## DistanceFromHome Education EducationField EmployeeCount EmployeeNumber
## 1 13 4 Life Sciences 1 859
## 2 14 3 Medical 1 1128
## 3 18 2 Life Sciences 1 1412
## 4 1 4 Marketing 1 2016
## 5 2 1 Technical Degree 1 1646
## 6 10 2 Life Sciences 1 733
## EnvironmentSatisfaction Gender HourlyRate JobInvolvement JobLevel
## 1 2 Male 73 3 2
## 2 3 Male 44 2 5
## 3 3 Male 60 3 3
## 4 3 Female 48 3 3
## 5 1 Female 32 3 1
## 6 4 Male 32 3 3
## JobRole JobSatisfaction MaritalStatus MonthlyIncome
## 1 Sales Executive 4 Divorced 4403
## 2 Research Director 3 Single 19626
## 3 Manufacturing Director 4 Single 9362
## 4 Sales Executive 4 Married 10422
## 5 Research Scientist 4 Single 3760
## 6 Manufacturing Director 1 Divorced 8793
## MonthlyRate NumCompaniesWorked Over18 OverTime PercentSalaryHike
## 1 9250 2 Y No 11
## 2 17544 1 Y No 14
## 3 19944 2 Y No 11
## 4 24032 1 Y No 19
## 5 17218 1 Y Yes 13
## 6 4809 1 Y No 21
## PerformanceRating RelationshipSatisfaction StandardHours StockOptionLevel
## 1 3 3 80 1
## 2 3 1 80 0
## 3 3 3 80 0
## 4 3 3 80 2
## 5 3 3 80 0
## 6 4 3 80 2
## TotalWorkingYears TrainingTimesLastYear WorkLifeBalance YearsAtCompany
## 1 8 3 2 5
## 2 21 2 4 20
## 3 10 2 3 2
## 4 14 3 3 14
## 5 6 2 3 6
## 6 9 4 2 9
## YearsInCurrentRole YearsSinceLastPromotion YearsWithCurrManager
## 1 2 0 3
## 2 7 4 9
## 3 2 2 2
## 4 10 5 7
## 5 3 1 3
## 6 7 1 7
## IncomeGroup IncomeGroupCode
## 1 [4.38e+03,4.48e+03) 34
## 2 [1.96e+04,1.97e+04) 186
## 3 [9.28e+03,9.38e+03) 83
## 4 [1.04e+04,1.05e+04) 94
## 5 [3.68e+03,3.78e+03) 27
## 6 [8.78e+03,8.88e+03) 78train_data <- train_data %>%
select(Attrition, MonthlyIncome, JobLevel, TotalWorkingYears) %>%
mutate(MonthlyIncome = factor(MonthlyIncome),
Attrition = factor(Attrition, levels = c("No", "Yes")))
#Previous test with correlation-determined variables
#test_data <- test_data %>%
# select(OverTime, JobRole, MaritalStatus) %>%
# mutate(OverTime = factor(OverTime))
test_data <- test_data %>%
select(MonthlyIncome, JobLevel, TotalWorkingYears) %>%
mutate(MonthlyIncome = factor(MonthlyIncome))
# Splitting the training data
set.seed(123) # for reproducibility
training_indices <- createDataPartition(train_data$Attrition, p = 0.8, list = FALSE)
training_set <- train_data[training_indices, ]
validation_set <- train_data[-training_indices, ]
# Trying different values of k
k_values <- c(3, 5, 7, 9)
sensitivities <- c()
specificities <- c()
for (k in k_values) {
knn_model <- knn3(Attrition ~ ., data = train_data, k = k)
knn_pred <- predict(knn_model, validation_set, type = "class")
conf_matrix <- confusionMatrix(knn_pred, validation_set$Attrition)
sensitivities <- c(sensitivities, conf_matrix$byClass["Sensitivity"])
specificities <- c(specificities, conf_matrix$byClass["Specificity"])
}
# Find the best k value
best_k <- k_values[which.max(sensitivities + specificities)]
# Training KNN model
knn_model <- knn3(Attrition ~ ., data = training_set, k = 15)
# Training Naive Bayes model
nb_model <- naiveBayes(Attrition ~ ., data = training_set)
# Ensure the validation set has the same structure as the training set
validation_set_formatted <- validation_set %>% select(-Attrition)
# Predicting on the validation set
knn_pred <- predict(knn_model, validation_set_formatted, type = "class")
# Check if the number of predictions matches the number of observations
if(length(knn_pred) != nrow(validation_set)) {
stop("Number of predictions does not match the number of observations in the validation set.")
}
# Calculate confusion matrix and sensitivity, specificity
knn_conf_matrix <- confusionMatrix(knn_pred, validation_set$Attrition)
knn_sensitivity <- knn_conf_matrix$byClass["Sensitivity"]
knn_specificity <- knn_conf_matrix$byClass["Specificity"]
# Display KNN Sensitivity and Specificity
list(KNN_Sensitivity = knn_sensitivity, KNN_Specificity = knn_specificity)## $KNN_Sensitivity
## Sensitivity
## 1
##
## $KNN_Specificity
## Specificity
## 0nb_pred <- predict(nb_model, validation_set)
# Calculate sensitivity and specificity
knn_conf_matrix <- confusionMatrix(knn_pred, validation_set$Attrition)
nb_conf_matrix <- confusionMatrix(nb_pred, validation_set$Attrition)
# Sensitivity and Specificity for KNN
knn_sensitivity <- knn_conf_matrix$byClass["Sensitivity"]
knn_specificity <- knn_conf_matrix$byClass["Specificity"]
# Sensitivity and Specificity for Naive Bayes
nb_sensitivity <- nb_conf_matrix$byClass["Sensitivity"]
nb_specificity <- nb_conf_matrix$byClass["Specificity"]
# Display results
list(KNN_Sensitivity = knn_sensitivity, KNN_Specificity = knn_specificity,
NB_Sensitivity = nb_sensitivity, NB_Specificity = nb_specificity)## $KNN_Sensitivity
## Sensitivity
## 1
##
## $KNN_Specificity
## Specificity
## 0
##
## $NB_Sensitivity
## Sensitivity
## 0.9863014
##
## $NB_Specificity
## Specificity
## 0.03571429# Predicting on test data (example with KNN)
test_predictions <- predict(knn_model, test_data)
# Output predictions
test_predictions## No Yes
## [1,] 0.9047619 0.09523810
## [2,] 1.0000000 0.00000000
## [3,] 0.8095238 0.19047619
## [4,] 0.8666667 0.13333333
## [5,] 0.8285714 0.17142857
## [6,] 0.8750000 0.12500000
## [7,] 0.8076923 0.19230769
## [8,] 0.9047619 0.09523810
## [9,] 0.5789474 0.42105263
## [10,] 0.9047619 0.09523810
## [11,] 1.0000000 0.00000000
## [12,] 0.6666667 0.33333333
## [13,] 0.9047619 0.09523810
## [14,] 0.5789474 0.42105263
## [15,] 0.7272727 0.27272727
## [16,] 0.8888889 0.11111111
## [17,] 0.9047619 0.09523810
## [18,] 0.8589744 0.14102564
## [19,] 0.8285714 0.17142857
## [20,] 0.9672131 0.03278689
## [21,] 0.8648649 0.13513514
## [22,] 0.8648649 0.13513514
## [23,] 0.9672131 0.03278689
## [24,] 0.9672131 0.03278689
## [25,] 0.8500000 0.15000000
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## [30,] 0.7307692 0.26923077
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## [54,] 0.8888889 0.11111111
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## [57,] 0.8076923 0.19230769
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## [59,] 0.8571429 0.14285714
## [60,] 0.5789474 0.42105263
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## [65,] 0.5789474 0.42105263
## [66,] 0.8076923 0.19230769
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## [68,] 0.7307692 0.26923077
## [69,] 0.7307692 0.26923077
## [70,] 0.8095238 0.19047619
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## [74,] 0.8285714 0.17142857
## [75,] 0.8095238 0.19047619
## [76,] 0.8648649 0.13513514
## [77,] 0.8095238 0.19047619
## [78,] 0.9000000 0.10000000
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## [80,] 0.5789474 0.42105263
## [81,] 0.9375000 0.06250000
## [82,] 0.8571429 0.14285714
## [83,] 0.9672131 0.03278689
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## [93,] 0.8076923 0.19230769
## [94,] 0.9672131 0.03278689
## [95,] 1.0000000 0.00000000
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## [102,] 0.8461538 0.15384615
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## [107,] 0.9672131 0.03278689
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## [109,] 0.8648649 0.13513514
## [110,] 0.6842105 0.31578947
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## [117,] 0.8750000 0.12500000
## [118,] 0.9672131 0.03278689
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## [120,] 0.8888889 0.11111111
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## [124,] 0.9047619 0.09523810
## [125,] 0.9672131 0.03278689
## [126,] 0.9672131 0.03278689
## [127,] 0.7272727 0.27272727
## [128,] 0.9672131 0.03278689
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## [131,] 0.9672131 0.03278689
## [132,] 0.9047619 0.09523810
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## [135,] 0.8888889 0.11111111
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## [141,] 0.8666667 0.13333333
## [142,] 0.6666667 0.33333333
## [143,] 0.8461538 0.15384615
## [144,] 0.8589744 0.14102564
## [145,] 0.9375000 0.06250000
## [146,] 0.7906977 0.20930233
## [147,] 0.9259259 0.07407407
## [148,] 0.9047619 0.09523810
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## [150,] 0.8500000 0.15000000
## [151,] 0.8888889 0.11111111
## [152,] 0.9672131 0.03278689
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## [154,] 0.9176471 0.08235294
## [155,] 0.5789474 0.42105263
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## [157,] 0.9375000 0.06250000
## [158,] 1.0000000 0.00000000
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## [160,] 1.0000000 0.00000000
## [161,] 0.9672131 0.03278689
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## [163,] 0.8500000 0.15000000
## [164,] 0.9672131 0.03278689
## [165,] 0.8571429 0.14285714
## [166,] 0.6666667 0.33333333
## [167,] 0.9000000 0.10000000
## [168,] 0.8095238 0.19047619
## [169,] 0.9047619 0.09523810
## [170,] 0.7777778 0.22222222
## [171,] 0.9516129 0.04838710
## [172,] 0.8947368 0.10526316
## [173,] 1.0000000 0.00000000
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## [175,] 1.0000000 0.00000000
## [176,] 0.6666667 0.33333333
## [177,] 0.8235294 0.17647059
## [178,] 0.8285714 0.17142857
## [179,] 0.8750000 0.12500000
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## [182,] 0.9176471 0.08235294
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## [184,] 0.8750000 0.12500000
## [185,] 0.9259259 0.07407407
## [186,] 0.7307692 0.26923077
## [187,] 0.8589744 0.14102564
## [188,] 1.0000000 0.00000000
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## [190,] 0.8750000 0.12500000
## [191,] 0.9176471 0.08235294
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## [193,] 0.9545455 0.04545455
## [194,] 0.8888889 0.11111111
## [195,] 0.7307692 0.26923077
## [196,] 0.5789474 0.42105263
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## [200,] 0.5789474 0.42105263
## [201,] 1.0000000 0.00000000
## [202,] 0.9672131 0.03278689
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## [205,] 0.8285714 0.17142857
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## [207,] 0.8589744 0.14102564
## [208,] 0.8571429 0.14285714
## [209,] 0.9259259 0.07407407
## [210,] 0.8571429 0.14285714
## [211,] 1.0000000 0.00000000
## [212,] 1.0000000 0.00000000
## [213,] 0.6842105 0.31578947
## [214,] 0.9047619 0.09523810
## [215,] 0.7307692 0.26923077
## [216,] 0.9259259 0.07407407
## [217,] 0.9047619 0.09523810
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## [219,] 0.7307692 0.26923077
## [220,] 0.9259259 0.07407407
## [221,] 0.8500000 0.15000000
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## [224,] 0.5789474 0.42105263
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## [231,] 0.9672131 0.03278689
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## [245,] 0.9672131 0.03278689
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## [250,] 1.0000000 0.00000000
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## [253,] 0.5789474 0.42105263
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## [260,] 0.8076923 0.19230769
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## [264,] 0.6666667 0.33333333
## [265,] 0.8285714 0.17142857
## [266,] 0.8285714 0.17142857
## [267,] 0.8260870 0.17391304
## [268,] 0.5789474 0.42105263
## [269,] 0.8888889 0.11111111
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## [271,] 0.9672131 0.03278689
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## [273,] 0.8888889 0.11111111
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## [281,] 0.9672131 0.03278689
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## [285,] 0.8076923 0.19230769
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## [287,] 0.5789474 0.42105263
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## [297,] 0.9672131 0.03278689
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## [300,] 0.7307692 0.26923077
## [301,] 0.9672131 0.03278689
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## [303,] 0.9259259 0.07407407
## [304,] 0.9672131 0.03278689
## [305,] 0.8076923 0.19230769
## [306,] 0.8285714 0.17142857
## [307,] 0.9259259 0.07407407
## [308,] 0.8285714 0.17142857
## [309,] 0.8571429 0.14285714
## [310,] 0.7906977 0.20930233
## [311,] 0.8888889 0.11111111
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## [313,] 0.8076923 0.19230769
## [314,] 0.9672131 0.03278689
## [315,] 0.9672131 0.03278689
## [316,] 0.8888889 0.11111111
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## [318,] 0.7906977 0.20930233
## [319,] 0.9047619 0.09523810
## [320,] 0.5789474 0.42105263
## [321,] 0.7307692 0.26923077
## [322,] 0.7272727 0.27272727
## [323,] 0.7272727 0.27272727
## [324,] 0.9545455 0.04545455
## [325,] 1.0000000 0.00000000
## [326,] 0.5789474 0.42105263
## [327,] 0.8823529 0.11764706
## [328,] 0.8888889 0.11111111
## [329,] 1.0000000 0.00000000
## [330,] 1.0000000 0.00000000
## [331,] 0.8888889 0.11111111
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## [333,] 0.8285714 0.17142857
## [334,] 0.8750000 0.12500000
## [335,] 0.9545455 0.04545455
## [336,] 0.8888889 0.11111111
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## [338,] 0.8589744 0.14102564
## [339,] 0.8750000 0.12500000
## [340,] 0.5789474 0.42105263
## [341,] 0.8285714 0.17142857
## [342,] 0.6666667 0.33333333
## [343,] 0.8750000 0.12500000
## [344,] 0.5789474 0.42105263
## [345,] 0.9047619 0.09523810
## [346,] 1.0000000 0.00000000
## [347,] 0.8750000 0.12500000
## [348,] 0.8500000 0.15000000
## [349,] 0.8285714 0.17142857
## [350,] 0.9444444 0.05555556
## [351,] 0.9600000 0.04000000
## [352,] 0.9672131 0.03278689
## [353,] 0.8947368 0.10526316
## [354,] 0.9047619 0.09523810
## [355,] 0.9444444 0.05555556
## [356,] 0.9375000 0.06250000
## [357,] 0.7307692 0.26923077
## [358,] 0.8285714 0.17142857
## [359,] 0.8888889 0.11111111
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## [361,] 0.9333333 0.06666667
## [362,] 0.5789474 0.42105263
## [363,] 0.8666667 0.13333333
## [364,] 0.9500000 0.05000000
## [365,] 0.8823529 0.11764706
## [366,] 0.8823529 0.11764706
## [367,] 0.9375000 0.06250000
## [368,] 0.8888889 0.11111111
## [369,] 0.6842105 0.31578947
## [370,] 0.9672131 0.03278689
## [371,] 0.7906977 0.20930233
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## [373,] 0.8750000 0.12500000
## [374,] 0.9259259 0.07407407
## [375,] 0.6666667 0.33333333
## [376,] 0.8666667 0.13333333
## [377,] 0.8500000 0.15000000
## [378,] 0.8888889 0.11111111
## [379,] 0.8285714 0.17142857
## [380,] 0.8076923 0.19230769
## [381,] 1.0000000 0.00000000
## [382,] 0.9259259 0.07407407
## [383,] 0.9375000 0.06250000
## [384,] 0.6666667 0.33333333
## [385,] 0.8500000 0.15000000
## [386,] 0.8571429 0.14285714
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## [388,] 0.9047619 0.09523810
## [389,] 0.8571429 0.14285714
## [390,] 0.6666667 0.33333333
## [391,] 0.8500000 0.15000000
## [392,] 0.8750000 0.12500000
## [393,] 0.6842105 0.31578947
## [394,] 0.9545455 0.04545455
## [395,] 0.9259259 0.07407407
## [396,] 0.6666667 0.33333333
## [397,] 0.8666667 0.13333333
## [398,] 0.6666667 0.33333333
## [399,] 0.8648649 0.13513514
## [400,] 0.8064516 0.19354839
## [401,] 0.9176471 0.08235294
## [402,] 0.9176471 0.08235294
## [403,] 0.8076923 0.19230769
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## [405,] 0.8333333 0.16666667
## [406,] 1.0000000 0.00000000
## [407,] 0.8648649 0.13513514
## [408,] 0.8076923 0.19230769
## [409,] 0.9411765 0.05882353
## [410,] 1.0000000 0.00000000
## [411,] 0.8285714 0.17142857
## [412,] 0.8095238 0.19047619
## [413,] 0.9259259 0.07407407
## [414,] 0.7906977 0.20930233
## [415,] 0.6666667 0.33333333
## [416,] 0.9375000 0.06250000
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## [418,] 0.6842105 0.31578947
## [419,] 0.8888889 0.11111111
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## [421,] 0.8750000 0.12500000
## [422,] 0.9375000 0.06250000
## [423,] 0.8648649 0.13513514
## [424,] 0.5454545 0.45454545
## [425,] 0.8750000 0.12500000
## [426,] 0.9600000 0.04000000
## [427,] 0.5789474 0.42105263
## [428,] 0.6666667 0.33333333
## [429,] 0.6842105 0.31578947
## [430,] 0.8648649 0.13513514
## [431,] 0.8750000 0.12500000
## [432,] 0.8285714 0.17142857
## [433,] 1.0000000 0.00000000
## [434,] 0.5789474 0.42105263
## [435,] 0.8461538 0.15384615
## [436,] 0.9047619 0.09523810
## [437,] 0.7307692 0.26923077
## [438,] 0.9259259 0.07407407
## [439,] 0.6666667 0.33333333
## [440,] 0.9672131 0.03278689
## [441,] 0.9672131 0.03278689
## [442,] 0.8641975 0.13580247
## [443,] 0.7307692 0.26923077
## [444,] 0.9259259 0.07407407
## [445,] 0.8235294 0.17647059
## [446,] 0.8095238 0.19047619
## [447,] 0.9545455 0.04545455
## [448,] 0.9672131 0.03278689
## [449,] 0.9672131 0.03278689
## [450,] 0.9672131 0.03278689
## [451,] 0.9672131 0.03278689
## [452,] 0.8285714 0.17142857
## [453,] 0.9672131 0.03278689
## [454,] 0.9672131 0.03278689
## [455,] 1.0000000 0.00000000
## [456,] 1.0000000 0.00000000
## [457,] 0.9672131 0.03278689
## [458,] 0.9176471 0.08235294
## [459,] 0.7307692 0.26923077
## [460,] 0.9672131 0.03278689
## [461,] 0.9259259 0.07407407
## [462,] 0.9545455 0.04545455
## [463,] 0.8064516 0.19354839
## [464,] 0.8888889 0.11111111
## [465,] 0.8285714 0.17142857
## [466,] 0.8285714 0.17142857
## [467,] 0.8076923 0.19230769
## [468,] 0.7307692 0.26923077
## [469,] 0.8589744 0.14102564
## [470,] 0.8750000 0.12500000
## [471,] 0.8285714 0.17142857
## [472,] 0.5789474 0.42105263
## [473,] 0.9047619 0.09523810
## [474,] 0.8641975 0.13580247
## [475,] 0.6842105 0.31578947
## [476,] 0.8888889 0.11111111
## [477,] 0.8888889 0.11111111
## [478,] 0.9047619 0.09523810
## [479,] 0.7777778 0.22222222
## [480,] 0.8064516 0.19354839
## [481,] 0.8500000 0.15000000
## [482,] 0.9259259 0.07407407
## [483,] 0.8947368 0.10526316
## [484,] 0.8695652 0.13043478
## [485,] 0.8666667 0.13333333
## [486,] 0.9090909 0.09090909
## [487,] 0.5789474 0.42105263
## [488,] 0.7307692 0.26923077
## [489,] 0.9444444 0.05555556
## [490,] 0.9672131 0.03278689
## [491,] 0.9500000 0.05000000
## [492,] 0.8421053 0.15789474
## [493,] 0.9047619 0.09523810
## [494,] 0.8461538 0.15384615
## [495,] 0.9672131 0.03278689
## [496,] 1.0000000 0.00000000
## [497,] 0.9259259 0.07407407
## [498,] 0.6842105 0.31578947
## [499,] 0.8571429 0.14285714
## [500,] 0.9672131 0.03278689
## [501,] 0.9444444 0.05555556
## [502,] 0.8285714 0.17142857
## [503,] 0.8695652 0.13043478
## [504,] 0.8095238 0.19047619
## [505,] 0.8666667 0.13333333
## [506,] 0.8648649 0.13513514
## [507,] 0.5789474 0.42105263
## [508,] 0.8666667 0.13333333
## [509,] 0.8636364 0.13636364
## [510,] 0.8823529 0.11764706
## [511,] 0.9672131 0.03278689
## [512,] 0.8461538 0.15384615
## [513,] 0.7272727 0.27272727
## [514,] 0.8571429 0.14285714
## [515,] 0.6363636 0.36363636
## [516,] 0.8648649 0.13513514
## [517,] 0.5789474 0.42105263
## [518,] 0.8076923 0.19230769
## [519,] 0.9672131 0.03278689
## [520,] 0.7307692 0.26923077
## [521,] 0.8285714 0.17142857
## [522,] 0.5789474 0.42105263
## [523,] 0.8750000 0.12500000
## [524,] 0.8666667 0.13333333
## [525,] 0.8148148 0.18518519
## [526,] 0.9444444 0.05555556
## [527,] 0.8888889 0.11111111
## [528,] 0.8500000 0.15000000
## [529,] 0.8285714 0.17142857
## [530,] 0.8076923 0.19230769
## [531,] 1.0000000 0.00000000
## [532,] 0.9375000 0.06250000
## [533,] 0.7272727 0.27272727
## [534,] 0.8888889 0.11111111
## [535,] 0.8076923 0.19230769
## [536,] 0.8076923 0.19230769
## [537,] 0.8095238 0.19047619
## [538,] 0.6842105 0.31578947
## [539,] 0.8285714 0.17142857
## [540,] 0.8888889 0.11111111
## [541,] 0.9672131 0.03278689
## [542,] 0.9444444 0.05555556
## [543,] 0.5789474 0.42105263
## [544,] 0.8888889 0.11111111
## [545,] 0.8285714 0.17142857
## [546,] 0.7272727 0.27272727
## [547,] 0.9411765 0.05882353
## [548,] 0.9672131 0.03278689
## [549,] 1.0000000 0.00000000
## [550,] 0.8333333 0.16666667
## [551,] 0.9500000 0.05000000
## [552,] 0.8285714 0.17142857
## [553,] 0.9672131 0.03278689
## [554,] 0.8636364 0.13636364
## [555,] 0.8750000 0.12500000
## [556,] 0.8571429 0.14285714
## [557,] 0.9545455 0.04545455
## [558,] 0.8285714 0.17142857
## [559,] 0.9672131 0.03278689
## [560,] 0.9047619 0.09523810
## [561,] 0.8636364 0.13636364
## [562,] 0.8888889 0.11111111
## [563,] 0.6842105 0.31578947
## [564,] 0.8461538 0.15384615
## [565,] 0.8076923 0.19230769
## [566,] 0.8285714 0.17142857
## [567,] 0.8888889 0.11111111
## [568,] 0.9672131 0.03278689
## [569,] 0.9672131 0.03278689
## [570,] 1.0000000 0.00000000
## [571,] 0.8888889 0.11111111
## [572,] 0.5789474 0.42105263
## [573,] 0.8589744 0.14102564
## [574,] 0.9672131 0.03278689
## [575,] 0.8500000 0.15000000
## [576,] 0.8589744 0.14102564
## [577,] 0.9444444 0.05555556
## [578,] 0.8148148 0.18518519
## [579,] 0.9672131 0.03278689
## [580,] 0.8500000 0.15000000
## [581,] 0.8076923 0.19230769
## [582,] 0.8260870 0.17391304
## [583,] 0.9375000 0.06250000
## [584,] 0.9047619 0.09523810
## [585,] 0.8888889 0.11111111
## [586,] 0.9375000 0.06250000
## [587,] 0.8571429 0.14285714
## [588,] 0.7272727 0.27272727
## [589,] 0.9259259 0.07407407
## [590,] 0.6842105 0.31578947
## [591,] 0.6842105 0.31578947
## [592,] 0.8947368 0.10526316
## [593,] 0.7307692 0.26923077
## [594,] 0.7272727 0.27272727
## [595,] 0.9600000 0.04000000
## [596,] 0.8888889 0.11111111
## [597,] 0.8064516 0.19354839
## [598,] 1.0000000 0.00000000
## [599,] 0.8500000 0.15000000
## [600,] 0.8285714 0.17142857
## [601,] 0.5789474 0.42105263
## [602,] 0.8888889 0.11111111
## [603,] 0.8750000 0.12500000
## [604,] 0.7272727 0.27272727
## [605,] 0.6666667 0.33333333
## [606,] 0.8666667 0.13333333
## [607,] 1.0000000 0.00000000
## [608,] 0.9047619 0.09523810
## [609,] 0.9259259 0.07407407
## [610,] 0.6666667 0.33333333
## [611,] 0.9672131 0.03278689
## [612,] 0.9672131 0.03278689
## [613,] 0.8636364 0.13636364
## [614,] 0.5789474 0.42105263
## [615,] 0.8095238 0.19047619
## [616,] 0.9375000 0.06250000
## [617,] 0.9259259 0.07407407
## [618,] 0.8888889 0.11111111
## [619,] 0.8750000 0.12500000
## [620,] 0.5789474 0.42105263
## [621,] 0.5789474 0.42105263
## [622,] 1.0000000 0.00000000
## [623,] 0.7272727 0.27272727
## [624,] 0.8750000 0.12500000
## [625,] 0.9259259 0.07407407
## [626,] 0.7307692 0.26923077
## [627,] 0.8750000 0.12500000
## [628,] 0.8571429 0.14285714
## [629,] 0.9444444 0.05555556
## [630,] 0.8750000 0.12500000
## [631,] 0.8695652 0.13043478
## [632,] 0.8666667 0.13333333
## [633,] 0.9545455 0.04545455
## [634,] 0.8076923 0.19230769
## [635,] 0.8095238 0.19047619
## [636,] 0.6666667 0.33333333
## [637,] 0.8888889 0.11111111
## [638,] 0.8750000 0.12500000
## [639,] 0.8285714 0.17142857
## [640,] 0.7307692 0.26923077
## [641,] 0.5789474 0.42105263
## [642,] 0.9375000 0.06250000
## [643,] 0.9411765 0.05882353
## [644,] 0.7307692 0.26923077
## [645,] 0.7307692 0.26923077
## [646,] 0.8571429 0.14285714
## [647,] 0.5454545 0.45454545
## [648,] 0.6666667 0.33333333
## [649,] 0.8947368 0.10526316
## [650,] 0.7272727 0.27272727
## [651,] 0.6666667 0.33333333
## [652,] 0.8648649 0.13513514
## [653,] 1.0000000 0.00000000
## [654,] 0.8571429 0.14285714
## [655,] 0.6842105 0.31578947
## [656,] 0.8750000 0.12500000
## [657,] 0.8064516 0.19354839
## [658,] 0.8666667 0.13333333
## [659,] 0.9047619 0.09523810
## [660,] 0.8500000 0.15000000
## [661,] 0.9672131 0.03278689
## [662,] 0.9444444 0.05555556
## [663,] 0.8461538 0.15384615
## [664,] 0.6666667 0.33333333
## [665,] 0.9672131 0.03278689
## [666,] 0.9672131 0.03278689
## [667,] 0.8461538 0.15384615
## [668,] 0.9259259 0.07407407
## [669,] 0.9672131 0.03278689
## [670,] 0.8823529 0.11764706
## [671,] 0.8064516 0.19354839
## [672,] 0.8500000 0.15000000
## [673,] 0.8750000 0.12500000
## [674,] 0.7272727 0.27272727
## [675,] 0.7307692 0.26923077
## [676,] 0.8500000 0.15000000
## [677,] 0.9672131 0.03278689
## [678,] 0.9672131 0.03278689
## [679,] 0.9047619 0.09523810
## [680,] 0.8636364 0.13636364
## [681,] 0.8750000 0.12500000
## [682,] 0.9259259 0.07407407
## [683,] 0.9672131 0.03278689
## [684,] 0.8571429 0.14285714
## [685,] 0.7307692 0.26923077
## [686,] 0.8461538 0.15384615
## [687,] 0.8750000 0.12500000
## [688,] 0.8076923 0.19230769
## [689,] 0.5789474 0.42105263
## [690,] 0.8636364 0.13636364
## [691,] 0.9672131 0.03278689
## [692,] 0.8095238 0.19047619
## [693,] 0.8888889 0.11111111
## [694,] 0.6666667 0.33333333
## [695,] 0.8500000 0.15000000
## [696,] 0.6666667 0.33333333
## [697,] 0.8888889 0.11111111
## [698,] 0.8947368 0.10526316
## [699,] 0.5454545 0.45454545
## [700,] 0.8125000 0.18750000
## [701,] 0.5789474 0.42105263
## [702,] 0.8500000 0.15000000
## [703,] 0.8064516 0.19354839
## [704,] 0.8285714 0.17142857
## [705,] 0.8076923 0.19230769
## [706,] 0.8947368 0.10526316
## [707,] 0.8888889 0.11111111
## [708,] 0.9259259 0.07407407
## [709,] 0.7307692 0.26923077
## [710,] 0.9411765 0.05882353
## [711,] 0.8750000 0.12500000
## [712,] 0.8666667 0.13333333
## [713,] 0.8214286 0.17857143
## [714,] 0.8064516 0.19354839
## [715,] 0.8095238 0.19047619
## [716,] 0.5789474 0.42105263
## [717,] 0.9672131 0.03278689
## [718,] 0.9672131 0.03278689
## [719,] 0.8648649 0.13513514
## [720,] 0.8095238 0.19047619
## [721,] 0.8095238 0.19047619
## [722,] 0.8888889 0.11111111
## [723,] 0.7272727 0.27272727
## [724,] 0.8571429 0.14285714
## [725,] 0.9259259 0.07407407
## [726,] 0.8750000 0.12500000
## [727,] 0.7272727 0.27272727
## [728,] 0.7307692 0.26923077
## [729,] 0.5789474 0.42105263
## [730,] 0.6666667 0.33333333
## [731,] 0.7906977 0.20930233
## [732,] 0.8648649 0.13513514
## [733,] 0.5789474 0.42105263
## [734,] 0.8500000 0.15000000
## [735,] 0.5789474 0.42105263
## [736,] 0.8888889 0.11111111
## [737,] 1.0000000 0.00000000
## [738,] 0.8648649 0.13513514
## [739,] 0.8750000 0.12500000
## [740,] 0.8888889 0.11111111
## [741,] 0.8500000 0.15000000
## [742,] 0.8095238 0.19047619
## [743,] 0.9672131 0.03278689
## [744,] 0.6666667 0.33333333
## [745,] 0.8500000 0.15000000
## [746,] 0.6666667 0.33333333
## [747,] 0.6842105 0.31578947
## [748,] 0.8888889 0.11111111
## [749,] 0.8285714 0.17142857
## [750,] 0.6842105 0.31578947
## [751,] 0.6666667 0.33333333
## [752,] 0.6666667 0.33333333
## [753,] 0.8666667 0.13333333
## [754,] 0.8666667 0.13333333
## [755,] 0.8064516 0.19354839
## [756,] 0.8641975 0.13580247
## [757,] 0.9672131 0.03278689
## [758,] 1.0000000 0.00000000
## [759,] 0.8076923 0.19230769
## [760,] 0.8500000 0.15000000
## [761,] 0.6666667 0.33333333
## [762,] 0.8666667 0.13333333
## [763,] 0.9545455 0.04545455
## [764,] 0.9545455 0.04545455
## [765,] 0.6842105 0.31578947
## [766,] 0.9672131 0.03278689
## [767,] 0.7272727 0.27272727
## [768,] 1.0000000 0.00000000
## [769,] 0.8648649 0.13513514
## [770,] 0.9375000 0.06250000
## [771,] 0.8888889 0.11111111
## [772,] 0.8750000 0.12500000
## [773,] 1.0000000 0.00000000
## [774,] 0.6666667 0.33333333
## [775,] 0.8750000 0.12500000
## [776,] 0.6666667 0.33333333
## [777,] 0.8285714 0.17142857
## [778,] 0.5789474 0.42105263
## [779,] 0.8076923 0.19230769
## [780,] 0.6842105 0.31578947
## [781,] 0.6842105 0.31578947
## [782,] 1.0000000 0.00000000
## [783,] 0.8076923 0.19230769
## [784,] 0.9672131 0.03278689
## [785,] 0.7906977 0.20930233
## [786,] 0.8750000 0.12500000
## [787,] 0.8571429 0.14285714
## [788,] 0.9176471 0.08235294
## [789,] 0.9333333 0.06666667
## [790,] 0.6666667 0.33333333
## [791,] 0.9672131 0.03278689
## [792,] 0.8641975 0.13580247
## [793,] 0.8095238 0.19047619
## [794,] 0.9047619 0.09523810
## [795,] 0.8589744 0.14102564
## [796,] 0.7272727 0.27272727
## [797,] 1.0000000 0.00000000
## [798,] 0.5789474 0.42105263
## [799,] 0.5789474 0.42105263
## [800,] 0.8648649 0.13513514
## [801,] 0.9672131 0.03278689
## [802,] 0.9672131 0.03278689
## [803,] 1.0000000 0.00000000
## [804,] 0.8750000 0.12500000
## [805,] 0.8571429 0.14285714
## [806,] 0.8571429 0.14285714
## [807,] 0.8500000 0.15000000
## [808,] 0.6666667 0.33333333
## [809,] 0.7272727 0.27272727
## [810,] 0.8285714 0.17142857
## [811,] 0.8648649 0.13513514
## [812,] 0.8076923 0.19230769
## [813,] 0.8750000 0.12500000
## [814,] 0.9333333 0.06666667
## [815,] 0.6666667 0.33333333
## [816,] 0.9545455 0.04545455
## [817,] 0.8648649 0.13513514
## [818,] 0.8666667 0.13333333
## [819,] 0.8285714 0.17142857
## [820,] 0.8500000 0.15000000
## [821,] 0.8285714 0.17142857
## [822,] 0.9672131 0.03278689
## [823,] 0.9047619 0.09523810
## [824,] 0.6666667 0.33333333
## [825,] 0.8589744 0.14102564
## [826,] 0.8823529 0.11764706
## [827,] 0.8095238 0.19047619
## [828,] 0.7906977 0.20930233
## [829,] 0.8641975 0.13580247
## [830,] 0.8823529 0.11764706
## [831,] 0.8888889 0.11111111
## [832,] 0.5454545 0.45454545
## [833,] 0.8285714 0.17142857
## [834,] 0.5789474 0.42105263
## [835,] 0.9333333 0.06666667
## [836,] 0.8750000 0.12500000
## [837,] 0.9259259 0.07407407
## [838,] 0.9672131 0.03278689
## [839,] 1.0000000 0.00000000
## [840,] 1.0000000 0.00000000
## [841,] 0.5454545 0.45454545
## [842,] 0.8095238 0.19047619
## [843,] 0.9411765 0.05882353
## [844,] 0.8095238 0.19047619
## [845,] 0.8500000 0.15000000
## [846,] 0.9672131 0.03278689
## [847,] 0.5789474 0.42105263
## [848,] 1.0000000 0.00000000
## [849,] 0.9047619 0.09523810
## [850,] 0.9259259 0.07407407
## [851,] 0.7906977 0.20930233
## [852,] 0.7272727 0.27272727
## [853,] 0.9672131 0.03278689
## [854,] 0.8888889 0.11111111
## [855,] 0.7906977 0.20930233
## [856,] 0.5789474 0.42105263
## [857,] 0.9259259 0.07407407
## [858,] 0.8095238 0.19047619
## [859,] 0.8076923 0.19230769
## [860,] 0.8095238 0.19047619
## [861,] 0.9259259 0.07407407
## [862,] 0.9444444 0.05555556
## [863,] 0.8888889 0.11111111
## [864,] 1.0000000 0.00000000
## [865,] 0.8095238 0.19047619
## [866,] 0.8461538 0.15384615
## [867,] 0.7906977 0.20930233
## [868,] 0.9176471 0.08235294
## [869,] 0.8076923 0.19230769
## [870,] 0.9672131 0.03278689data$OverTime## [1] "No" "No" "No" "No" "Yes" "No" "Yes" "Yes" "Yes" "No" "No" "No"
## [13] "No" "No" "No" "No" "No" "No" "Yes" "No" "Yes" "No" "Yes" "No"
## [25] "No" "No" "No" "Yes" "Yes" "No" "No" "No" "Yes" "No" "No" "No"
## [37] "No" "Yes" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "Yes"
## [49] "Yes" "No" "No" "Yes" "No" "No" "No" "No" "Yes" "Yes" "Yes" "Yes"
## [61] "Yes" "No" "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "No"
## [73] "Yes" "Yes" "Yes" "No" "Yes" "No" "No" "Yes" "No" "No" "No" "Yes"
## [85] "Yes" "Yes" "No" "Yes" "No" "No" "Yes" "No" "Yes" "Yes" "No" "No"
## [97] "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes"
## [109] "No" "No" "Yes" "No" "No" "No" "Yes" "Yes" "No" "Yes" "No" "No"
## [121] "No" "Yes" "Yes" "No" "No" "Yes" "Yes" "No" "Yes" "No" "Yes" "No"
## [133] "No" "No" "No" "No" "Yes" "No" "Yes" "No" "Yes" "No" "No" "No"
## [145] "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes"
## [157] "No" "No" "No" "Yes" "Yes" "No" "No" "Yes" "No" "No" "No" "No"
## [169] "Yes" "No" "No" "No" "No" "Yes" "No" "Yes" "Yes" "Yes" "No" "No"
## [181] "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## [193] "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "Yes"
## [205] "No" "Yes" "No" "Yes" "No" "Yes" "No" "No" "No" "Yes" "No" "No"
## [217] "No" "No" "No" "Yes" "No" "No" "Yes" "No" "No" "No" "No" "Yes"
## [229] "No" "Yes" "No" "No" "No" "No" "Yes" "No" "No" "Yes" "No" "No"
## [241] "Yes" "No" "No" "No" "Yes" "No" "Yes" "No" "Yes" "No" "No" "No"
## [253] "No" "No" "No" "No" "No" "No" "Yes" "Yes" "No" "No" "Yes" "No"
## [265] "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## [277] "No" "No" "Yes" "Yes" "Yes" "Yes" "No" "No" "No" "Yes" "Yes" "No"
## [289] "No" "No" "No" "No" "No" "No" "Yes" "Yes" "No" "Yes" "Yes" "Yes"
## [301] "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "No" "No"
## [313] "No" "No" "No" "Yes" "No" "No" "Yes" "Yes" "No" "No" "No" "Yes"
## [325] "No" "No" "Yes" "Yes" "Yes" "No" "No" "No" "Yes" "No" "No" "No"
## [337] "No" "No" "Yes" "No" "Yes" "Yes" "No" "No" "No" "No" "No" "No"
## [349] "No" "No" "No" "No" "Yes" "Yes" "Yes" "No" "No" "No" "Yes" "No"
## [361] "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## [373] "No" "No" "No" "Yes" "No" "Yes" "Yes" "Yes" "No" "No" "No" "No"
## [385] "Yes" "No" "No" "No" "No" "Yes" "No" "Yes" "Yes" "No" "Yes" "Yes"
## [397] "No" "No" "No" "Yes" "No" "No" "No" "No" "No" "Yes" "No" "No"
## [409] "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## [421] "No" "Yes" "Yes" "No" "No" "No" "No" "No" "Yes" "No" "Yes" "No"
## [433] "No" "No" "No" "No" "No" "No" "Yes" "No" "Yes" "No" "No" "Yes"
## [445] "Yes" "No" "No" "No" "No" "No" "Yes" "No" "Yes" "No" "No" "No"
## [457] "No" "Yes" "No" "No" "No" "No" "No" "No" "Yes" "Yes" "Yes" "No"
## [469] "No" "No" "No" "Yes" "Yes" "No" "No" "Yes" "No" "No" "No" "Yes"
## [481] "No" "Yes" "Yes" "Yes" "No" "Yes" "No" "No" "Yes" "No" "Yes" "Yes"
## [493] "No" "No" "Yes" "No" "No" "Yes" "No" "No" "Yes" "Yes" "Yes" "No"
## [505] "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "Yes" "No" "No"
## [517] "Yes" "No" "No" "No" "No" "Yes" "No" "Yes" "No" "No" "Yes" "Yes"
## [529] "No" "Yes" "No" "No" "No" "No" "Yes" "No" "No" "Yes" "Yes" "No"
## [541] "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## [553] "No" "No" "No" "Yes" "No" "Yes" "No" "No" "No" "Yes" "No" "No"
## [565] "No" "Yes" "No" "No" "No" "Yes" "No" "No" "Yes" "No" "No" "No"
## [577] "No" "No" "No" "Yes" "No" "No" "Yes" "Yes" "Yes" "Yes" "Yes" "No"
## [589] "No" "Yes" "Yes" "Yes" "No" "No" "No" "No" "No" "No" "Yes" "Yes"
## [601] "No" "No" "Yes" "No" "No" "No" "No" "Yes" "No" "No" "No" "Yes"
## [613] "No" "Yes" "No" "No" "No" "Yes" "No" "No" "Yes" "Yes" "No" "Yes"
## [625] "No" "No" "Yes" "Yes" "No" "No" "No" "No" "Yes" "No" "No" "No"
## [637] "No" "No" "Yes" "No" "No" "No" "No" "Yes" "No" "No" "No" "No"
## [649] "No" "Yes" "No" "Yes" "No" "No" "No" "Yes" "No" "No" "Yes" "No"
## [661] "No" "No" "Yes" "No" "No" "Yes" "No" "No" "No" "No" "No" "No"
## [673] "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No" "Yes"
## [685] "No" "No" "Yes" "No" "No" "No" "No" "Yes" "No" "Yes" "No" "Yes"
## [697] "No" "No" "Yes" "No" "No" "No" "Yes" "Yes" "No" "No" "No" "No"
## [709] "No" "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "Yes" "No"
## [721] "No" "No" "No" "No" "No" "No" "No" "Yes" "Yes" "No" "No" "Yes"
## [733] "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## [745] "Yes" "No" "Yes" "No" "No" "No" "Yes" "Yes" "Yes" "No" "No" "No"
## [757] "Yes" "No" "No" "Yes" "Yes" "Yes" "No" "No" "No" "Yes" "No" "No"
## [769] "No" "No" "No" "No" "No" "Yes" "Yes" "No" "No" "No" "No" "Yes"
## [781] "Yes" "No" "Yes" "No" "No" "No" "No" "No" "No" "No" "No" "No"
## [793] "Yes" "No" "Yes" "Yes" "Yes" "Yes" "Yes" "No" "No" "Yes" "Yes" "Yes"
## [805] "No" "Yes" "No" "No" "No" "Yes" "No" "No" "Yes" "No" "No" "No"
## [817] "Yes" "No" "No" "Yes" "No" "No" "No" "No" "Yes" "No" "No" "Yes"
## [829] "No" "No" "Yes" "Yes" "No" "No" "Yes" "No" "Yes" "No" "Yes" "No"
## [841] "No" "No" "No" "No" "No" "No" "No" "No" "Yes" "No" "Yes" "No"
## [853] "Yes" "No" "Yes" "No" "Yes" "No" "No" "No" "No" "No" "Yes" "Yes"
## [865] "Yes" "No" "No" "Yes" "Yes" "No"# Assuming 'data' is your dataframe
data$OverTime <- as.factor(data$OverTime) # Convert to factor if it's not
data$JobRole <- as.factor(data$JobRole) # Convert to factor if it's not
data$MaritalStatus <- as.factor(data$MaritalStatus) # Convert to factor if it's not
# Building the model
model <- lm(MonthlyIncome ~ OverTime + JobRole + MaritalStatus, data = data)
# Summary of the model to see coefficients and statistics
summary(model)##
## Call:
## lm(formula = MonthlyIncome ~ OverTime + JobRole + MaritalStatus,
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5603.6 -1185.5 -422.4 1150.1 6846.8
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7395.68 267.57 27.640 <2e-16 ***
## OverTimeYes 70.09 151.91 0.461 0.645
## JobRoleHuman Resources -4145.07 451.47 -9.181 <2e-16 ***
## JobRoleLaboratory Technician -4207.64 283.22 -14.856 <2e-16 ***
## JobRoleManager 9764.88 365.14 26.743 <2e-16 ***
## JobRoleManufacturing Director 71.73 316.35 0.227 0.821
## JobRoleResearch Director 8311.58 364.73 22.788 <2e-16 ***
## JobRoleResearch Scientist -4180.24 277.96 -15.039 <2e-16 ***
## JobRoleSales Executive -542.60 271.56 -1.998 0.046 *
## JobRoleSales Representative -4783.88 362.22 -13.207 <2e-16 ***
## MaritalStatusMarried 35.24 177.01 0.199 0.842
## MaritalStatusSingle 6.65 192.45 0.035 0.972
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2014 on 858 degrees of freedom
## Multiple R-squared: 0.8105, Adjusted R-squared: 0.8081
## F-statistic: 333.7 on 11 and 858 DF, p-value: < 2.2e-16# Conclusion
Given the results of the t-test determined variables, the results were still disappointing. With hours of work put into researching models, and each of these models being no-good, there were no leads towards a better method, the deadline came and went without a good solution. This is not how I wanted this project to come out, nor how I imagined it would come out. This took hours upon hours, and even one all-nighter attempting to find a better way, but in the end, I was unable to do so.