##DataMining Group Assignment
##Loading Required Libraries
setwd("C:/Users/acer/Documents/PGPBABI/Data Mining/GrpAssignment")
library(rpart)
library(rpart.plot)
library(neuralnet)
library(rattle)
## Rattle: A free graphical interface for data science with R.
## Version 5.1.0 Copyright (c) 2006-2017 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.
library(RColorBrewer)
library(ggplot2)
library(grid)
library(gridExtra)
library(corrplot)
## corrplot 0.84 loaded
##Reading Data into a DataFrame
HRData<-read.csv(file ="HR_Employee_Attrition_Data.csv", header = TRUE)
##View the data structure
str(HRData)
## 'data.frame': 2940 obs. of 35 variables:
## $ Age : int 41 49 37 33 27 32 59 30 38 36 ...
## $ Attrition : Factor w/ 2 levels "No","Yes": 2 1 2 1 1 1 1 1 1 1 ...
## $ BusinessTravel : Factor w/ 3 levels "Non-Travel","Travel_Frequently",..: 3 2 3 2 3 2 3 3 2 3 ...
## $ DailyRate : int 1102 279 1373 1392 591 1005 1324 1358 216 1299 ...
## $ Department : Factor w/ 3 levels "Human Resources",..: 3 2 2 2 2 2 2 2 2 2 ...
## $ DistanceFromHome : int 1 8 2 3 2 2 3 24 23 27 ...
## $ Education : int 2 1 2 4 1 2 3 1 3 3 ...
## $ EducationField : Factor w/ 6 levels "Human Resources",..: 2 2 5 2 4 2 4 2 2 4 ...
## $ EmployeeCount : int 1 1 1 1 1 1 1 1 1 1 ...
## $ EmployeeNumber : int 1 2 3 4 5 6 7 8 9 10 ...
## $ EnvironmentSatisfaction : int 2 3 4 4 1 4 3 4 4 3 ...
## $ Gender : Factor w/ 2 levels "Female","Male": 1 2 2 1 2 2 1 2 2 2 ...
## $ HourlyRate : int 94 61 92 56 40 79 81 67 44 94 ...
## $ JobInvolvement : int 3 2 2 3 3 3 4 3 2 3 ...
## $ JobLevel : int 2 2 1 1 1 1 1 1 3 2 ...
## $ JobRole : Factor w/ 9 levels "Healthcare Representative",..: 8 7 3 7 3 3 3 3 5 1 ...
## $ JobSatisfaction : int 4 2 3 3 2 4 1 3 3 3 ...
## $ MaritalStatus : Factor w/ 3 levels "Divorced","Married",..: 3 2 3 2 2 3 2 1 3 2 ...
## $ MonthlyIncome : int 5993 5130 2090 2909 3468 3068 2670 2693 9526 5237 ...
## $ MonthlyRate : int 19479 24907 2396 23159 16632 11864 9964 13335 8787 16577 ...
## $ NumCompaniesWorked : int 8 1 6 1 9 0 4 1 0 6 ...
## $ Over18 : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
## $ OverTime : Factor w/ 2 levels "No","Yes": 2 1 2 2 1 1 2 1 1 1 ...
## $ PercentSalaryHike : int 11 23 15 11 12 13 20 22 21 13 ...
## $ PerformanceRating : int 3 4 3 3 3 3 4 4 4 3 ...
## $ RelationshipSatisfaction: int 1 4 2 3 4 3 1 2 2 2 ...
## $ StandardHours : int 80 80 80 80 80 80 80 80 80 80 ...
## $ StockOptionLevel : int 0 1 0 0 1 0 3 1 0 2 ...
## $ TotalWorkingYears : int 8 10 7 8 6 8 12 1 10 17 ...
## $ TrainingTimesLastYear : int 0 3 3 3 3 2 3 2 2 3 ...
## $ WorkLifeBalance : int 1 3 3 3 3 2 2 3 3 2 ...
## $ YearsAtCompany : int 6 10 0 8 2 7 1 1 9 7 ...
## $ YearsInCurrentRole : int 4 7 0 7 2 7 0 0 7 7 ...
## $ YearsSinceLastPromotion : int 0 1 0 3 2 3 0 0 1 7 ...
## $ YearsWithCurrManager : int 5 7 0 0 2 6 0 0 8 7 ...
summary(HRData)
## Age Attrition BusinessTravel DailyRate
## Min. :18.00 No :2466 Non-Travel : 300 Min. : 102.0
## 1st Qu.:30.00 Yes: 474 Travel_Frequently: 554 1st Qu.: 465.0
## Median :36.00 Travel_Rarely :2086 Median : 802.0
## Mean :36.92 Mean : 802.5
## 3rd Qu.:43.00 3rd Qu.:1157.0
## Max. :60.00 Max. :1499.0
##
## Department DistanceFromHome Education
## Human Resources : 126 Min. : 1.000 Min. :1.000
## Research & Development:1922 1st Qu.: 2.000 1st Qu.:2.000
## Sales : 892 Median : 7.000 Median :3.000
## Mean : 9.193 Mean :2.913
## 3rd Qu.:14.000 3rd Qu.:4.000
## Max. :29.000 Max. :5.000
##
## EducationField EmployeeCount EmployeeNumber
## Human Resources : 54 Min. :1 Min. : 1.0
## Life Sciences :1212 1st Qu.:1 1st Qu.: 735.8
## Marketing : 318 Median :1 Median :1470.5
## Medical : 928 Mean :1 Mean :1470.5
## Other : 164 3rd Qu.:1 3rd Qu.:2205.2
## Technical Degree: 264 Max. :1 Max. :2940.0
##
## EnvironmentSatisfaction Gender HourlyRate JobInvolvement
## Min. :1.000 Female:1176 Min. : 30.00 Min. :1.00
## 1st Qu.:2.000 Male :1764 1st Qu.: 48.00 1st Qu.:2.00
## Median :3.000 Median : 66.00 Median :3.00
## Mean :2.722 Mean : 65.89 Mean :2.73
## 3rd Qu.:4.000 3rd Qu.: 84.00 3rd Qu.:3.00
## Max. :4.000 Max. :100.00 Max. :4.00
##
## JobLevel JobRole JobSatisfaction
## Min. :1.000 Sales Executive :652 Min. :1.000
## 1st Qu.:1.000 Research Scientist :584 1st Qu.:2.000
## Median :2.000 Laboratory Technician :518 Median :3.000
## Mean :2.064 Manufacturing Director :290 Mean :2.729
## 3rd Qu.:3.000 Healthcare Representative:262 3rd Qu.:4.000
## Max. :5.000 Manager :204 Max. :4.000
## (Other) :430
## MaritalStatus MonthlyIncome MonthlyRate NumCompaniesWorked
## Divorced: 654 Min. : 1009 Min. : 2094 Min. :0.000
## Married :1346 1st Qu.: 2911 1st Qu.: 8045 1st Qu.:1.000
## Single : 940 Median : 4919 Median :14236 Median :2.000
## Mean : 6503 Mean :14313 Mean :2.693
## 3rd Qu.: 8380 3rd Qu.:20462 3rd Qu.:4.000
## Max. :19999 Max. :26999 Max. :9.000
##
## Over18 OverTime PercentSalaryHike PerformanceRating
## Y:2940 No :2108 Min. :11.00 Min. :3.000
## Yes: 832 1st Qu.:12.00 1st Qu.:3.000
## Median :14.00 Median :3.000
## Mean :15.21 Mean :3.154
## 3rd Qu.:18.00 3rd Qu.:3.000
## Max. :25.00 Max. :4.000
##
## RelationshipSatisfaction StandardHours StockOptionLevel TotalWorkingYears
## Min. :1.000 Min. :80 Min. :0.0000 Min. : 0.00
## 1st Qu.:2.000 1st Qu.:80 1st Qu.:0.0000 1st Qu.: 6.00
## Median :3.000 Median :80 Median :1.0000 Median :10.00
## Mean :2.712 Mean :80 Mean :0.7939 Mean :11.28
## 3rd Qu.:4.000 3rd Qu.:80 3rd Qu.:1.0000 3rd Qu.:15.00
## Max. :4.000 Max. :80 Max. :3.0000 Max. :40.00
##
## TrainingTimesLastYear WorkLifeBalance YearsAtCompany YearsInCurrentRole
## Min. :0.000 Min. :1.000 Min. : 0.000 Min. : 0.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.: 3.000 1st Qu.: 2.000
## Median :3.000 Median :3.000 Median : 5.000 Median : 3.000
## Mean :2.799 Mean :2.761 Mean : 7.008 Mean : 4.229
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.: 9.000 3rd Qu.: 7.000
## Max. :6.000 Max. :4.000 Max. :40.000 Max. :18.000
##
## YearsSinceLastPromotion YearsWithCurrManager
## Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.: 2.000
## Median : 1.000 Median : 3.000
## Mean : 2.188 Mean : 4.123
## 3rd Qu.: 3.000 3rd Qu.: 7.000
## Max. :15.000 Max. :17.000
##
##Standard Hours, Over 18, Employee Count & Employee number attributes are not useful for analysis
HRData1<-subset(HRData,select = c(1:8,11:21,23:26,28:35))
##Separating Data into Dev & Holdout (Train & Test)
set.seed(200)
HRData$Random<-runif(nrow(HRData1),0,1)
HRData.Train<-HRData1[which(HRData$Random<=0.70),]
HRData.Test<-HRData1[which(HRData$Random>0.70),]
##Exploratory Data Analysis
##We will compare each of variables in data set to the Target Variable (Attrition)
attach(HRData.Train)
##We shall consider the variables in group of 4 to observe the impact on Attrition
AgeAttrition<-ggplot(data = HRData.Train, aes(Age,fill = Attrition))+geom_density()+facet_grid(~Attrition)
TravelAttrition<-ggplot(data = HRData.Train, aes(BusinessTravel, fill = Attrition))+geom_bar()
TotWorkAttrition<-ggplot(data = HRData.Train, aes(TotalWorkingYears, fill = Attrition))+geom_bar()
DepartAttrition<-ggplot(data = HRData.Train, aes(Department, fill = Attrition))+geom_bar()
grid.arrange(AgeAttrition,TravelAttrition,TotWorkAttrition,DepartAttrition,ncol = 2, top = "Attrition Analysis - Age, Travel, Total Experience & Department")
##Second Group of Variables
DistanceAttrition<-ggplot(data = HRData.Train, aes(DistanceFromHome,fill = Attrition))+geom_bar()
EduAttrition<-ggplot(data = HRData.Train, aes(Education, fill = Attrition))+geom_bar()
EduFieldAttrition<-ggplot(data = HRData.Train, aes(EducationField, fill = Attrition))+geom_bar()
EnvSatisAttrition<-ggplot(data = HRData.Train, aes(EnvironmentSatisfaction, fill = Attrition))+geom_bar()
grid.arrange(DistanceAttrition,EduAttrition,EduFieldAttrition,EnvSatisAttrition, ncol = 2, top = "Attrition Analysis - Distance from Home, Education & Environment satisfaction ")
##Gender, Marital Status View
GenderAttrition<-ggplot(data = HRData.Train, aes(Gender,fill = Attrition))+geom_bar()
MaritalAttrition<-ggplot(data = HRData.Train, aes(MaritalStatus, fill = Attrition))+geom_bar()
grid.arrange(GenderAttrition,MaritalAttrition, ncol = 2, top = "Attrition Analysis - Gender & Marital Status")
##Daily Hourly & Monthly Rate View
DRateAttrition<-ggplot(data = HRData.Train,aes(DailyRate,Attrition))+geom_point()
HRateAttrition<-ggplot(data = HRData.Train, aes(HourlyRate,Attrition))+geom_point()
MRateAttriion<-ggplot(data = HRData.Train, aes(MonthlyRate,Attrition))+geom_point()
grid.arrange(DRateAttrition,HRateAttrition,MRateAttriion, ncol = 2, top = "Attrition Analysis - Daily, Hourly & MOnthly Rate")
##Job Parameters View
JobInvolAttrition<-ggplot(data = HRData.Train, aes(JobInvolvement, fill = Attrition))+geom_bar()
JobLevelAttrition<-ggplot(data = HRData.Train, aes(JobLevel, fill = Attrition))+geom_bar()
JobRoleAttrition<-ggplot(data = HRData.Train, aes(JobRole, fill = Attrition))+geom_bar()
JobSatisAttrition<-ggplot(data = HRData.Train, aes(JobSatisfaction, fill = Attrition))+geom_bar()
grid.arrange(JobInvolAttrition,JobLevelAttrition,JobRoleAttrition,JobSatisAttrition, ncol = 2, top = "Attrition Analysis - Job Role, Level, Satisfaction & Involvement ")
##Income & Related Parameters View
MonthlyIncAttrition<-ggplot(data = HRData.Train, aes(MonthlyIncome, fill = Attrition))+geom_density()+facet_grid(~Attrition)
OverTAttrition<-ggplot(data = HRData.Train, aes(OverTime, fill = Attrition))+geom_bar()
PerfRateAttrition<-ggplot(data = HRData.Train, aes(PerformanceRating, fill = Attrition))+geom_bar()
PercentHikeAttrition<-ggplot(data = HRData.Train, aes(PercentSalaryHike, fill = Attrition))+geom_bar()
grid.arrange(MonthlyIncAttrition,OverTAttrition,PerfRateAttrition,PercentHikeAttrition, ncol = 2, top = "Attrition Analysis - Monthly Income, Over Time Perf, Rating & Percent Hike")
##Training, Relationship Satisfaction & Work Life Balance
WorkLifBalAttrition<-ggplot(data = HRData.Train, aes(WorkLifeBalance, fill = Attrition))+geom_bar()
NumCompAttrition<-ggplot(data = HRData.Train, aes(NumCompaniesWorked, fill = Attrition))+geom_bar()
TrainTimeAttrition<-ggplot(data = HRData.Train, aes(TrainingTimesLastYear, fill = Attrition))+geom_bar()
StockOptAttrition<-ggplot(data = HRData.Train, aes(StockOptionLevel, fill = Attrition))+geom_bar()
RelSatisAttrition<-ggplot(data = HRData.Train, aes(RelationshipSatisfaction, fill = Attrition))+geom_bar()
grid.arrange(WorkLifBalAttrition,NumCompAttrition,RelSatisAttrition,StockOptAttrition,TrainTimeAttrition, ncol = 2, top = "Attrition Analysis - WorkLife Balance, No. Companies Worked, Training Time, Relationship Satisfaction & Stock Options")
##Promotion, Role, Current Manager & Years at Company
YearsCompAttrition<-ggplot(data = HRData.Train, aes(YearsAtCompany, fill = Attrition))+geom_bar()
YearsRoleAttrition<-ggplot(data = HRData.Train, aes(YearsInCurrentRole, fill = Attrition))+geom_bar()
YearsPromoAttrition<-ggplot(data = HRData.Train, aes(YearsSinceLastPromotion, fill = Attrition))+geom_bar()
YearsMgrAttrition<-ggplot(data = HRData.Train, aes(YearsWithCurrManager, fill = Attrition))+geom_bar()
grid.arrange(YearsCompAttrition,YearsRoleAttrition,YearsPromoAttrition,YearsMgrAttrition, ncol = 2, top = "Attrition Analysis - Years in Role, Promotion, Manager and Company")
##Construct the Classification & Regression Tree
## setting the control paramter inputs for rpart
r.ctrl<-rpart.control(minsplit=60, cp = 0, xval = 10)
Tree1 <- rpart(formula = Attrition ~ ., data = HRData.Train, method = "class", control = r.ctrl)
printcp(Tree1)
##
## Classification tree:
## rpart(formula = Attrition ~ ., data = HRData.Train, method = "class",
## control = r.ctrl)
##
## Variables actually used in tree construction:
## [1] Age BusinessTravel
## [3] DailyRate EnvironmentSatisfaction
## [5] HourlyRate JobRole
## [7] MaritalStatus MonthlyIncome
## [9] NumCompaniesWorked OverTime
## [11] TotalWorkingYears
##
## Root node error: 354/2120 = 0.16698
##
## n= 2120
##
## CP nsplit rel error xerror xstd
## 1 0.0579096 0 1.00000 1.00000 0.048509
## 2 0.0353107 2 0.88418 0.95763 0.047672
## 3 0.0254237 4 0.81356 0.89266 0.046322
## 4 0.0183616 5 0.78814 0.87571 0.045957
## 5 0.0141243 7 0.75141 0.85028 0.045397
## 6 0.0047081 8 0.73729 0.83616 0.045080
## 7 0.0000000 11 0.72316 0.84463 0.045271
fancyRpartPlot(Tree1)
##Prune the Tree
Tree1Pruned<-prune(Tree1,cp = 0.005,"CP")
printcp(Tree1Pruned)
##
## Classification tree:
## rpart(formula = Attrition ~ ., data = HRData.Train, method = "class",
## control = r.ctrl)
##
## Variables actually used in tree construction:
## [1] BusinessTravel DailyRate HourlyRate JobRole
## [5] MaritalStatus MonthlyIncome OverTime TotalWorkingYears
##
## Root node error: 354/2120 = 0.16698
##
## n= 2120
##
## CP nsplit rel error xerror xstd
## 1 0.057910 0 1.00000 1.00000 0.048509
## 2 0.035311 2 0.88418 0.95763 0.047672
## 3 0.025424 4 0.81356 0.89266 0.046322
## 4 0.018362 5 0.78814 0.87571 0.045957
## 5 0.014124 7 0.75141 0.85028 0.045397
## 6 0.005000 8 0.73729 0.83616 0.045080
fancyRpartPlot(Tree1Pruned)
##Scoring Syntax on Train Data
HRData.Train$predictclass<-predict(Tree1Pruned,HRData.Train,type = "class")
HRData.Train$predictscore<-predict(Tree1Pruned,HRData.Train)
##Scoring Syntax on Test Data
HRData.Test$predictclass<-predict(Tree1Pruned,HRData.Test,type = "class")
HRData.Test$predictscore<-predict(Tree1Pruned,HRData.Test)
##KS Statstic for Train Data
library(ROCR)
## Loading required package: gplots
##
## Attaching package: 'gplots'
## The following object is masked from 'package:stats':
##
## lowess
##
## Attaching package: 'ROCR'
## The following object is masked from 'package:neuralnet':
##
## prediction
TrainCart.p.scores<-prediction(HRData.Train$predictscore[,2],HRData.Train$Attrition)
TrainCart.p.perf<-performance(TrainCart.p.scores,"tpr","fpr")
ks.TrainCart<-max(attr(TrainCart.p.perf, "y.values")[[1]] -(attr(TrainCart.p.perf, "x.values")[[1]]))
ks.TrainCart
## [1] 0.4414842
##KS Statstic for Test Data
library(ROCR)
TestCart.p.scores<-prediction(HRData.Test$predictscore[,2],HRData.Test$Attrition)
TestCart.p.perf<-performance(TestCart.p.scores,"tpr","fpr")
ks.TestCart<-max(attr(TestCart.p.perf, "y.values")[[1]] -(attr(TestCart.p.perf, "x.values")[[1]]))
ks.TestCart
## [1] 0.3388095
##AUC for Train & Test Data
AUCTrain<-performance(TrainCart.p.scores,"auc")
AUCTrain<-as.numeric(AUCTrain@y.values)
AUCTrain
## [1] 0.7580763
AUCTest<-performance(TestCart.p.scores,"auc")
AUCTest<-as.numeric(AUCTest@y.values)
AUCTest
## [1] 0.6966429
##Accuracy performance of CART
library(caret)
## Loading required package: lattice
AccuracyTrainCart<-postResample(HRData.Train$predictclass,HRData.Train$Attrition)
AccuracyTrainCart
## Accuracy Kappa
## 0.8768868 0.4693718
AccuracyTestCart<-postResample(HRData.Test$predictclass,HRData.Test$Attrition)
AccuracyTestCart
## Accuracy Kappa
## 0.8548780 0.3233948
##Using Ensemble methods
##Load Librares
library(mlbench)
library(caret)
library(caretEnsemble)
##
## Attaching package: 'caretEnsemble'
## The following object is masked from 'package:ggplot2':
##
## autoplot
library(C50)
library(rattle)
##Refreshing the dataset for ensmble purpose
HRData.TrainE<-subset(HRData.Train, select = c(1:31))
HRData.TestE<-subset(HRData.Test, select = c(1:31))
##Boosting using C5.0
C50Tree<-C5.0(Attrition~., data = HRData.TrainE)
C50Tree
##
## Call:
## C5.0.formula(formula = Attrition ~ ., data = HRData.TrainE)
##
## Classification Tree
## Number of samples: 2120
## Number of predictors: 30
##
## Tree size: 94
##
## Non-standard options: attempt to group attributes
##Assigning Predicted class and Predict score
HRData.TrainE$predictclass<-predict(C50Tree,HRData.TrainE, type = "class")
HRData.TrainE$predictscore<-predict(C50Tree,HRData.TrainE, type = "prob")
##Assigning Predicted class and Predict score in Test Data
HRData.TestE$predictclass<-predict(C50Tree,HRData.TestE, type = "class")
HRData.TestE$predictscore<-predict(C50Tree,HRData.TestE, type = "prob")
##Model performance of C5.0
AccuracyTrain<-postResample(HRData.TrainE$predictclass,HRData.TrainE$Attrition)
AccuracyTrain
## Accuracy Kappa
## 0.9721698 0.8968160
AccuracyTest<-postResample(HRData.TestE$predictclass,HRData.TestE$Attrition)
AccuracyTest
## Accuracy Kappa
## 0.9060976 0.6007335
##KS Statistic for Train & Test C5.0
library(ROCR)
TrainC50.p.scores<-prediction(HRData.TrainE$predictscore[,2],HRData.TrainE$Attrition)
TrainC50.p.perf<-performance(TrainC50.p.scores,"tpr","fpr")
ks.TrainC50<-max(attr(TrainC50.p.perf, "y.values")[[1]] -(attr(TrainC50.p.perf, "x.values")[[1]]))
ks.TrainC50
## [1] 0.8694711
TestC50.p.scores<-prediction(HRData.TestE$predictscore[,2],HRData.TestE$Attrition)
TestC50.p.perf<-performance(TestC50.p.scores,"tpr","fpr")
ks.TestC50<-max(attr(TestC50.p.perf, "y.values")[[1]] -(attr(TestC50.p.perf, "x.values")[[1]]))
ks.TestC50
## [1] 0.645
##Trying Bagged Cart
HRData.TrainE2<-subset(HRData.Train, select = c(1:31))
HRData.TestE2<-subset(HRData.Test, select = c(1:31))
bcartcontrol <- trainControl(method="repeatedcv", number=10, repeats=3)
# Bagged CART
set.seed(7)
fit.treebag <- train(Attrition~., data=HRData.TrainE2, method="treebag", metric="Accuracy", trControl=bcartcontrol)
##Assigning Predicted class and Predict score
HRData.TrainE2$predictclass<-predict(fit.treebag,HRData.TrainE2)
HRData.TrainE2$predictscore<-predict(C50Tree,HRData.TrainE2, type = "prob")
##Assigning Predicted class and Predict score in Test Data
HRData.TestE2$predictclass<-predict(C50Tree,HRData.TestE2)
HRData.TestE2$predictscore<-predict(C50Tree,HRData.TestE2, type = "prob")
##Model performance of bcart
AccuracyTrainBC<-postResample(HRData.TrainE2$predictclass,HRData.TrainE2$Attrition)
AccuracyTrainBC
## Accuracy Kappa
## 0.9990566 0.9966012
AccuracyTestBC<-postResample(HRData.TestE2$predictclass,HRData.TestE2$Attrition)
AccuracyTestBC
## Accuracy Kappa
## 0.9060976 0.6007335
##KS Statistic for Train & Test bcart
library(ROCR)
Trainbcart.p.scores<-prediction(HRData.TrainE2$predictscore[,2],HRData.TrainE2$Attrition)
Trainbcart.p.perf<-performance(Trainbcart.p.scores,"tpr","fpr")
ks.Trainbcart<-max(attr(Trainbcart.p.perf, "y.values")[[1]] -(attr(Trainbcart.p.perf, "x.values")[[1]]))
ks.Trainbcart
## [1] 0.8694711
Testbcart.p.scores<-prediction(HRData.TestE2$predictscore[,2],HRData.TestE2$Attrition)
Testbcart.p.perf<-performance(Testbcart.p.scores,"tpr","fpr")
ks.Testbcart<-max(attr(Testbcart.p.perf, "y.values")[[1]] -(attr(Testbcart.p.perf, "x.values")[[1]]))
ks.Testbcart
## [1] 0.645