MBA Starting Salaries Analysis
Ananya Gupta
December 26, 2017
Reading the data set
Here we read the data set and create a summary analysis showing the mean, median etc. of each variable.
mbasalaries.df <- read.csv(paste("MBA Starting Salaries Data.csv",sep=""))
library(psych)## Warning: package 'psych' was built under R version 3.4.3describe(mbasalaries.df)## vars n mean sd median trimmed mad min max
## age 1 274 27.36 3.71 27 26.76 2.97 22 48
## sex 2 274 1.25 0.43 1 1.19 0.00 1 2
## gmat_tot 3 274 619.45 57.54 620 618.86 59.30 450 790
## gmat_qpc 4 274 80.64 14.87 83 82.31 14.83 28 99
## gmat_vpc 5 274 78.32 16.86 81 80.33 14.83 16 99
## gmat_tpc 6 274 84.20 14.02 87 86.12 11.86 0 99
## s_avg 7 274 3.03 0.38 3 3.03 0.44 2 4
## f_avg 8 274 3.06 0.53 3 3.09 0.37 0 4
## quarter 9 274 2.48 1.11 2 2.47 1.48 1 4
## work_yrs 10 274 3.87 3.23 3 3.29 1.48 0 22
## frstlang 11 274 1.12 0.32 1 1.02 0.00 1 2
## salary 12 274 39025.69 50951.56 999 33607.86 1481.12 0 220000
## satis 13 274 172.18 371.61 6 91.50 1.48 1 998
## range skew kurtosis se
## age 26 2.16 6.45 0.22
## sex 1 1.16 -0.66 0.03
## gmat_tot 340 -0.01 0.06 3.48
## gmat_qpc 71 -0.92 0.30 0.90
## gmat_vpc 83 -1.04 0.74 1.02
## gmat_tpc 99 -2.28 9.02 0.85
## s_avg 2 -0.06 -0.38 0.02
## f_avg 4 -2.08 10.85 0.03
## quarter 3 0.02 -1.35 0.07
## work_yrs 22 2.78 9.80 0.20
## frstlang 1 2.37 3.65 0.02
## salary 220000 0.70 -1.05 3078.10
## satis 997 1.77 1.13 22.45Box plots/ Bar plots
Here we make the box plots and bar plots for each variable to understand it better.
hist(mbasalaries.df$age, breaks=20,col="pink",xlab="Age in years", main="Graph showing age distribution")
hist(mbasalaries.df$sex, main = "Graph showing the number of males and females", xlab = "Females - 2 and Males - 1",col = "pink")
hist(mbasalaries.df$work_yrs, breaks=20,col="green",xlab="Work Experience in years", main="Work experience distribution")
hist(mbasalaries.df$gmat_tot, breaks=40,col="blue",xlab="score out of 800", main="Gmat Score distribution")
plot(mbasalaries.df$s_avg, main = "Spring MBA average")
plot(mbasalaries.df$f_avg, main = "Fall MBA average")
hist(mbasalaries.df$work_yrs, main = "Years of work experience",col="green",xlab = "Number of years")
plot(mbasalaries.df$frstlang, main = "First language")
hist(mbasalaries.df$salary, main = "Starting salaries", xlab = "Starting salary", col = "pink")
newdata <- mbasalaries.df[ which(mbasalaries.df$satis<='7'), ]
hist(newdata$satis, breaks=5,col="magenta",xlab="Degree of Satisfaction,1=low 7=high", main="Satisfaction distribution")
Scatter plots
library(car)## Warning: package 'car' was built under R version 3.4.3##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitscatterplot(salary ~age, data=mbasalaries.df,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of salary vs age",
xlab="age",
ylab="salary")
scatterplot(salary ~sex, data=mbasalaries.df,
spread=FALSE, smoother.args=list(lty=2),
main="Scatter plot of salary vs sex",
xlab="sex",
ylab="salary")
scatterplot(salary ~frstlang, data=mbasalaries.df,
main="Scatter plot of salary vs first language",
xlab="first language",
ylab="salary")
scatterplot(salary ~ gmat_tot, data=mbasalaries.df,
main="Scatter plot of salary vs first language",
xlab="first language",
ylab="salary")
scatterplot(salary ~work_yrs, data=mbasalaries.df,
main="Scatter plot of salary vs Work exp.",
xlab="Work experience in years",
ylab="salary")
Comparing different factors that affect starting salaries
Take subset of those people who got a job.
newdata <- subset(mbasalaries.df, salary>0)Drawing some contingency tables, as appropriate.
mytable1 <- xtabs(~salary+gmat_tot+frstlang, data = newdata)
mytable1## , , frstlang = 1
##
## gmat_tot
## salary 450 460 500 520 530 540 550 560 570 580 590 600 610 620 630 640
## 998 0 1 0 0 0 0 0 2 0 2 2 4 4 0 6 3
## 999 0 0 1 0 0 0 0 1 3 0 1 1 0 3 1 2
## 64000 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## 77000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 78256 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
## 82000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 85000 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## 86000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## 88000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 88500 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## 90000 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0
## 92000 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## 93000 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0
## 95000 0 0 0 0 1 0 0 2 0 0 0 0 2 0 0 0
## 96000 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0
## 96500 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
## 97000 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0
## 98000 0 0 0 0 0 0 0 1 2 1 1 0 1 0 0 0
## 99000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 100000 0 0 0 0 0 0 0 2 0 1 0 1 1 0 1 0
## 100400 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## 101000 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0
## 101100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 101600 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## 102500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 103000 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## 104000 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## 105000 0 0 0 0 0 0 2 0 2 3 0 1 0 1 0 0
## 106000 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## 107000 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
## 107300 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 107500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## 108000 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0
## 110000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
## 112000 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
## 115000 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0
## 118000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 120000 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
## 126710 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
## 130000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 145800 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## 146000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## 162000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 220000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## gmat_tot
## salary 650 660 670 680 690 700 710 720 730 740 790
## 998 1 2 3 2 2 0 1 1 0 2 0
## 999 2 3 1 1 2 0 1 0 1 1 1
## 64000 0 0 0 0 0 0 0 0 0 0 0
## 77000 0 1 0 0 0 0 0 0 0 0 0
## 78256 0 0 0 0 0 0 0 0 0 0 0
## 82000 0 0 1 0 0 0 0 0 0 0 0
## 85000 0 1 0 0 0 1 0 1 0 0 0
## 86000 0 0 0 1 0 0 0 0 0 0 0
## 88000 1 0 0 0 0 0 0 0 0 0 0
## 88500 0 0 0 0 0 0 0 0 0 0 0
## 90000 1 0 0 0 0 0 0 0 0 0 0
## 92000 0 1 0 0 0 0 1 0 0 0 0
## 93000 0 0 0 0 0 0 0 0 0 0 0
## 95000 0 0 2 0 0 0 0 0 0 0 0
## 96000 1 0 0 0 0 0 0 0 0 0 0
## 96500 0 0 0 0 0 0 0 0 0 0 0
## 97000 0 0 0 0 0 0 0 0 0 0 0
## 98000 0 0 1 0 0 0 1 0 0 0 0
## 99000 0 0 0 0 0 0 0 0 0 0 0
## 100000 2 0 0 0 0 0 1 0 0 0 0
## 100400 0 0 0 0 0 0 0 0 0 0 0
## 101000 0 0 0 0 0 0 0 0 0 0 0
## 101100 0 1 0 0 0 0 0 0 0 0 0
## 101600 0 0 0 0 0 0 0 0 0 0 0
## 102500 0 0 1 0 0 0 0 0 0 0 0
## 103000 0 0 0 0 0 0 0 0 0 0 0
## 104000 0 0 0 0 0 0 0 0 0 0 0
## 105000 1 0 0 1 0 0 0 0 0 0 0
## 106000 0 0 0 2 0 0 0 0 0 0 0
## 107000 0 0 0 0 0 0 0 0 0 0 0
## 107300 0 0 0 0 0 0 0 0 0 0 0
## 107500 0 0 0 0 0 0 0 0 0 0 0
## 108000 0 0 0 0 0 0 0 0 0 0 0
## 110000 0 0 0 0 0 0 0 0 0 0 0
## 112000 0 0 1 1 0 0 0 0 0 0 0
## 115000 0 0 0 0 0 0 1 0 0 0 0
## 118000 0 0 0 0 0 0 0 0 0 0 0
## 120000 0 0 1 0 0 1 0 0 0 0 0
## 126710 0 0 0 0 0 0 0 0 0 0 0
## 130000 1 0 0 0 0 0 0 0 0 0 0
## 145800 0 0 0 0 0 0 0 0 0 0 0
## 146000 0 0 0 0 0 0 0 0 0 0 0
## 162000 0 0 0 0 0 1 0 0 0 0 0
## 220000 0 0 0 0 0 0 0 0 0 0 0
##
## , , frstlang = 2
##
## gmat_tot
## salary 450 460 500 520 530 540 550 560 570 580 590 600 610 620 630 640
## 998 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0
## 999 0 0 0 0 0 0 1 1 1 1 1 2 0 1 1 0
## 64000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 77000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 78256 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 85000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 86000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 88000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 88500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 90000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 92000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 93000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 95000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 96000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 96500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 97000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 98000 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
## 99000 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
## 100000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 100400 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 101000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 101100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 101600 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 102500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 103000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 104000 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
## 105000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 106000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 107000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 107300 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 107500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 108000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 110000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 112000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 115000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 118000 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## 120000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 126710 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 130000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 145800 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 146000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 162000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 220000 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
## gmat_tot
## salary 650 660 670 680 690 700 710 720 730 740 790
## 998 1 1 2 0 0 0 0 0 0 0 0
## 999 0 0 0 0 0 0 0 0 0 0 0
## 64000 0 0 0 0 0 0 0 0 0 0 0
## 77000 0 0 0 0 0 0 0 0 0 0 0
## 78256 0 0 0 0 0 0 0 0 0 0 0
## 82000 0 0 0 0 0 0 0 0 0 0 0
## 85000 0 0 0 0 0 0 0 0 0 0 0
## 86000 0 0 0 0 0 0 0 0 0 0 0
## 88000 0 0 0 0 0 0 0 0 0 0 0
## 88500 0 0 0 0 0 0 0 0 0 0 0
## 90000 0 0 0 0 0 0 0 0 0 0 0
## 92000 0 0 0 0 0 0 0 0 0 0 0
## 93000 0 0 0 0 0 0 0 0 0 0 0
## 95000 0 0 0 0 0 0 0 0 0 0 0
## 96000 0 0 0 0 0 0 0 0 0 0 0
## 96500 0 0 0 0 0 0 0 0 0 0 0
## 97000 0 0 0 0 0 0 0 0 0 0 0
## 98000 0 0 0 1 0 0 0 0 0 0 0
## 99000 0 0 0 0 0 0 0 0 0 0 0
## 100000 0 0 0 0 0 0 0 0 0 0 0
## 100400 0 0 0 0 0 0 0 0 0 0 0
## 101000 0 0 0 0 0 0 0 0 0 0 0
## 101100 0 0 0 0 0 0 0 0 0 0 0
## 101600 0 0 0 0 0 0 0 0 0 0 0
## 102500 0 0 0 0 0 0 0 0 0 0 0
## 103000 0 0 0 0 0 0 0 0 0 0 0
## 104000 0 0 0 0 0 0 0 0 0 0 0
## 105000 0 0 0 0 0 0 0 0 0 0 0
## 106000 0 0 0 0 0 0 0 0 0 0 0
## 107000 0 0 0 0 0 0 0 0 0 0 0
## 107300 0 1 0 0 0 0 0 0 0 0 0
## 107500 0 0 0 0 0 0 0 0 0 0 0
## 108000 0 0 0 0 0 0 0 0 0 0 0
## 110000 0 0 0 0 0 0 0 0 0 0 0
## 112000 0 0 0 0 0 0 0 0 0 0 0
## 115000 0 0 0 0 0 0 0 0 0 0 0
## 118000 0 0 0 0 0 0 0 0 0 0 0
## 120000 0 0 0 0 0 0 0 0 0 0 0
## 126710 0 0 0 0 0 0 0 0 0 0 0
## 130000 0 0 0 0 0 0 0 0 0 0 0
## 145800 0 0 0 0 0 0 0 0 0 0 0
## 146000 0 0 0 0 0 0 0 0 0 0 0
## 162000 0 0 0 0 0 0 0 0 0 0 0
## 220000 0 0 0 0 0 0 0 0 0 0 0mytable2 <- xtabs(~salary + sex + work_yrs, data = newdata)
mytable2## , , work_yrs = 0
##
## sex
## salary 1 2
## 998 0 0
## 999 1 0
## 64000 0 0
## 77000 0 0
## 78256 0 0
## 82000 0 0
## 85000 0 0
## 86000 0 0
## 88000 0 0
## 88500 0 0
## 90000 0 0
## 92000 0 0
## 93000 0 0
## 95000 1 0
## 96000 0 0
## 96500 0 0
## 97000 0 0
## 98000 0 0
## 99000 0 0
## 100000 0 0
## 100400 0 0
## 101000 0 0
## 101100 0 0
## 101600 0 0
## 102500 0 0
## 103000 0 0
## 104000 0 0
## 105000 0 0
## 106000 0 0
## 107000 0 0
## 107300 0 0
## 107500 0 0
## 108000 0 0
## 110000 0 0
## 112000 0 0
## 115000 0 0
## 118000 0 0
## 120000 0 0
## 126710 0 0
## 130000 0 0
## 145800 0 0
## 146000 0 0
## 162000 0 0
## 220000 0 0
##
## , , work_yrs = 1
##
## sex
## salary 1 2
## 998 2 0
## 999 2 0
## 64000 0 0
## 77000 0 0
## 78256 0 1
## 82000 0 1
## 85000 0 1
## 86000 0 0
## 88000 0 0
## 88500 0 0
## 90000 0 0
## 92000 0 0
## 93000 0 0
## 95000 0 1
## 96000 1 0
## 96500 0 0
## 97000 0 0
## 98000 0 0
## 99000 0 0
## 100000 0 0
## 100400 0 0
## 101000 0 0
## 101100 0 0
## 101600 0 0
## 102500 0 0
## 103000 0 0
## 104000 0 0
## 105000 0 0
## 106000 0 0
## 107000 0 0
## 107300 0 0
## 107500 0 0
## 108000 0 0
## 110000 0 0
## 112000 0 0
## 115000 2 0
## 118000 0 0
## 120000 0 0
## 126710 0 0
## 130000 0 0
## 145800 0 0
## 146000 0 0
## 162000 1 0
## 220000 0 0
##
## , , work_yrs = 2
##
## sex
## salary 1 2
## 998 13 3
## 999 4 2
## 64000 0 1
## 77000 1 0
## 78256 0 0
## 82000 0 0
## 85000 1 1
## 86000 0 1
## 88000 0 0
## 88500 0 0
## 90000 2 0
## 92000 2 1
## 93000 0 0
## 95000 2 0
## 96000 2 0
## 96500 1 0
## 97000 0 0
## 98000 4 3
## 99000 0 0
## 100000 1 5
## 100400 0 0
## 101000 0 2
## 101100 0 0
## 101600 0 0
## 102500 0 0
## 103000 0 0
## 104000 0 0
## 105000 4 0
## 106000 0 0
## 107000 1 0
## 107300 1 0
## 107500 0 0
## 108000 0 0
## 110000 0 0
## 112000 1 0
## 115000 0 0
## 118000 0 0
## 120000 0 0
## 126710 0 0
## 130000 0 0
## 145800 1 0
## 146000 0 0
## 162000 0 0
## 220000 0 0
##
## , , work_yrs = 3
##
## sex
## salary 1 2
## 998 11 2
## 999 7 1
## 64000 0 0
## 77000 0 0
## 78256 0 0
## 82000 0 0
## 85000 0 1
## 86000 0 1
## 88000 0 1
## 88500 1 0
## 90000 0 0
## 92000 0 0
## 93000 0 0
## 95000 1 1
## 96000 0 0
## 96500 0 0
## 97000 1 0
## 98000 0 1
## 99000 0 0
## 100000 1 0
## 100400 1 0
## 101000 0 0
## 101100 0 0
## 101600 1 0
## 102500 0 0
## 103000 1 0
## 104000 0 0
## 105000 4 0
## 106000 0 0
## 107000 0 0
## 107300 0 0
## 107500 1 0
## 108000 1 0
## 110000 0 0
## 112000 0 0
## 115000 1 0
## 118000 0 0
## 120000 1 0
## 126710 1 0
## 130000 0 0
## 145800 0 0
## 146000 0 0
## 162000 0 0
## 220000 0 0
##
## , , work_yrs = 4
##
## sex
## salary 1 2
## 998 8 4
## 999 10 1
## 64000 0 0
## 77000 0 0
## 78256 0 0
## 82000 0 0
## 85000 0 0
## 86000 0 0
## 88000 0 0
## 88500 0 0
## 90000 0 0
## 92000 0 0
## 93000 1 0
## 95000 0 0
## 96000 0 1
## 96500 0 0
## 97000 1 0
## 98000 1 0
## 99000 0 0
## 100000 1 0
## 100400 0 0
## 101000 0 0
## 101100 0 0
## 101600 0 0
## 102500 0 0
## 103000 0 0
## 104000 2 0
## 105000 0 0
## 106000 0 0
## 107000 0 0
## 107300 0 0
## 107500 0 0
## 108000 1 0
## 110000 0 0
## 112000 0 0
## 115000 2 0
## 118000 0 0
## 120000 0 0
## 126710 0 0
## 130000 1 0
## 145800 0 0
## 146000 0 0
## 162000 0 0
## 220000 0 0
##
## , , work_yrs = 5
##
## sex
## salary 1 2
## 998 0 0
## 999 2 0
## 64000 0 0
## 77000 0 0
## 78256 0 0
## 82000 0 0
## 85000 0 0
## 86000 0 0
## 88000 0 0
## 88500 0 0
## 90000 1 0
## 92000 0 0
## 93000 0 1
## 95000 0 1
## 96000 0 0
## 96500 0 0
## 97000 0 0
## 98000 0 0
## 99000 0 1
## 100000 0 0
## 100400 0 0
## 101000 0 0
## 101100 0 0
## 101600 0 0
## 102500 0 0
## 103000 0 0
## 104000 0 0
## 105000 1 0
## 106000 0 0
## 107000 0 0
## 107300 0 0
## 107500 0 0
## 108000 0 0
## 110000 0 0
## 112000 0 0
## 115000 0 0
## 118000 0 0
## 120000 2 0
## 126710 0 0
## 130000 0 0
## 145800 0 0
## 146000 0 0
## 162000 0 0
## 220000 0 0
##
## , , work_yrs = 6
##
## sex
## salary 1 2
## 998 1 0
## 999 1 1
## 64000 0 0
## 77000 0 0
## 78256 0 0
## 82000 0 0
## 85000 0 0
## 86000 0 0
## 88000 0 0
## 88500 0 0
## 90000 0 0
## 92000 0 0
## 93000 0 0
## 95000 0 0
## 96000 0 0
## 96500 0 0
## 97000 0 0
## 98000 0 0
## 99000 0 0
## 100000 1 0
## 100400 0 0
## 101000 0 0
## 101100 0 0
## 101600 0 0
## 102500 1 0
## 103000 0 0
## 104000 0 0
## 105000 1 0
## 106000 1 1
## 107000 0 0
## 107300 0 0
## 107500 0 0
## 108000 0 0
## 110000 0 1
## 112000 1 0
## 115000 0 0
## 118000 0 0
## 120000 0 0
## 126710 0 0
## 130000 0 0
## 145800 0 0
## 146000 0 0
## 162000 0 0
## 220000 0 0
##
## , , work_yrs = 7
##
## sex
## salary 1 2
## 998 1 0
## 999 2 0
## 64000 0 0
## 77000 0 0
## 78256 0 0
## 82000 0 0
## 85000 0 0
## 86000 0 0
## 88000 0 0
## 88500 0 0
## 90000 0 0
## 92000 0 0
## 93000 0 0
## 95000 0 0
## 96000 0 0
## 96500 0 0
## 97000 0 0
## 98000 1 0
## 99000 0 0
## 100000 0 0
## 100400 0 0
## 101000 0 0
## 101100 0 0
## 101600 0 0
## 102500 0 0
## 103000 0 0
## 104000 0 0
## 105000 0 0
## 106000 0 0
## 107000 0 0
## 107300 0 0
## 107500 0 0
## 108000 0 0
## 110000 0 0
## 112000 0 0
## 115000 0 0
## 118000 0 0
## 120000 0 0
## 126710 0 0
## 130000 0 0
## 145800 0 0
## 146000 0 0
## 162000 0 0
## 220000 0 0
##
## , , work_yrs = 8
##
## sex
## salary 1 2
## 998 1 0
## 999 0 0
## 64000 0 0
## 77000 0 0
## 78256 0 0
## 82000 0 0
## 85000 0 0
## 86000 0 0
## 88000 0 0
## 88500 0 0
## 90000 0 0
## 92000 0 0
## 93000 1 0
## 95000 0 0
## 96000 0 0
## 96500 0 0
## 97000 0 0
## 98000 0 0
## 99000 0 0
## 100000 0 0
## 100400 0 0
## 101000 0 0
## 101100 1 0
## 101600 0 0
## 102500 0 0
## 103000 0 0
## 104000 0 0
## 105000 0 0
## 106000 1 0
## 107000 0 0
## 107300 0 0
## 107500 0 0
## 108000 0 0
## 110000 0 0
## 112000 0 0
## 115000 0 0
## 118000 0 0
## 120000 0 1
## 126710 0 0
## 130000 0 0
## 145800 0 0
## 146000 0 0
## 162000 0 0
## 220000 0 0
##
## , , work_yrs = 9
##
## sex
## salary 1 2
## 998 0 0
## 999 1 0
## 64000 0 0
## 77000 0 0
## 78256 0 0
## 82000 0 0
## 85000 0 0
## 86000 0 0
## 88000 0 0
## 88500 0 0
## 90000 0 0
## 92000 0 0
## 93000 0 0
## 95000 0 0
## 96000 0 0
## 96500 0 0
## 97000 0 0
## 98000 0 0
## 99000 0 0
## 100000 0 0
## 100400 0 0
## 101000 0 0
## 101100 0 0
## 101600 0 0
## 102500 0 0
## 103000 0 0
## 104000 0 0
## 105000 0 0
## 106000 0 0
## 107000 0 0
## 107300 0 0
## 107500 0 0
## 108000 0 0
## 110000 0 0
## 112000 0 0
## 115000 0 0
## 118000 0 0
## 120000 0 0
## 126710 0 0
## 130000 0 0
## 145800 0 0
## 146000 0 0
## 162000 0 0
## 220000 0 0
##
## , , work_yrs = 10
##
## sex
## salary 1 2
## 998 0 0
## 999 0 0
## 64000 0 0
## 77000 0 0
## 78256 0 0
## 82000 0 0
## 85000 0 0
## 86000 0 0
## 88000 0 0
## 88500 0 0
## 90000 0 0
## 92000 0 0
## 93000 0 0
## 95000 0 0
## 96000 0 0
## 96500 0 0
## 97000 0 0
## 98000 0 0
## 99000 0 0
## 100000 0 0
## 100400 0 0
## 101000 0 0
## 101100 0 0
## 101600 0 0
## 102500 0 0
## 103000 0 0
## 104000 0 0
## 105000 0 0
## 106000 0 0
## 107000 0 0
## 107300 0 0
## 107500 0 0
## 108000 0 0
## 110000 0 0
## 112000 0 0
## 115000 0 0
## 118000 1 0
## 120000 0 0
## 126710 0 0
## 130000 0 0
## 145800 0 0
## 146000 0 0
## 162000 0 0
## 220000 0 0
##
## , , work_yrs = 15
##
## sex
## salary 1 2
## 998 0 0
## 999 0 0
## 64000 0 0
## 77000 0 0
## 78256 0 0
## 82000 0 0
## 85000 0 0
## 86000 0 0
## 88000 0 0
## 88500 0 0
## 90000 0 0
## 92000 0 0
## 93000 0 0
## 95000 0 0
## 96000 0 0
## 96500 0 0
## 97000 0 0
## 98000 0 0
## 99000 0 0
## 100000 0 0
## 100400 0 0
## 101000 0 0
## 101100 0 0
## 101600 0 0
## 102500 0 0
## 103000 0 0
## 104000 0 0
## 105000 0 0
## 106000 0 0
## 107000 0 0
## 107300 0 0
## 107500 0 0
## 108000 0 0
## 110000 0 0
## 112000 0 0
## 115000 0 0
## 118000 0 0
## 120000 0 0
## 126710 0 0
## 130000 0 0
## 145800 0 0
## 146000 1 0
## 162000 0 0
## 220000 0 1
##
## , , work_yrs = 16
##
## sex
## salary 1 2
## 998 0 0
## 999 0 0
## 64000 0 0
## 77000 0 0
## 78256 0 0
## 82000 0 0
## 85000 0 0
## 86000 0 0
## 88000 0 0
## 88500 0 0
## 90000 0 0
## 92000 0 0
## 93000 0 0
## 95000 0 0
## 96000 0 0
## 96500 0 0
## 97000 0 0
## 98000 0 0
## 99000 0 0
## 100000 0 0
## 100400 0 0
## 101000 0 0
## 101100 0 0
## 101600 0 0
## 102500 0 0
## 103000 0 0
## 104000 0 0
## 105000 1 0
## 106000 0 0
## 107000 0 0
## 107300 0 0
## 107500 0 0
## 108000 0 0
## 110000 0 0
## 112000 1 0
## 115000 0 0
## 118000 0 0
## 120000 0 0
## 126710 0 0
## 130000 0 0
## 145800 0 0
## 146000 0 0
## 162000 0 0
## 220000 0 0chisq.test(xtabs(~salary + gmat_tpc, data = newdata))## Warning in chisq.test(xtabs(~salary + gmat_tpc, data = newdata)): Chi-
## squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: xtabs(~salary + gmat_tpc, data = newdata)
## X-squared = 1829.5, df = 1548, p-value = 8.178e-07This shows that p value is less than 0.05 and we can reject the null hypothesis. Hence, there is a relation between overall gmat percentile and starting salary.
chisq.test(xtabs(~salary+sex, data = newdata))## Warning in chisq.test(xtabs(~salary + sex, data = newdata)): Chi-squared
## approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: xtabs(~salary + sex, data = newdata)
## X-squared = 64.319, df = 43, p-value = 0.0192Here, as p value is less than 0.05 we can reject the null hypothesis and state that there is a relation between sex and starting mba salary.
chisq.test(xtabs(~salary+work_yrs, data = newdata))## Warning in chisq.test(xtabs(~salary + work_yrs, data = newdata)): Chi-
## squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: xtabs(~salary + work_yrs, data = newdata)
## X-squared = 773.16, df = 516, p-value = 1.433e-12Here as p value is less than 0.05 we can reject the null hypothesis and state that there is a relation between work experience and starting salaries.
chisq.test(newdata$salary, newdata$frstlang)## Warning in chisq.test(newdata$salary, newdata$frstlang): Chi-squared
## approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: newdata$salary and newdata$frstlang
## X-squared = 48.273, df = 43, p-value = 0.2682Since p-value > 0.05, we cannot reject the null hypothesis stating that there is no relation between first language and starting mba salaries.
Linear Regression model
fit.sex <- lm(salary ~ sex, data = newdata)
summary(fit.sex)##
## Call:
## lm(formula = salary ~ sex, data = newdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -67185 -53857 24317 45145 151817
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 41527 11820 3.513 0.000558 ***
## sex 13328 8977 1.485 0.139343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 52340 on 182 degrees of freedom
## Multiple R-squared: 0.01197, Adjusted R-squared: 0.006539
## F-statistic: 2.204 on 1 and 182 DF, p-value: 0.1393Since the p-value>0.05, there is no relation between starting salaries and sex.
fit.gmat <- lm(salary ~ gmat_tpc, data = newdata)
summary(fit.gmat)##
## Call:
## lm(formula = salary ~ gmat_tpc, data = newdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -82171 -55389 30525 43427 151841
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 83169.6 25831.5 3.220 0.00152 **
## gmat_tpc -294.3 300.0 -0.981 0.32788
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 52520 on 182 degrees of freedom
## Multiple R-squared: 0.00526, Adjusted R-squared: -0.0002054
## F-statistic: 0.9624 on 1 and 182 DF, p-value: 0.3279Since p value is greater than 0.05, there’s no relation between gmat percentile and starting salaries.
fit.exp <- lm(salary ~ work_yrs, data = newdata)
summary(fit.exp)##
## Call:
## lm(formula = salary ~ work_yrs, data = newdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -77149 -55208 29637 45450 119911
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 45236 6632 6.821 1.29e-10 ***
## work_yrs 3657 1539 2.377 0.0185 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 51860 on 182 degrees of freedom
## Multiple R-squared: 0.0301, Adjusted R-squared: 0.02477
## F-statistic: 5.649 on 1 and 182 DF, p-value: 0.01851Since p value is < 0.05, there is a relation between work experience in years and the starting salaries of MBA graduates. R-square: 3.01% Adjusted R-square: 2.4%
fitted(fit.exp)## 5 9 10 11 12 13 14
## 52549.55 52549.55 52549.55 52549.55 52549.55 56206.41 52549.55
## 15 16 17 18 19 20 21
## 59863.28 52549.55 59863.28 56206.41 52549.55 59863.28 59863.28
## 26 30 35 36 37 38 39
## 63520.14 59863.28 48892.68 52549.55 52549.55 56206.41 52549.55
## 40 41 42 43 44 45 46
## 63520.14 45235.82 48892.68 56206.41 48892.68 59863.28 52549.55
## 47 48 49 50 51 52 53
## 52549.55 67177.01 52549.55 56206.41 56206.41 52549.55 63520.14
## 54 55 56 57 58 59 60
## 67177.01 74490.74 67177.01 56206.41 56206.41 67177.01 103745.66
## 61 62 63 64 65 66 67
## 59863.28 48892.68 81804.47 56206.41 63520.14 63520.14 74490.74
## 68 69 78 79 80 81 82
## 100088.80 48892.68 56206.41 52549.55 52549.55 56206.41 52549.55
## 83 84 85 86 87 91 94
## 52549.55 56206.41 52549.55 52549.55 56206.41 52549.55 59863.28
## 95 96 99 101 105 108 115
## 59863.28 59863.28 59863.28 59863.28 67177.01 59863.28 48892.68
## 116 117 118 119 120 121 122
## 52549.55 74490.74 52549.55 56206.41 52549.55 52549.55 52549.55
## 123 124 125 126 127 128 129
## 52549.55 56206.41 63520.14 52549.55 59863.28 52549.55 56206.41
## 130 131 132 133 134 135 136
## 59863.28 56206.41 56206.41 103745.66 52549.55 67177.01 48892.68
## 137 138 139 145 148 149 152
## 59863.28 59863.28 52549.55 48892.68 59863.28 52549.55 56206.41
## 153 154 155 156 157 158 161
## 56206.41 52549.55 59863.28 56206.41 56206.41 59863.28 59863.28
## 166 170 171 172 173 174 175
## 45235.82 52549.55 56206.41 56206.41 52549.55 59863.28 56206.41
## 176 177 178 179 181 186 187
## 59863.28 59863.28 59863.28 78147.61 59863.28 48892.68 56206.41
## 188 189 190 191 192 193 194
## 52549.55 52549.55 59863.28 63520.14 59863.28 56206.41 52549.55
## 195 196 197 198 199 200 201
## 52549.55 52549.55 52549.55 59863.28 70833.87 56206.41 52549.55
## 202 203 204 205 206 207 208
## 52549.55 74490.74 67177.01 52549.55 67177.01 52549.55 59863.28
## 209 210 211 212 214 215 216
## 52549.55 52549.55 48892.68 52549.55 56206.41 48892.68 56206.41
## 217 221 223 224 225 226 228
## 52549.55 56206.41 56206.41 56206.41 56206.41 59863.28 59863.28
## 231 235 239 240 245 246 247
## 48892.68 56206.41 70833.87 56206.41 63520.14 67177.01 70833.87
## 248 249 251 252 256 257 258
## 67177.01 74490.74 70833.87 59863.28 52549.55 52549.55 56206.41
## 259 260 261 262 263 264 265
## 52549.55 56206.41 63520.14 52549.55 52549.55 52549.55 52549.55
## 266 267 268 269 270 271 272
## 52549.55 52549.55 56206.41 56206.41 59863.28 52549.55 56206.41
## 273 274
## 56206.41 100088.80fit.lang <- lm(salary ~ frstlang, data = newdata)
summary(fit.lang)##
## Call:
## lm(formula = salary ~ frstlang, data = newdata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -60451 -60450 26801 40376 184114
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 87011 13411 6.488 7.97e-10 ***
## frstlang -25562 11369 -2.248 0.0258 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 51940 on 182 degrees of freedom
## Multiple R-squared: 0.02702, Adjusted R-squared: 0.02168
## F-statistic: 5.055 on 1 and 182 DF, p-value: 0.02575Since p-value is < 0.05, there is a relation between first language and MBA starting salaries. R-Squared: 2.7% Adjusted R-Squared: 2.1%
Cleary, the most significant factor is work experience in determining the starting salaries of MBA salaries.
Those who did not get a job
newdata2 <- subset(mbasalaries.df, salary==0)
newdata2## age sex gmat_tot gmat_qpc gmat_vpc gmat_tpc s_avg f_avg quarter
## 1 23 2 620 77 87 87 3.40 3.00 1
## 2 24 1 610 90 71 87 3.50 4.00 1
## 3 24 1 670 99 78 95 3.30 3.25 1
## 4 24 1 570 56 81 75 3.30 2.67 1
## 6 24 1 640 82 89 91 3.90 3.75 1
## 7 25 1 610 89 74 87 3.40 3.50 1
## 8 25 2 650 88 89 92 3.30 3.75 1
## 22 27 1 740 99 96 99 3.50 3.50 1
## 23 27 1 750 99 98 99 3.40 3.50 1
## 24 28 2 540 75 50 65 3.60 4.00 1
## 25 29 1 580 56 87 78 3.64 3.33 1
## 27 31 2 560 60 78 72 3.30 3.75 1
## 28 32 1 760 99 99 99 3.40 3.00 1
## 29 32 1 640 79 91 91 3.60 3.75 1
## 31 34 2 620 75 89 87 3.30 3.00 1
## 32 37 2 560 43 87 72 3.40 3.50 1
## 33 42 2 650 75 98 93 3.38 3.00 1
## 34 48 1 590 84 62 81 3.80 4.00 1
## 70 22 1 600 95 54 83 3.00 3.00 2
## 71 23 1 640 89 87 92 3.00 3.00 2
## 72 24 1 550 73 63 69 3.10 3.00 2
## 73 24 1 570 82 58 75 3.09 3.50 2
## 74 24 1 620 82 84 87 3.10 3.50 2
## 75 25 2 570 61 81 76 3.00 3.25 2
## 76 25 1 660 94 84 94 3.27 3.75 2
## 77 25 1 680 94 92 97 3.17 3.50 2
## 88 26 2 560 64 71 72 3.20 3.25 2
## 89 26 1 560 87 41 72 3.00 3.00 2
## 90 26 1 530 68 54 62 3.09 3.17 2
## 92 27 1 720 99 95 99 3.10 3.25 2
## 93 27 1 590 60 87 81 3.00 2.75 2
## 97 28 1 620 81 90 89 3.20 3.00 2
## 98 28 2 610 85 78 86 3.10 3.00 2
## 100 29 1 660 94 87 94 3.00 3.00 2
## 102 29 1 510 57 50 55 3.27 3.40 2
## 103 29 2 640 90 84 92 3.20 3.00 2
## 104 29 1 610 91 62 86 3.10 3.67 2
## 106 29 1 580 79 67 78 3.00 3.25 2
## 107 30 1 680 97 87 96 3.00 3.00 2
## 109 32 2 610 64 89 86 3.25 0.00 2
## 110 35 1 540 43 78 65 3.20 3.25 2
## 111 35 1 630 66 95 90 3.08 3.25 2
## 112 36 2 530 48 71 62 3.00 2.50 2
## 113 36 1 650 87 89 93 3.00 3.20 2
## 114 43 1 630 82 87 89 3.10 3.00 2
## 140 23 1 720 95 98 99 2.80 2.50 3
## 141 24 2 640 94 78 92 2.90 3.25 3
## 142 24 1 710 96 97 99 2.80 2.75 3
## 143 24 1 670 94 89 96 2.70 3.00 3
## 144 24 2 710 97 97 99 2.80 3.00 3
## 146 24 1 600 89 62 83 2.90 3.00 3
## 147 24 2 640 96 71 91 2.70 2.50 3
## 150 25 1 550 72 58 69 2.90 3.00 3
## 151 25 1 710 99 91 98 2.90 3.25 3
## 159 26 1 560 56 81 72 2.80 3.25 3
## 160 26 1 540 52 71 65 2.70 2.75 3
## 162 26 2 570 48 89 75 2.82 2.50 3
## 163 26 1 610 82 81 86 2.90 2.75 3
## 164 27 1 650 89 84 93 2.90 3.00 3
## 165 27 2 550 66 63 69 2.90 3.00 3
## 167 27 1 610 97 45 86 2.70 2.50 3
## 168 27 2 630 82 89 89 2.70 3.25 3
## 169 27 2 560 61 74 73 2.80 3.25 3
## 180 29 1 590 92 58 81 2.80 2.75 3
## 182 32 1 550 52 78 71 2.70 2.75 3
## 183 34 1 610 79 81 86 2.80 3.00 3
## 184 34 1 610 82 78 86 2.70 3.00 3
## 185 43 1 480 49 41 45 2.90 3.25 3
## 213 25 1 730 98 96 99 2.40 2.75 4
## 218 25 1 700 99 87 98 2.00 2.00 4
## 219 26 1 660 93 87 95 2.60 2.00 4
## 220 26 1 450 28 46 34 2.10 2.00 4
## 222 26 1 600 75 78 83 2.20 2.25 4
## 227 27 2 560 59 74 73 2.40 2.50 4
## 229 27 1 630 93 78 91 2.10 2.50 4
## 230 27 1 580 84 58 78 2.70 2.75 4
## 232 27 1 670 89 91 95 3.60 3.25 4
## 233 27 1 580 74 70 78 3.40 3.25 4
## 234 28 1 560 74 67 73 3.60 3.60 4
## 236 28 1 710 94 98 99 3.40 3.75 4
## 237 28 1 570 69 71 0 2.30 2.50 4
## 238 29 1 530 35 81 62 3.30 2.75 4
## 241 29 1 670 91 91 95 3.30 3.25 4
## 242 29 1 630 99 50 89 2.90 3.25 4
## 243 29 2 680 89 96 96 2.80 3.00 4
## 244 30 1 650 88 92 93 3.45 3.83 4
## 250 31 1 570 75 62 75 2.80 3.00 4
## 253 32 1 510 79 22 54 2.30 2.25 4
## 254 35 1 570 72 71 75 3.30 4.00 4
## 255 39 2 700 89 98 98 3.30 3.25 4
## work_yrs frstlang salary satis
## 1 2 1 0 7
## 2 2 1 0 6
## 3 2 1 0 6
## 4 1 1 0 7
## 6 2 1 0 6
## 7 2 1 0 5
## 8 2 1 0 6
## 22 3 1 0 6
## 23 1 2 0 5
## 24 5 1 0 5
## 25 3 1 0 5
## 27 10 1 0 7
## 28 5 1 0 5
## 29 7 1 0 6
## 31 7 1 0 6
## 32 9 1 0 6
## 33 13 1 0 5
## 34 22 1 0 6
## 70 1 1 0 5
## 71 2 1 0 7
## 72 0 2 0 5
## 73 2 1 0 6
## 74 1 1 0 5
## 75 3 1 0 4
## 76 2 1 0 5
## 77 2 1 0 6
## 88 3 1 0 6
## 89 3 1 0 6
## 90 4 2 0 5
## 92 5 1 0 5
## 93 3 1 0 6
## 97 4 1 0 6
## 98 5 1 0 6
## 100 1 1 0 6
## 102 5 1 0 5
## 103 3 1 0 5
## 104 7 1 0 5
## 106 4 1 0 6
## 107 4 1 0 5
## 109 11 1 0 7
## 110 8 1 0 5
## 111 12 1 0 5
## 112 7 1 0 5
## 113 18 1 0 6
## 114 16 1 0 5
## 140 1 1 0 5
## 141 2 2 0 4
## 142 2 1 0 7
## 143 2 1 0 7
## 144 2 1 0 7
## 146 1 1 0 6
## 147 2 1 0 6
## 150 3 1 0 6
## 151 1 1 0 6
## 159 4 1 0 6
## 160 2 1 0 6
## 162 3 1 0 5
## 163 3 1 0 6
## 164 2 1 0 6
## 165 3 1 0 4
## 167 4 2 0 5
## 168 5 1 0 6
## 169 5 1 0 6
## 180 3 2 0 5
## 182 7 1 0 6
## 183 11 1 0 6
## 184 12 1 0 5
## 185 22 1 0 5
## 213 2 1 0 6
## 218 1 1 0 7
## 219 2 1 0 5
## 220 4 1 0 6
## 222 2 1 0 6
## 227 2 1 0 5
## 229 4 1 0 5
## 230 1 1 0 5
## 232 5 1 0 6
## 233 3 1 0 6
## 234 5 1 0 5
## 236 6 1 0 6
## 237 5 1 0 5
## 238 6 1 0 7
## 241 3 1 0 5
## 242 1 2 0 4
## 243 4 1 0 5
## 244 2 1 0 6
## 250 1 1 0 6
## 253 5 2 0 5
## 254 8 1 0 6
## 255 5 1 0 5chisq.test(newdata2$satis, newdata2$gmat_tot)## Warning in chisq.test(newdata2$satis, newdata2$gmat_tot): Chi-squared
## approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: newdata2$satis and newdata2$gmat_tot
## X-squared = 54.864, df = 75, p-value = 0.9611Since p-value is > 0.05, there is no relation between gmat total score and satisfaction levels of MBA graduates.