MBA starting salary case analysis
Srijani Das
February 20, 2018
This is my R markdown document of the case study on MBA starting salary.
Read the data in R
# Read the data
salary.df <- read.csv(paste("MBASalData.csv", sep=""))
View(salary.df)Summarize the data set.
# Summarize the data
attach(salary.df)
library(psych)
describe(salary.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 22.45Generate boxplots to visualize the distribution of each varible independently
boxplot(salary.df$gmat_tot, horizontal=TRUE,
main="GMAT Total score")
boxplot(salary.df$gmat_qpc, horizontal=TRUE,
main="quantitative GMAT percentile")
boxplot(salary.df$gmat_vpc, horizontal=TRUE,
main="verbal GMAT percentile")
boxplot(salary.df$gmat_tpc, horizontal=TRUE,
main="total GMAT percentile")
boxplot(salary.df$s_avg, horizontal=TRUE,
main="spring MBA average")
boxplot(salary.df$f_avg, horizontal=TRUE,
main="fall MBA average")
boxplot(salary.df$work_yrs, horizontal=TRUE,
main="years of work experience")
boxplot(salary.df$salary, horizontal=TRUE,
main="Starting salary")
boxplot(salary.df$satis, horizontal=TRUE,
main="degree of satisfaction with MBA program ")
Draw Scatter Plots to understand how are the variables correlated pair-wise
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitlibrary(psych)
scatterplotMatrix(formula = ~ gmat_tot + gmat_qpc + gmat_vpc + gmat_tpc ,
data = salary.df, diagonal="histogram")
library(car)
library(psych)
scatterplotMatrix(formula = ~ gmat_tpc + work_yrs + salary + satis ,
data = salary.df, diagonal="histogram")
CORRELATION MATRIX
library(Hmisc)## Loading required package: lattice## Loading required package: survival## Loading required package: Formula## Loading required package: ggplot2##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alpha##
## Attaching package: 'Hmisc'## The following object is masked from 'package:psych':
##
## describe## The following objects are masked from 'package:base':
##
## format.pval, unitscolsalary <- c("salary","age","sex","work_yrs")
corMatrix <- rcorr(as.matrix(salary.df[,colsalary]))
corMatrix## salary age sex work_yrs
## salary 1.00 -0.06 0.07 0.01
## age -0.06 1.00 -0.03 0.86
## sex 0.07 -0.03 1.00 -0.01
## work_yrs 0.01 0.86 -0.01 1.00
##
## n= 274
##
##
## P
## salary age sex work_yrs
## salary 0.3020 0.2560 0.8818
## age 0.3020 0.6432 0.0000
## sex 0.2560 0.6432 0.8523
## work_yrs 0.8818 0.0000 0.8523Corrgram
library(corrgram)
corrgram(salary.df, order=FALSE,
lower.panel=panel.shade,
upper.panel=panel.pie,
diag.panel=panel.minmax,
text.panel=panel.txt,
main="Corrgram of MBA Salary Data")
Take a subset of the dataset consisting of both of these 2 types of students people who actually got and did not get job.
job.df<-salary.df[which(salary.df$salary!=998 & salary.df$salary!=999),]
View(job.df)Take a subset of the dataset consisting of only those people who actually got a job.
gotjob.df<-job.df[which(job.df$salary!=0),]
View(gotjob.df)Here y=salary, and this salary depends upon various factors like GMAT percentile, sex, first language, work experience, spring MBA average, fall MBA average etc which are considered here as ‘x’.
Draw Contingency Tables
mytable <- xtabs(~ salary+sex , data=gotjob.df)
mytable## sex
## salary 1 2
## 64000 0 1
## 77000 1 0
## 78256 0 1
## 82000 0 1
## 85000 1 3
## 86000 0 2
## 88000 0 1
## 88500 1 0
## 90000 3 0
## 92000 2 1
## 93000 2 1
## 95000 4 3
## 96000 3 1
## 96500 1 0
## 97000 2 0
## 98000 6 4
## 99000 0 1
## 100000 4 5
## 100400 1 0
## 101000 0 2
## 101100 1 0
## 101600 1 0
## 102500 1 0
## 103000 1 0
## 104000 2 0
## 105000 11 0
## 106000 2 1
## 107000 1 0
## 107300 1 0
## 107500 1 0
## 108000 2 0
## 110000 0 1
## 112000 3 0
## 115000 5 0
## 118000 1 0
## 120000 3 1
## 126710 1 0
## 130000 1 0
## 145800 1 0
## 146000 1 0
## 162000 1 0
## 220000 0 1mytable <- xtabs(~ frstlang+salary , data=gotjob.df)
mytable## salary
## frstlang 64000 77000 78256 82000 85000 86000 88000 88500 90000 92000 93000
## 1 1 1 1 1 4 2 1 1 3 3 3
## 2 0 0 0 0 0 0 0 0 0 0 0
## salary
## frstlang 95000 96000 96500 97000 98000 99000 100000 100400 101000 101100
## 1 7 4 1 2 8 0 9 1 2 1
## 2 0 0 0 0 2 1 0 0 0 0
## salary
## frstlang 101600 102500 103000 104000 105000 106000 107000 107300 107500
## 1 1 1 1 1 11 3 1 0 1
## 2 0 0 0 1 0 0 0 1 0
## salary
## frstlang 108000 110000 112000 115000 118000 120000 126710 130000 145800
## 1 2 1 3 5 0 4 1 1 1
## 2 0 0 0 0 1 0 0 0 0
## salary
## frstlang 146000 162000 220000
## 1 1 1 0
## 2 0 0 1mytable <- xtabs(~ salary+work_yrs , data=gotjob.df)
mytable## work_yrs
## salary 0 1 2 3 4 5 6 7 8 10 15 16
## 64000 0 0 1 0 0 0 0 0 0 0 0 0
## 77000 0 0 1 0 0 0 0 0 0 0 0 0
## 78256 0 1 0 0 0 0 0 0 0 0 0 0
## 82000 0 1 0 0 0 0 0 0 0 0 0 0
## 85000 0 1 2 1 0 0 0 0 0 0 0 0
## 86000 0 0 1 1 0 0 0 0 0 0 0 0
## 88000 0 0 0 1 0 0 0 0 0 0 0 0
## 88500 0 0 0 1 0 0 0 0 0 0 0 0
## 90000 0 0 2 0 0 1 0 0 0 0 0 0
## 92000 0 0 3 0 0 0 0 0 0 0 0 0
## 93000 0 0 0 0 1 1 0 0 1 0 0 0
## 95000 1 1 2 2 0 1 0 0 0 0 0 0
## 96000 0 1 2 0 1 0 0 0 0 0 0 0
## 96500 0 0 1 0 0 0 0 0 0 0 0 0
## 97000 0 0 0 1 1 0 0 0 0 0 0 0
## 98000 0 0 7 1 1 0 0 1 0 0 0 0
## 99000 0 0 0 0 0 1 0 0 0 0 0 0
## 100000 0 0 6 1 1 0 1 0 0 0 0 0
## 100400 0 0 0 1 0 0 0 0 0 0 0 0
## 101000 0 0 2 0 0 0 0 0 0 0 0 0
## 101100 0 0 0 0 0 0 0 0 1 0 0 0
## 101600 0 0 0 1 0 0 0 0 0 0 0 0
## 102500 0 0 0 0 0 0 1 0 0 0 0 0
## 103000 0 0 0 1 0 0 0 0 0 0 0 0
## 104000 0 0 0 0 2 0 0 0 0 0 0 0
## 105000 0 0 4 4 0 1 1 0 0 0 0 1
## 106000 0 0 0 0 0 0 2 0 1 0 0 0
## 107000 0 0 1 0 0 0 0 0 0 0 0 0
## 107300 0 0 1 0 0 0 0 0 0 0 0 0
## 107500 0 0 0 1 0 0 0 0 0 0 0 0
## 108000 0 0 0 1 1 0 0 0 0 0 0 0
## 110000 0 0 0 0 0 0 1 0 0 0 0 0
## 112000 0 0 1 0 0 0 1 0 0 0 0 1
## 115000 0 2 0 1 2 0 0 0 0 0 0 0
## 118000 0 0 0 0 0 0 0 0 0 1 0 0
## 120000 0 0 0 1 0 2 0 0 1 0 0 0
## 126710 0 0 0 1 0 0 0 0 0 0 0 0
## 130000 0 0 0 0 1 0 0 0 0 0 0 0
## 145800 0 0 1 0 0 0 0 0 0 0 0 0
## 146000 0 0 0 0 0 0 0 0 0 0 1 0
## 162000 0 1 0 0 0 0 0 0 0 0 0 0
## 220000 0 0 0 0 0 0 0 0 0 0 1 0t-test analysis
t.test(salary,age , data=gotjob.df)##
## Welch Two Sample t-test
##
## data: salary and age
## t = 12.67, df = 273, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 32938.51 45058.15
## sample estimates:
## mean of x mean of y
## 39025.68978 27.35766t.test(salary,work_yrs , data=gotjob.df)##
## Welch Two Sample t-test
##
## data: salary and work_yrs
## t = 12.677, df = 273, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 32961.99 45081.64
## sample estimates:
## mean of x mean of y
## 39025.689781 3.872263Regression analysis
m1 <- lm(salary ~
gmat_tpc
+ s_avg
+ f_avg,
data=gotjob.df)
summary(m1)##
## Call:
## lm(formula = salary ~ gmat_tpc + s_avg + f_avg, data = gotjob.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -45140 -7934 -1887 3623 112357
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 114442.5 19076.0 5.999 3.26e-08 ***
## gmat_tpc -239.5 159.7 -1.499 0.1370
## s_avg 9719.3 5176.8 1.877 0.0634 .
## f_avg -6867.3 3988.1 -1.722 0.0882 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17580 on 99 degrees of freedom
## Multiple R-squared: 0.06029, Adjusted R-squared: 0.03182
## F-statistic: 2.117 on 3 and 99 DF, p-value: 0.1029m2 <- lm(salary ~
work_yrs
+ frstlang
+ sex
+ age,
data=gotjob.df)
summary(m2)##
## Call:
## lm(formula = salary ~ work_yrs + frstlang + sex + age, data = gotjob.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29056 -9070 -1211 5858 79078
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 51623.0 24708.1 2.089 0.0393 *
## work_yrs 916.9 1119.1 0.819 0.4146
## frstlang 10017.9 6785.8 1.476 0.1431
## sex -4655.5 3418.8 -1.362 0.1764
## age 1620.5 1089.7 1.487 0.1402
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15510 on 98 degrees of freedom
## Multiple R-squared: 0.2763, Adjusted R-squared: 0.2468
## F-statistic: 9.355 on 4 and 98 DF, p-value: 1.907e-06m3 <- lm(salary ~
+ frstlang
+ sex
+ s_avg
+ f_avg
+ age
+ work_yrs,
data=gotjob.df)
summary(m3)##
## Call:
## lm(formula = salary ~ +frstlang + sex + s_avg + f_avg + age +
## work_yrs, data = gotjob.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -30413 -8757 -1921 5966 81580
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 45104.8 27753.7 1.625 0.107
## frstlang 11264.2 7061.9 1.595 0.114
## sex -4954.4 3490.7 -1.419 0.159
## s_avg 3456.5 4953.5 0.698 0.487
## f_avg -603.8 3812.6 -0.158 0.874
## age 1499.4 1113.9 1.346 0.181
## work_yrs 915.9 1130.2 0.810 0.420
##
## Residual standard error: 15620 on 96 degrees of freedom
## Multiple R-squared: 0.2804, Adjusted R-squared: 0.2354
## F-statistic: 6.233 on 6 and 96 DF, p-value: 1.481e-05m4 <- lm(salary ~
work_yrs
+ frstlang,
data=gotjob.df)
summary(m4)##
## Call:
## lm(formula = salary ~ work_yrs + frstlang, data = gotjob.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -33972 -8955 -455 4545 76681
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 79941.4 6788.8 11.775 < 2e-16 ***
## work_yrs 2483.3 527.9 4.704 8.18e-06 ***
## frstlang 13064.0 6283.2 2.079 0.0402 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15740 on 100 degrees of freedom
## Multiple R-squared: 0.2396, Adjusted R-squared: 0.2244
## F-statistic: 15.75 on 2 and 100 DF, p-value: 1.128e-06m5 <- lm(salary ~
work_yrs
+ sex
+ age,
data=gotjob.df)
summary(m5)##
## Call:
## lm(formula = salary ~ work_yrs + sex + age, data = gotjob.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29250 -9239 -1146 5429 84318
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 45674.9 24522.2 1.863 0.0655 .
## work_yrs 478.2 1085.3 0.441 0.6604
## sex -3852.2 3395.2 -1.135 0.2593
## age 2263.4 1004.8 2.253 0.0265 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15600 on 99 degrees of freedom
## Multiple R-squared: 0.2602, Adjusted R-squared: 0.2378
## F-statistic: 11.61 on 3 and 99 DF, p-value: 1.389e-06m6 <- lm(salary ~
work_yrs
+ age,
data=gotjob.df)
summary(m6)##
## Call:
## lm(formula = salary ~ work_yrs + age, data = gotjob.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -31675 -8099 -2108 4411 80650
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36967.5 23323.8 1.585 0.1161
## work_yrs 388.8 1084.0 0.359 0.7206
## age 2413.8 997.4 2.420 0.0173 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15620 on 100 degrees of freedom
## Multiple R-squared: 0.2506, Adjusted R-squared: 0.2356
## F-statistic: 16.72 on 2 and 100 DF, p-value: 5.438e-07m7 <- lm(salary ~ age, data=gotjob.df)
summary(m7)##
## Call:
## lm(formula = salary ~ age, data = gotjob.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -31454 -8533 -2182 4546 80886
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 29962.6 12697.8 2.360 0.0202 *
## age 2728.8 470.7 5.797 7.75e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15550 on 101 degrees of freedom
## Multiple R-squared: 0.2496, Adjusted R-squared: 0.2422
## F-statistic: 33.6 on 1 and 101 DF, p-value: 7.748e-08m8 <- lm(salary ~
s_avg
+ f_avg
+ age,
data=gotjob.df)
summary(m8)##
## Call:
## lm(formula = salary ~ s_avg + f_avg + age, data = gotjob.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32079 -8073 -2362 4671 82120
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 28077.5 18901.4 1.485 0.141
## s_avg 1435.6 4795.8 0.299 0.765
## f_avg -469.6 3765.6 -0.125 0.901
## age 2687.6 508.7 5.283 7.55e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15700 on 99 degrees of freedom
## Multiple R-squared: 0.2503, Adjusted R-squared: 0.2276
## F-statistic: 11.02 on 3 and 99 DF, p-value: 2.635e-06m9 <- lm(salary ~
work_yrs
+ frstlang
+ gmat_tpc
+ sex
+ age
+ s_avg
+ f_avg,
data=gotjob.df)
summary(m9)##
## Call:
## lm(formula = salary ~ work_yrs + frstlang + gmat_tpc + sex +
## age + s_avg + f_avg, data = gotjob.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32354 -9144 -1995 6557 78985
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 53884.7 29504.9 1.826 0.0709 .
## work_yrs 775.0 1142.7 0.678 0.4993
## frstlang 10442.9 7130.6 1.465 0.1464
## gmat_tpc -128.9 145.8 -0.885 0.3786
## sex -5095.5 3498.3 -1.457 0.1485
## age 1578.8 1118.7 1.411 0.1614
## s_avg 4030.7 5001.4 0.806 0.4223
## f_avg -669.5 3817.7 -0.175 0.8612
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15640 on 95 degrees of freedom
## Multiple R-squared: 0.2862, Adjusted R-squared: 0.2336
## F-statistic: 5.442 on 7 and 95 DF, p-value: 2.828e-05From the above analysis of of all the models I found that the adjusted R-squared value is highest for the model 2(m2) that is 0.2468.So,model 2 is the best model that fits data. Although this 24.68% is not that high percentage but still we can conclude that starting salary mostly depends upon work experience, first language, sex and age.