MBA starting salaries
Pooja Gundu
December 26, 2017
->Since,rating of MBA programs uses graduates’ salaries as a large component of its rating system in many of the surveys, various dependencies of the staring salary of the students should be signified. Also the degree of satisfaction of the MBA program plays a prominent role for analyzing purposes.
->Here, the dependence of various variables such as GMAT score, GMAT percentile, Spring average , Fall average , years of work experience , Quartile ranking , first language, sx,etc may positively ,neutrally or negatively rely on the starting salary and the degree of satisfaction of the MBA program .
–>Reading and viewing the dataset into R
mba.df <- read.csv(paste("MBA Starting Salaries Data.csv", sep=""))
View(mba.df)–> Summarizing the data
library(psych)
describe(mba.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 22.45–> Visualizing the distribution of each variable independently
par(mfrow=c(2,2))
with(mba.df, boxplot(mba.df$age,
main="Boxplot of age",
col=c("yellow"),
horizontal=TRUE,
xlab="Age (in years)" ))
with(mba.df, boxplot(mba.df$gmat_tot,
main="Boxplot of GMAT Score",
col=c("yellow"),
horizontal=TRUE,
xlab="GMAT Score" ))
with(mba.df, boxplot(mba.df$gmat_tpc,
main="Boxplot of GMAT Percentile",
col=c("yellow"),
horizontal=TRUE,
xlab="Overall GMAT Percentile" ))
with(mba.df, boxplot(mba.df$work_yrs,
main="Boxplot of work experience",
col=c("yellow"),
horizontal=TRUE,
xlab="Work Years Experience" ))
par(mfrow=c(2,2))
with(mba.df, boxplot(mba.df$salary,
main="Boxplot of Starting salary",
col=c("yellow"),
horizontal=TRUE,
xlab="Starting salaries" ))
with(mba.df,boxplot(mba.df$quarter,
main="Boxplot of Quartile Ranking",
col=c("yellow"),
horizontal=TRUE,
xlab="Quartile Ranking" ))
with(mba.df, boxplot(mba.df$s_avg,
main="Boxplot of Spring MBA Average",
col=c("yellow"),
horizontal=TRUE,
xlab="Spring MBA Average" ))
with(mba.df, boxplot(mba.df$f_avg,
main="Boxplot of Fall MBA Average",
col=c("yellow"),
horizontal=TRUE,
xlab="Fall MBA Average" ))
Frequency table of each variable
table(mba.df$sex)##
## 1 2
## 206 68table(mba.df$quarter)##
## 1 2 3 4
## 69 70 70 65table(mba.df$frstlang)##
## 1 2
## 242 32table(mba.df$satis)##
## 1 2 3 4 5 6 7 998
## 1 1 5 17 74 97 33 46–>Pair-wise Visualization
boxplot(mba.df$salary ~ mba.df$sex, data=mba.df, horizontal=TRUE, yaxt="n",
ylab="Gender", xlab="Salary",
main="Comparison of Salaries of Males and Females")
axis(side=2, at=c(1,2), labels=c("Females", "Males"))
boxplot(mba.df$salary ~ mba.df$frstlang, data=mba.df, horizontal=TRUE, yaxt="n",
ylab="First language", xlab="Salary",
main="Comparison of Salaries based on their first language")
axis(side=2, at=c(1,2), labels=c("english", "others"))
boxplot(mba.df$salary ~ mba.df$quarter, data=mba.df, horizontal=TRUE, yaxt="n",
ylab="quartile rating", xlab="Salary",
main="Comparison of Salaries of Quartile ranking")
axis(side=2, at=c(1,2,3,4), labels=c("first", "secnd","thrd","fourth"))
boxplot(mba.df$salary ~ mba.df$satis, data=mba.df, horizontal=TRUE, yaxt="n",
ylab="Satisfactory degree", xlab="Salary",
main="Comparison of Salaries on degree of satisfaction of students")
axis(side=2, at=c(1,2,3,4,5,6,7,8), labels=c("1", "2","3","4","5","6","7","no"))
–>Scatterplots to understand variable correlation
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitscatterplot(salary ~ gmat_tpc, data=mba.df, spread=FALSE,
smoother.args=list(lty=2),pch=19,
main="Scatterplot of Salary vs. GMAT percentile",
xlab="gmat percentile",
ylab="salary ",cex=0.6)
scatterplot(salary ~ gmat_tot, data=mba.df, spread=FALSE,
smoother.args=list(lty=2),pch=19,xlim=c(1,1000),
main="Scatterplot of Salary vs. GMAT SCore",
xlab="GMAT Score",
ylab="salary ",cex=0.6)
scatterplot(salary ~ work_yrs, data=mba.df, spread=FALSE,
smoother.args=list(lty=2),pch=19,xlim=c(1,8),
main="Scatterplot of Salary vs. their work experience",
xlab="Work experience",
ylab="salary ",cex=0.6)
scatterplot(salary ~ s_avg, data=mba.df, spread=FALSE,
smoother.args=list(lty=2),pch=19,xlim=c(1,5),
main="Scatterplot of Salary vs. Spring average",
xlab="Spring average",
ylab="salary ",cex=0.6)
–>Jitter plots visualization
plot(jitter(mba.df$satis), jitter(mba.df$salary),
xlim = c(1,10),
xlab="Satisfaction degree", ylab="Salary")
plot(jitter(mba.df$quarter), jitter(mba.df$salary+1),
xlim = c(1,5),
xlab="Quartile rating", ylab="Salary")
–>Scatterplotmatrix
library(car)
scatterplotMatrix(formula = ~ age + gmat_tpc + gmat_qpc +
gmat_vpc+ s_avg + f_avg + gmat_tot + salary , cex=0.6,
spread=FALSE, smoother.args=list(lty=2),pch=19,
data=mba.df, diagonal="histogram")
–>Correlation between variables
round(cor(mba.df[ , ]),2)## age sex gmat_tot gmat_qpc gmat_vpc gmat_tpc s_avg f_avg
## age 1.00 -0.03 -0.15 -0.22 -0.04 -0.17 0.15 -0.02
## sex -0.03 1.00 -0.05 -0.16 0.07 -0.01 0.13 0.09
## gmat_tot -0.15 -0.05 1.00 0.72 0.75 0.85 0.11 0.10
## gmat_qpc -0.22 -0.16 0.72 1.00 0.15 0.65 -0.03 0.07
## gmat_vpc -0.04 0.07 0.75 0.15 1.00 0.67 0.20 0.08
## gmat_tpc -0.17 -0.01 0.85 0.65 0.67 1.00 0.12 0.08
## s_avg 0.15 0.13 0.11 -0.03 0.20 0.12 1.00 0.55
## f_avg -0.02 0.09 0.10 0.07 0.08 0.08 0.55 1.00
## quarter -0.05 -0.13 -0.09 0.04 -0.17 -0.08 -0.76 -0.45
## work_yrs 0.86 -0.01 -0.18 -0.24 -0.07 -0.17 0.13 -0.04
## frstlang 0.06 0.00 -0.14 0.14 -0.39 -0.10 -0.14 -0.04
## salary -0.06 0.07 -0.05 -0.04 -0.01 0.00 0.15 0.03
## satis -0.13 -0.05 0.08 0.06 0.06 0.09 -0.03 0.01
## quarter work_yrs frstlang salary satis
## age -0.05 0.86 0.06 -0.06 -0.13
## sex -0.13 -0.01 0.00 0.07 -0.05
## gmat_tot -0.09 -0.18 -0.14 -0.05 0.08
## gmat_qpc 0.04 -0.24 0.14 -0.04 0.06
## gmat_vpc -0.17 -0.07 -0.39 -0.01 0.06
## gmat_tpc -0.08 -0.17 -0.10 0.00 0.09
## s_avg -0.76 0.13 -0.14 0.15 -0.03
## f_avg -0.45 -0.04 -0.04 0.03 0.01
## quarter 1.00 -0.09 0.10 -0.16 0.00
## work_yrs -0.09 1.00 -0.03 0.01 -0.11
## frstlang 0.10 -0.03 1.00 -0.09 0.08
## salary -0.16 0.01 -0.09 1.00 -0.34
## satis 0.00 -0.11 0.08 -0.34 1.00–>Corrogram
library(corrgram)
corrgram(mba.df, order=FALSE,
lower.panel=panel.shade,
upper.panel=panel.pie,
diag.panel=panel.minmax,
text.panel=panel.txt,
main="Corrgram of all the intercorrelations")
–>Correlation visualization
library(corrplot) ## corrplot 0.84 loadedcorrplot(corr=cor(mba.df[ , ], use="complete.obs"),
method ="ellipse")
–> Covariance between variables
round(cov(mba.df[ , ]),2)## age sex gmat_tot gmat_qpc gmat_vpc gmat_tpc s_avg
## age 13.77 -0.05 -31.16 -11.93 -2.76 -8.84 0.21
## sex -0.05 0.19 -1.33 -1.05 0.55 -0.05 0.02
## gmat_tot -31.16 -1.33 3310.69 620.02 726.00 683.99 2.48
## gmat_qpc -11.93 -1.05 620.02 221.07 38.15 135.80 -0.17
## gmat_vpc -2.76 0.55 726.00 38.15 284.25 157.49 1.31
## gmat_tpc -8.84 -0.05 683.99 135.80 157.49 196.61 0.63
## s_avg 0.21 0.02 2.48 -0.17 1.31 0.63 0.15
## f_avg -0.03 0.02 3.15 0.58 0.67 0.59 0.11
## quarter -0.20 -0.06 -5.89 0.60 -3.27 -1.29 -0.32
## work_yrs 10.29 -0.02 -33.92 -11.37 -3.62 -7.86 0.16
## frstlang 0.07 0.00 -2.50 0.66 -2.11 -0.47 -0.02
## salary -11830.42 1518.26 -161159.99 -33358.23 -5273.85 3522.75 2831.60
## satis -176.35 -8.78 1765.26 334.84 392.36 484.25 -4.63
## f_avg quarter work_yrs frstlang salary satis
## age -0.03 -0.20 10.29 0.07 -11830.42 -176.35
## sex 0.02 -0.06 -0.02 0.00 1518.26 -8.78
## gmat_tot 3.15 -5.89 -33.92 -2.50 -161159.99 1765.26
## gmat_qpc 0.58 0.60 -11.37 0.66 -33358.23 334.84
## gmat_vpc 0.67 -3.27 -3.62 -2.11 -5273.85 392.36
## gmat_tpc 0.59 -1.29 -7.86 -0.47 3522.75 484.25
## s_avg 0.11 -0.32 0.16 -0.02 2831.60 -4.63
## f_avg 0.28 -0.26 -0.07 -0.01 787.66 2.13
## quarter -0.26 1.23 -0.31 0.04 -9296.21 -0.01
## work_yrs -0.07 -0.31 10.45 -0.03 1486.15 -131.24
## frstlang -0.01 0.04 -0.03 0.10 -1419.59 9.48
## salary 787.66 -9296.21 1486.15 -1419.59 2596061571.52 -6347115.38
## satis 2.13 -0.01 -131.24 9.48 -6347115.38 138097.38–>Dimensions of dataset
dim(mba.df)## [1] 274 13–>Finding the dimensions of the subset with people who actually got the job
-subset with people who didnt get job
nojob.df<- mba.df[which(mba.df$salary=="0" ), ]
View(nojob.df)-subset with people who did not fill the survey
nojob1.df<- mba.df[which(mba.df$salary=="998" ), ]
View(nojob1.df)-subset with people who answered the survey but did not disclose salary data
nojob2.df<- mba.df[which(mba.df$salary=="999" ), ]
View(nojob2.df)–>Dimensions of each subset
dim(nojob.df)## [1] 90 13- 90 people did not get the job
dim(nojob1.df)## [1] 46 13*46 people did not fill the survey
dim(nojob2.df)## [1] 35 13*35 people answered the survey but did not disclose salary data
-So,on a total , 171 people have no entry or no job
-Implying 103 (274-171) people had got the job
–>Subset (job) with people who got the job
attach(mba.df)
job <- mba.df[order(-salary)[1:103], ]
View(job)–>Contingency table
-One-way contingency tables
mytable <- with(job, table(satis))
mytable ## satis
## 3 4 5 6 7
## 1 1 29 50 22mytable1 <- with(job, table(sex))
mytable1 ## sex
## 1 2
## 72 31mytable2 <- with(job, table(quarter))
mytable2 ## quarter
## 1 2 3 4
## 35 25 24 19mytable3 <- with(job, table(frstlang))
mytable3## frstlang
## 1 2
## 96 7-Three-way Contingency tables
mytable21 <- xtabs(~ sex+quarter+satis, data=job)
ftable(mytable21)## satis 3 4 5 6 7
## sex quarter
## 1 1 0 1 7 10 5
## 2 0 0 4 13 2
## 3 0 0 4 9 4
## 4 0 0 2 8 3
## 2 1 1 0 6 3 2
## 2 0 0 4 1 1
## 3 0 0 1 3 3
## 4 0 0 1 3 2mytable22 <- xtabs(~ frstlang+sex+satis, data=job)
ftable(mytable22)## satis 3 4 5 6 7
## frstlang sex
## 1 1 0 1 17 38 12
## 2 1 0 11 8 8
## 2 1 0 0 0 2 2
## 2 0 0 1 2 0–>Chi-squared test
mytable11 <- xtabs(~ satis+sex, data=job)
mytable11## sex
## satis 1 2
## 3 0 1
## 4 1 0
## 5 17 12
## 6 40 10
## 7 14 8chisq.test(mytable11)## Warning in chisq.test(mytable11): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test
##
## data: mytable11
## X-squared = 7.3413, df = 4, p-value = 0.1189mytable12 <- xtabs(~ satis+quarter, data=job)
mytable12## quarter
## satis 1 2 3 4
## 3 1 0 0 0
## 4 1 0 0 0
## 5 13 8 5 3
## 6 13 14 12 11
## 7 7 3 7 5chisq.test(mytable12)## Warning in chisq.test(mytable12): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test
##
## data: mytable12
## X-squared = 10.045, df = 12, p-value = 0.612mytable13 <- xtabs(~ satis+frstlang, data=job)
mytable13## frstlang
## satis 1 2
## 3 1 0
## 4 1 0
## 5 28 1
## 6 46 4
## 7 20 2chisq.test(mytable13)## Warning in chisq.test(mytable13): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test
##
## data: mytable13
## X-squared = 0.95627, df = 4, p-value = 0.9164mytable14 <- xtabs(~ sex+frstlang, data=job)
mytable14## frstlang
## sex 1 2
## 1 68 4
## 2 28 3chisq.test(mytable14)## Warning in chisq.test(mytable14): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: mytable14
## X-squared = 0.11264, df = 1, p-value = 0.7372mytable15 <- xtabs(~ sex+quarter, data=job)
mytable15## quarter
## sex 1 2 3 4
## 1 23 19 17 13
## 2 12 6 7 6chisq.test(mytable15)##
## Pearson's Chi-squared test
##
## data: mytable15
## X-squared = 0.76332, df = 3, p-value = 0.8582mytable16 <- xtabs(~ quarter+frstlang, data=job)
mytable16## frstlang
## quarter 1 2
## 1 34 1
## 2 23 2
## 3 22 2
## 4 17 2chisq.test(mytable16)## Warning in chisq.test(mytable16): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test
##
## data: mytable16
## X-squared = 1.4214, df = 3, p-value = 0.7005-From the above Pearson’s chi-squared tests , it is clear that there does not appear to be any relationship between any two categorical variables since p-value > 0.05 in ach of the possible cases.
-Hence, we fail to reject the null hypothesis that each of the paired variables are independent.
–>Running appropriate t-tests
t.test(satis~sex, data=job)##
## Welch Two Sample t-test
##
## data: satis by sex
## t = 0.82112, df = 44.389, p-value = 0.416
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.2273204 0.5400444
## sample estimates:
## mean in group 1 mean in group 2
## 5.930556 5.774194t.test(satis~frstlang, data=job)##
## Welch Two Sample t-test
##
## data: satis by frstlang
## t = -1.0194, df = 7.1964, p-value = 0.3411
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.9202355 0.3636879
## sample estimates:
## mean in group 1 mean in group 2
## 5.864583 6.142857t.test(quarter~sex,data=job)##
## Welch Two Sample t-test
##
## data: quarter by sex
## t = 0.20966, df = 53.827, p-value = 0.8347
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.4450450 0.5489876
## sample estimates:
## mean in group 1 mean in group 2
## 2.277778 2.225806t.test(sex~frstlang, data=job)##
## Welch Two Sample t-test
##
## data: sex by frstlang
## t = -0.66028, df = 6.6552, p-value = 0.5313
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.6323891 0.3585796
## sample estimates:
## mean in group 1 mean in group 2
## 1.291667 1.428571t.test(frstlang~sex,data=job)##
## Welch Two Sample t-test
##
## data: frstlang by sex
## t = -0.68201, df = 45.9, p-value = 0.4987
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1628792 0.0804419
## sample estimates:
## mean in group 1 mean in group 2
## 1.055556 1.096774t.test(quarter~frstlang,data=job)##
## Welch Two Sample t-test
##
## data: quarter by frstlang
## t = -1.1132, df = 6.9152, p-value = 0.3028
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1.5181693 0.5479312
## sample estimates:
## mean in group 1 mean in group 2
## 2.229167 2.714286-From the above t-tests , it is clear that all the paired variables are independent , with a p-value >0.05
- None of the variable effects the action of the other variable.
–>Regression model
- All the variables are integer vectors
-Fitting the model
fit<-lm(salary~age+sex+gmat_qpc+gmat_vpc+gmat_tot+gmat_tpc+s_avg+f_avg+quarter+
work_yrs+frstlang+satis, data=job)
summary(fit)##
## Call:
## lm(formula = salary ~ age + sex + gmat_qpc + gmat_vpc + gmat_tot +
## gmat_tpc + s_avg + f_avg + quarter + work_yrs + frstlang +
## satis, data = job)
##
## Residuals:
## Min 1Q Median 3Q Max
## -26489 -7983 -373 5923 70602
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 78005.66 52981.93 1.472 0.1444
## age 1750.65 1130.92 1.548 0.1251
## sex -3584.07 3595.85 -0.997 0.3216
## gmat_qpc 796.55 496.78 1.603 0.1123
## gmat_vpc 546.31 501.97 1.088 0.2794
## gmat_tot 16.19 178.85 0.090 0.9281
## gmat_tpc -1457.09 714.94 -2.038 0.0445 *
## s_avg -931.53 8240.31 -0.113 0.9102
## f_avg -2222.82 3894.57 -0.571 0.5696
## quarter -2336.56 2721.89 -0.858 0.3929
## work_yrs 749.66 1135.90 0.660 0.5110
## frstlang 7719.42 7373.27 1.047 0.2979
## satis -1086.54 2157.76 -0.504 0.6158
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15430 on 90 degrees of freedom
## Multiple R-squared: 0.3422, Adjusted R-squared: 0.2545
## F-statistic: 3.902 on 12 and 90 DF, p-value: 8.086e-05- Beta coefficients values
fit$coefficients## (Intercept) age sex gmat_qpc gmat_vpc gmat_tot
## 78005.66171 1750.65216 -3584.07221 796.54809 546.30750 16.18545
## gmat_tpc s_avg f_avg quarter work_yrs frstlang
## -1457.08759 -931.53478 -2222.82135 -2336.55542 749.66083 7719.42304
## satis
## -1086.54069-Fitted values of Starting salaries ( Predicted values )
job$salary## [1] 220000 162000 146000 145800 130000 126710 120000 120000 120000 120000
## [11] 118000 115000 115000 115000 115000 115000 112000 112000 112000 110000
## [21] 108000 108000 107500 107300 107000 106000 106000 106000 105000 105000
## [31] 105000 105000 105000 105000 105000 105000 105000 105000 105000 104000
## [41] 104000 103000 102500 101600 101100 101000 101000 100400 100000 100000
## [51] 100000 100000 100000 100000 100000 100000 100000 99000 98000 98000
## [61] 98000 98000 98000 98000 98000 98000 98000 98000 97000 97000
## [71] 96500 96000 96000 96000 96000 95000 95000 95000 95000 95000
## [81] 95000 95000 93000 93000 93000 92000 92000 92000 90000 90000
## [91] 90000 88500 88000 86000 86000 85000 85000 85000 85000 82000
## [101] 78256 77000 64000fitted(fit)## 274 69 68 139 138 273 64
## 149398.28 104602.16 136886.06 98698.76 101605.57 102906.99 101991.06
## 65 66 67 63 61 62 136
## 110813.72 111969.57 111539.59 123387.17 105944.40 109162.92 98124.50
## 137 272 60 135 209 59 58
## 101332.25 106938.92 131710.65 112372.72 97072.00 106077.91 103332.66
## 208 57 207 134 55 56 206
## 101699.75 106244.01 114012.72 100678.80 104293.45 110392.90 102646.51
## 49 50 51 52 53 54 131
## 104295.07 104340.23 104267.61 107844.22 105534.72 117003.43 98990.78
## 132 133 205 271 130 270 129
## 104492.05 131489.13 100340.38 92509.57 109427.51 125479.19 104309.68
## 204 269 203 128 202 268 46
## 108064.28 98365.05 110014.17 97637.02 92620.45 99994.57 93884.52
## 47 48 126 127 200 201 266
## 102921.62 102001.73 93821.35 113592.03 99865.37 96527.43 88378.10
## 267 125 122 123 124 194 195
## 92917.86 110371.32 95635.59 101205.47 109265.61 88146.31 84770.11
## 196 197 198 199 265 192 193
## 92335.22 112385.70 102417.83 110646.67 95647.25 101244.93 102476.61
## 121 44 45 120 264 41 42
## 116400.42 94605.99 93758.43 92996.97 97349.69 98952.20 94274.66
## 43 118 119 191 263 40 117
## 100859.19 102167.87 99344.77 103009.25 97034.18 90278.44 117353.34
## 190 39 116 262 188 189 261
## 101175.19 108809.43 97637.02 89968.42 94419.48 97955.82 105666.52
## 187 38 37 260 35 36 258
## 102495.59 94280.82 99728.91 92634.78 94121.52 105118.73 94852.84
## 259 115 186 257 256
## 96624.19 95874.74 93074.55 89360.18 86668.13- Regression model after converting the integer categorical variables into factor variables
-Converting the integer variables into factor variables
str(job)## 'data.frame': 103 obs. of 13 variables:
## $ age : int 40 25 40 24 26 26 27 28 30 30 ...
## $ sex : int 2 1 1 1 1 1 1 1 1 2 ...
## $ gmat_tot: int 500 700 630 620 650 550 600 700 600 670 ...
## $ gmat_qpc: int 60 98 71 88 89 72 67 95 77 87 ...
## $ gmat_vpc: int 45 93 95 74 87 58 84 95 81 95 ...
## $ gmat_tpc: int 51 98 91 87 93 69 83 98 84 95 ...
## $ s_avg : num 2.5 3.6 4 3.1 3.2 2.6 3.5 3.8 3.5 3.3 ...
## $ f_avg : num 2.75 3.75 0 3 3.25 2.75 3 4 3.25 3.25 ...
## $ quarter : int 4 1 1 2 2 4 1 1 1 1 ...
## $ work_yrs: int 15 1 15 2 4 3 3 5 5 8 ...
## $ frstlang: int 2 1 1 1 1 1 1 1 1 1 ...
## $ salary : int 220000 162000 146000 145800 130000 126710 120000 120000 120000 120000 ...
## $ satis : int 6 5 6 6 7 6 5 5 6 6 ...job$sex[job$sex==1]<-'Male'
job$sex[job$sex==2]<-'Female'
job$sex<-factor(job$sex)
job$quarter<-factor(job$quarter)
job$satis<-factor(job$satis)
job$frstlang[job$frstlang==1]<-'English'
job$frstlang[job$frstlang==2]<-'Other'
job$frstlang<-factor(job$frstlang)
str(job)## 'data.frame': 103 obs. of 13 variables:
## $ age : int 40 25 40 24 26 26 27 28 30 30 ...
## $ sex : Factor w/ 2 levels "Female","Male": 1 2 2 2 2 2 2 2 2 1 ...
## $ gmat_tot: int 500 700 630 620 650 550 600 700 600 670 ...
## $ gmat_qpc: int 60 98 71 88 89 72 67 95 77 87 ...
## $ gmat_vpc: int 45 93 95 74 87 58 84 95 81 95 ...
## $ gmat_tpc: int 51 98 91 87 93 69 83 98 84 95 ...
## $ s_avg : num 2.5 3.6 4 3.1 3.2 2.6 3.5 3.8 3.5 3.3 ...
## $ f_avg : num 2.75 3.75 0 3 3.25 2.75 3 4 3.25 3.25 ...
## $ quarter : Factor w/ 4 levels "1","2","3","4": 4 1 1 2 2 4 1 1 1 1 ...
## $ work_yrs: int 15 1 15 2 4 3 3 5 5 8 ...
## $ frstlang: Factor w/ 2 levels "English","Other": 2 1 1 1 1 1 1 1 1 1 ...
## $ salary : int 220000 162000 146000 145800 130000 126710 120000 120000 120000 120000 ...
## $ satis : Factor w/ 5 levels "3","4","5","6",..: 4 3 4 4 5 4 3 3 4 4 ...-Fitting the model
fit1<-lm(salary~age+sex+gmat_qpc+gmat_vpc+gmat_tot+gmat_tpc+s_avg+f_avg+quarter+
work_yrs+frstlang+satis, data=job)
summary(fit1)##
## Call:
## lm(formula = salary ~ age + sex + gmat_qpc + gmat_vpc + gmat_tot +
## gmat_tpc + s_avg + f_avg + quarter + work_yrs + frstlang +
## satis, data = job)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24954 -6770 -738 6286 68558
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 68070.03 57512.21 1.184 0.240
## age 1702.40 1162.20 1.465 0.147
## sexMale 3562.39 3746.26 0.951 0.344
## gmat_qpc 724.79 517.91 1.399 0.165
## gmat_vpc 508.37 515.89 0.985 0.327
## gmat_tot 26.48 185.10 0.143 0.887
## gmat_tpc -1397.38 744.64 -1.877 0.064 .
## s_avg -2203.55 8656.50 -0.255 0.800
## f_avg -1761.46 4040.47 -0.436 0.664
## quarter2 -4501.19 5228.76 -0.861 0.392
## quarter3 -8555.83 6985.38 -1.225 0.224
## quarter4 -6913.29 8477.17 -0.816 0.417
## work_yrs 737.61 1167.26 0.632 0.529
## frstlangOther 8151.67 7550.06 1.080 0.283
## satis4 827.83 23405.78 0.035 0.972
## satis5 5217.70 17062.76 0.306 0.761
## satis6 4987.12 17224.96 0.290 0.773
## satis7 1932.31 17443.97 0.111 0.912
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15750 on 85 degrees of freedom
## Multiple R-squared: 0.3529, Adjusted R-squared: 0.2234
## F-statistic: 2.726 on 17 and 85 DF, p-value: 0.00126-Beta coefficients values
fit1$coefficients## (Intercept) age sexMale gmat_qpc gmat_vpc
## 68070.03198 1702.40208 3562.39249 724.78984 508.36517
## gmat_tot gmat_tpc s_avg f_avg quarter2
## 26.48354 -1397.37709 -2203.54692 -1761.45997 -4501.18529
## quarter3 quarter4 work_yrs frstlangOther satis4
## -8555.83307 -6913.29417 737.61280 8151.67046 827.82618
## satis5 satis6 satis7
## 5217.69668 4987.12257 1932.30731-Fitted values of Starting salaries ( Predicted values )
job$salary## [1] 220000 162000 146000 145800 130000 126710 120000 120000 120000 120000
## [11] 118000 115000 115000 115000 115000 115000 112000 112000 112000 110000
## [21] 108000 108000 107500 107300 107000 106000 106000 106000 105000 105000
## [31] 105000 105000 105000 105000 105000 105000 105000 105000 105000 104000
## [41] 104000 103000 102500 101600 101100 101000 101000 100400 100000 100000
## [51] 100000 100000 100000 100000 100000 100000 100000 99000 98000 98000
## [61] 98000 98000 98000 98000 98000 98000 98000 98000 97000 97000
## [71] 96500 96000 96000 96000 96000 95000 95000 95000 95000 95000
## [81] 95000 95000 93000 93000 93000 92000 92000 92000 90000 90000
## [91] 90000 88500 88000 86000 86000 85000 85000 85000 85000 82000
## [101] 78256 77000 64000fitted(fit1)## 274 69 68 139 138 273 64
## 151442.28 105512.43 136243.72 98584.38 99492.65 105425.28 103202.44
## 65 66 67 63 61 62 136
## 111531.37 113439.36 113378.22 123671.63 106489.88 109989.89 98286.15
## 137 272 60 135 209 59 58
## 101495.57 108183.27 130932.61 112025.31 95653.47 106754.81 104914.89
## 208 57 207 134 55 56 206
## 100590.00 107087.52 111135.20 99963.18 104679.34 111728.71 101631.54
## 49 50 51 52 53 54 131
## 103859.86 106111.92 105753.32 108537.82 108039.67 118292.94 99363.57
## 132 133 205 271 130 270 129
## 103620.59 129954.37 97552.96 95895.17 108254.60 128084.88 103742.56
## 204 269 203 128 202 268 46
## 105842.83 100805.37 108317.02 96799.02 91059.72 100898.69 93697.64
## 47 48 126 127 200 201 266
## 104739.05 104441.34 93427.87 113315.74 98446.31 94950.84 91434.88
## 267 125 122 123 124 194 195
## 93729.90 110557.98 95772.93 100885.42 108466.15 85237.46 82554.78
## 196 197 198 199 265 192 193
## 91285.76 110941.87 98939.94 108400.43 98737.53 97626.68 101133.33
## 121 44 45 120 264 41 42
## 115359.30 95220.17 95774.66 91706.61 100014.60 95000.00 96234.86
## 43 118 119 191 263 40 117
## 95000.00 102029.86 99092.08 99529.67 97869.85 92902.36 117155.98
## 190 39 116 262 188 189 261
## 99489.09 110866.05 96799.02 90046.34 91093.50 95931.61 107346.98
## 187 38 37 260 35 36 258
## 100971.54 94510.65 100627.87 94440.10 95286.67 107046.34 96990.51
## 259 115 186 257 256
## 99447.11 94149.12 91340.45 92799.55 87117.69–> Comparing the beta coefficients of the two models
fit$coefficients## (Intercept) age sex gmat_qpc gmat_vpc gmat_tot
## 78005.66171 1750.65216 -3584.07221 796.54809 546.30750 16.18545
## gmat_tpc s_avg f_avg quarter work_yrs frstlang
## -1457.08759 -931.53478 -2222.82135 -2336.55542 749.66083 7719.42304
## satis
## -1086.54069fit1$coefficients## (Intercept) age sexMale gmat_qpc gmat_vpc
## 68070.03198 1702.40208 3562.39249 724.78984 508.36517
## gmat_tot gmat_tpc s_avg f_avg quarter2
## 26.48354 -1397.37709 -2203.54692 -1761.45997 -4501.18529
## quarter3 quarter4 work_yrs frstlangOther satis4
## -8555.83307 -6913.29417 737.61280 8151.67046 827.82618
## satis5 satis6 satis7
## 5217.69668 4987.12257 1932.30731–>Comparing multiple models
summary(fit)##
## Call:
## lm(formula = salary ~ age + sex + gmat_qpc + gmat_vpc + gmat_tot +
## gmat_tpc + s_avg + f_avg + quarter + work_yrs + frstlang +
## satis, data = job)
##
## Residuals:
## Min 1Q Median 3Q Max
## -26489 -7983 -373 5923 70602
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 78005.66 52981.93 1.472 0.1444
## age 1750.65 1130.92 1.548 0.1251
## sex -3584.07 3595.85 -0.997 0.3216
## gmat_qpc 796.55 496.78 1.603 0.1123
## gmat_vpc 546.31 501.97 1.088 0.2794
## gmat_tot 16.19 178.85 0.090 0.9281
## gmat_tpc -1457.09 714.94 -2.038 0.0445 *
## s_avg -931.53 8240.31 -0.113 0.9102
## f_avg -2222.82 3894.57 -0.571 0.5696
## quarter -2336.56 2721.89 -0.858 0.3929
## work_yrs 749.66 1135.90 0.660 0.5110
## frstlang 7719.42 7373.27 1.047 0.2979
## satis -1086.54 2157.76 -0.504 0.6158
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15430 on 90 degrees of freedom
## Multiple R-squared: 0.3422, Adjusted R-squared: 0.2545
## F-statistic: 3.902 on 12 and 90 DF, p-value: 8.086e-05summary(fit1)##
## Call:
## lm(formula = salary ~ age + sex + gmat_qpc + gmat_vpc + gmat_tot +
## gmat_tpc + s_avg + f_avg + quarter + work_yrs + frstlang +
## satis, data = job)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24954 -6770 -738 6286 68558
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 68070.03 57512.21 1.184 0.240
## age 1702.40 1162.20 1.465 0.147
## sexMale 3562.39 3746.26 0.951 0.344
## gmat_qpc 724.79 517.91 1.399 0.165
## gmat_vpc 508.37 515.89 0.985 0.327
## gmat_tot 26.48 185.10 0.143 0.887
## gmat_tpc -1397.38 744.64 -1.877 0.064 .
## s_avg -2203.55 8656.50 -0.255 0.800
## f_avg -1761.46 4040.47 -0.436 0.664
## quarter2 -4501.19 5228.76 -0.861 0.392
## quarter3 -8555.83 6985.38 -1.225 0.224
## quarter4 -6913.29 8477.17 -0.816 0.417
## work_yrs 737.61 1167.26 0.632 0.529
## frstlangOther 8151.67 7550.06 1.080 0.283
## satis4 827.83 23405.78 0.035 0.972
## satis5 5217.70 17062.76 0.306 0.761
## satis6 4987.12 17224.96 0.290 0.773
## satis7 1932.31 17443.97 0.111 0.912
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15750 on 85 degrees of freedom
## Multiple R-squared: 0.3529, Adjusted R-squared: 0.2234
## F-statistic: 2.726 on 17 and 85 DF, p-value: 0.00126-The multiple R-squared are as above.
-The second model gives the accurate assertion since the critically reliable factors have higher beta coefficients in this model.
-Hence, the second model is the best fit
–>Creating subset of those who did not get a job
nojob <- mba.df[order(salary)[1:171], ]
View(nojob)–>Contingency table
-One-way contingency tables
mytable <- with(nojob, table(satis))
mytable ## satis
## 1 2 3 4 5 6 7 998
## 1 1 4 16 45 47 11 46mytable1 <- with(nojob, table(sex))
mytable1 ## sex
## 1 2
## 134 37mytable2 <- with(nojob, table(quarter))
mytable2 ## quarter
## 1 2 3 4
## 34 45 46 46mytable3 <- with(nojob, table(frstlang))
mytable3## frstlang
## 1 2
## 146 25-Three-way Contingency tables
mytable21 <- xtabs(~ sex+quarter+satis, data=nojob)
ftable(mytable21)## satis 1 2 3 4 5 6 7 998
## sex quarter
## 1 1 0 0 0 2 4 7 1 7
## 2 1 0 1 2 14 9 1 8
## 3 0 0 0 0 9 12 2 14
## 4 0 0 3 7 9 11 2 8
## 2 1 0 0 0 1 3 3 2 4
## 2 0 0 0 1 2 2 1 3
## 3 0 1 0 2 1 3 1 1
## 4 0 0 0 1 3 0 1 1mytable22 <- xtabs(~ frstlang+sex+satis, data=nojob)
ftable(mytable22)## satis 1 2 3 4 5 6 7 998
## frstlang sex
## 1 1 1 0 2 6 30 38 6 31
## 2 0 0 0 3 9 8 5 7
## 2 1 0 0 2 5 6 1 0 6
## 2 0 1 0 2 0 0 0 2–>Chi-squared test
mytable11 <- xtabs(~ satis+sex, data=nojob)
mytable11## sex
## satis 1 2
## 1 1 0
## 2 0 1
## 3 4 0
## 4 11 5
## 5 36 9
## 6 39 8
## 7 6 5
## 998 37 9chisq.test(mytable11)## Warning in chisq.test(mytable11): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test
##
## data: mytable11
## X-squared = 10.333, df = 7, p-value = 0.1705mytable12 <- xtabs(~ satis+quarter, data=nojob)
mytable12## quarter
## satis 1 2 3 4
## 1 0 1 0 0
## 2 0 0 1 0
## 3 0 1 0 3
## 4 3 3 2 8
## 5 7 16 10 12
## 6 10 11 15 11
## 7 3 2 3 3
## 998 11 11 15 9chisq.test(mytable12)## Warning in chisq.test(mytable12): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test
##
## data: mytable12
## X-squared = 21.232, df = 21, p-value = 0.4449mytable13 <- xtabs(~ satis+frstlang, data=nojob)
mytable13## frstlang
## satis 1 2
## 1 1 0
## 2 0 1
## 3 2 2
## 4 9 7
## 5 39 6
## 6 46 1
## 7 11 0
## 998 38 8chisq.test(mytable13)## Warning in chisq.test(mytable13): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test
##
## data: mytable13
## X-squared = 29.002, df = 7, p-value = 0.0001446mytable14 <- xtabs(~ sex+frstlang, data=nojob)
mytable14## frstlang
## sex 1 2
## 1 114 20
## 2 32 5chisq.test(mytable14)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: mytable14
## X-squared = 2.3563e-30, df = 1, p-value = 1mytable15 <- xtabs(~ sex+quarter, data=nojob)
mytable15## quarter
## sex 1 2 3 4
## 1 21 36 37 40
## 2 13 9 9 6chisq.test(mytable15)##
## Pearson's Chi-squared test
##
## data: mytable15
## X-squared = 7.7155, df = 3, p-value = 0.05227mytable16 <- xtabs(~ quarter+frstlang, data=nojob)
mytable16## frstlang
## quarter 1 2
## 1 31 3
## 2 39 6
## 3 37 9
## 4 39 7chisq.test(mytable16)## Warning in chisq.test(mytable16): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test
##
## data: mytable16
## X-squared = 1.8892, df = 3, p-value = 0.5957-From the above Pearson’s chi-squared tests , it is clear that there does not appear to be any relationship between any two categorical variables since p-value > 0.05 in ach of the possible casees except the one between degree of satisfaction and the first language.
-Hence, we fail to reject the null hypothesis that each of the paired variables are independent except degree of satisfaction and first language which are dependent on each other.
-Hence , the the first language of the students effects the degree of satisfaction according to the survey.
–>Running appropriate t-tests
t.test(satis~sex, data=nojob)##
## Welch Two Sample t-test
##
## data: satis by sex
## t = 0.40356, df = 58.898, p-value = 0.688
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -128.9860 194.1554
## sample estimates:
## mean in group 1 mean in group 2
## 279.3955 246.8108t.test(satis~frstlang, data=nojob)##
## Welch Two Sample t-test
##
## data: satis by frstlang
## t = -0.57688, df = 31.413, p-value = 0.5681
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -264.9345 148.0573
## sample estimates:
## mean in group 1 mean in group 2
## 263.8014 322.2400t.test(quarter~sex,data=nojob)##
## Welch Two Sample t-test
##
## data: quarter by sex
## t = 2.4522, df = 55.471, p-value = 0.01737
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.09148911 0.90891428
## sample estimates:
## mean in group 1 mean in group 2
## 2.716418 2.216216t.test(sex~frstlang, data=nojob)##
## Welch Two Sample t-test
##
## data: sex by frstlang
## t = 0.2165, df = 33.079, p-value = 0.8299
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1610290 0.1993852
## sample estimates:
## mean in group 1 mean in group 2
## 1.219178 1.200000t.test(frstlang~sex,data=nojob)##
## Welch Two Sample t-test
##
## data: frstlang by sex
## t = 0.21782, df = 58.908, p-value = 0.8283
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1155836 0.1438208
## sample estimates:
## mean in group 1 mean in group 2
## 1.149254 1.135135t.test(quarter~frstlang,data=nojob)##
## Welch Two Sample t-test
##
## data: quarter by frstlang
## t = -1.0222, df = 34.743, p-value = 0.3137
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.6709289 0.2216138
## sample estimates:
## mean in group 1 mean in group 2
## 2.575342 2.800000-From the above t-tests , it is clear that all the paired variables are independent , with a p-value >0.05
- None of the variable effects the action of the other variable.
EXECUTIVE SUMMARY
-The starting salary of the Mba program of any individual student depends critically on the first language of the student and the degree of satisfaction estimated through various boxplots and the scatterplots.
-Even from the corrogram and the correlation matrices , it is quite clear that the starting salaries are strongly correlated with the first language.
-From the chi- squared tests and the t-tests between the people who got a job and those who did not get a job , it can be analysed that there is a significant relationship between the starting salaries , degree of satisfaction of the MBA program and the first language of the people.
-The Regression model ,ie the best fit model , here the second model helps us in concluding that the salary has more or less a positive effect from -age -sex -GMAT_score -GMAT_quantitative percentile -GMAT_verbalpercentile -work years experience -satisfaction degree and a negative effect from -first language -quarter -spring_average -fall_average -GMAT_overall percentile