MBA Starting Salaries
Aditi Gupta
March 6, 2018
Task 2b:
data.df <- read.csv(paste("MBA Starting Salaries Data.csv", sep=""))
library(psych)
View(data.df)Comments: 274 observations of 14 variables
Summary Statistics:
summary(data.df)## age sex gmat_tot gmat_qpc
## Min. :22.00 Min. :1.000 Min. :450.0 Min. :28.00
## 1st Qu.:25.00 1st Qu.:1.000 1st Qu.:580.0 1st Qu.:72.00
## Median :27.00 Median :1.000 Median :620.0 Median :83.00
## Mean :27.36 Mean :1.248 Mean :619.5 Mean :80.64
## 3rd Qu.:29.00 3rd Qu.:1.000 3rd Qu.:660.0 3rd Qu.:93.00
## Max. :48.00 Max. :2.000 Max. :790.0 Max. :99.00
## gmat_vpc gmat_tpc s_avg f_avg
## Min. :16.00 Min. : 0.0 Min. :2.000 Min. :0.000
## 1st Qu.:71.00 1st Qu.:78.0 1st Qu.:2.708 1st Qu.:2.750
## Median :81.00 Median :87.0 Median :3.000 Median :3.000
## Mean :78.32 Mean :84.2 Mean :3.025 Mean :3.062
## 3rd Qu.:91.00 3rd Qu.:94.0 3rd Qu.:3.300 3rd Qu.:3.250
## Max. :99.00 Max. :99.0 Max. :4.000 Max. :4.000
## quarter work_yrs frstlang salary
## Min. :1.000 Min. : 0.000 Min. :1.000 Min. : 0
## 1st Qu.:1.250 1st Qu.: 2.000 1st Qu.:1.000 1st Qu.: 0
## Median :2.000 Median : 3.000 Median :1.000 Median : 999
## Mean :2.478 Mean : 3.872 Mean :1.117 Mean : 39026
## 3rd Qu.:3.000 3rd Qu.: 4.000 3rd Qu.:1.000 3rd Qu.: 97000
## Max. :4.000 Max. :22.000 Max. :2.000 Max. :220000
## satis
## Min. : 1.0
## 1st Qu.: 5.0
## Median : 6.0
## Mean :172.2
## 3rd Qu.: 7.0
## Max. :998.0str(data.df)## 'data.frame': 274 obs. of 13 variables:
## $ age : int 23 24 24 24 24 24 25 25 25 25 ...
## $ sex : int 2 1 1 1 2 1 1 2 1 1 ...
## $ gmat_tot: int 620 610 670 570 710 640 610 650 630 680 ...
## $ gmat_qpc: int 77 90 99 56 93 82 89 88 79 99 ...
## $ gmat_vpc: int 87 71 78 81 98 89 74 89 91 81 ...
## $ gmat_tpc: int 87 87 95 75 98 91 87 92 89 96 ...
## $ s_avg : num 3.4 3.5 3.3 3.3 3.6 3.9 3.4 3.3 3.3 3.45 ...
## $ f_avg : num 3 4 3.25 2.67 3.75 3.75 3.5 3.75 3.25 3.67 ...
## $ quarter : int 1 1 1 1 1 1 1 1 1 1 ...
## $ work_yrs: int 2 2 2 1 2 2 2 2 2 2 ...
## $ frstlang: int 1 1 1 1 1 1 1 1 2 1 ...
## $ salary : int 0 0 0 0 999 0 0 0 999 998 ...
## $ satis : int 7 6 6 7 5 6 5 6 4 998 ...Visualization of distribution of variables
hist(data.df$age,
main="Distribution of Age",
xlab="Age",
ylab="Count",
breaks=10,
col="pink") 
boxplot(data.df$age)
Visualization of Sex
hist(data.df$gmat_tot,
main="Distribution of Gmat Total",
xlab="gmat_tot",
ylab="Count",
breaks=10,
col="yellow")
boxplot(data.df$gmat_tot)
Visualization of Work Experience
hist(data.df$work_yrs,
main="Distribution of Work Experience",
xlab="Work Experience (Years)",
ylab="Count",
breaks=10,
col="turquoise") 
boxplot(data.df$work_yrs)
Visualization of Salary
hist(data.df$salary,
main="Distribution of salary",
xlab="salary",
ylab="Count",
breaks=10,
col="green3") 
boxplot(data.df$salary)
Visulaization of Satisfaction
hist(data.df$satis,
main="Distribution of Satisfaction",
xlab="Satisfaction",
ylab="Count",
breaks=10,
col="peachpuff") 
boxplot(data.df$satis)
Pair-wise correlation of variables
pairs(formula = ~ age + sex + gmat_tot + s_avg + f_avg + quarter + work_yrs + frstlang + salary + satis, cex=0.5, data=data.df)
Corrgram, Variance-Covariance Matrix
library(corrgram)
corrgram(data.df, order=TRUE, lower.panel=panel.shade,
upper.panel=panel.pie, text.panel=panel.txt,
main="Corrgram of Dataset")
cov(data.df)## age sex gmat_tot gmat_qpc
## age 1.376904e+01 -4.513248e-02 -3.115879e+01 -1.192655e+01
## sex -4.513248e-02 1.872677e-01 -1.328841e+00 -1.053769e+00
## gmat_tot -3.115879e+01 -1.328841e+00 3.310688e+03 6.200233e+02
## gmat_qpc -1.192655e+01 -1.053769e+00 6.200233e+02 2.210731e+02
## gmat_vpc -2.763643e+00 5.463758e-01 7.260006e+02 3.814826e+01
## gmat_tpc -8.839978e+00 -4.908960e-02 6.839911e+02 1.357997e+02
## s_avg 2.116874e-01 2.096227e-02 2.480257e+00 -1.691233e-01
## f_avg -3.399348e-02 2.082698e-02 3.154688e+00 5.753854e-01
## quarter -2.045935e-01 -6.414267e-02 -5.891153e+00 6.001979e-01
## work_yrs 1.029494e+01 -1.580172e-02 -3.391634e+01 -1.137186e+01
## frstlang 6.796610e-02 2.138980e-04 -2.499933e+00 6.646346e-01
## salary -1.183042e+04 1.518264e+03 -1.611600e+05 -3.335823e+04
## satis -1.763499e+02 -8.780808e+00 1.765263e+03 3.348371e+02
## gmat_vpc gmat_tpc s_avg f_avg
## age -2.7636427 -8.8399775 0.21168739 -0.03399348
## sex 0.5463758 -0.0490896 0.02096227 0.02082698
## gmat_tot 726.0006417 683.9910698 2.48025721 3.15468838
## gmat_qpc 38.1482581 135.7996845 -0.16912329 0.57538542
## gmat_vpc 284.2481217 157.4932488 1.31357023 0.67207000
## gmat_tpc 157.4932488 196.6057057 0.62710008 0.58698618
## s_avg 1.3135702 0.6271001 0.14521760 0.11016898
## f_avg 0.6720700 0.5869862 0.11016898 0.27567237
## quarter -3.2676666 -1.2923719 -0.32237213 -0.26080880
## work_yrs -3.6181653 -7.8575172 0.15926392 -0.06628700
## frstlang -2.1145691 -0.4663244 -0.01671372 -0.00626026
## salary -5273.8523836 3522.7500067 2831.60098580 787.65597177
## satis 392.3562739 484.2466779 -4.62884495 2.12532927
## quarter work_yrs frstlang salary
## age -2.045935e-01 10.29493864 6.796610e-02 -1.183042e+04
## sex -6.414267e-02 -0.01580172 2.138980e-04 1.518264e+03
## gmat_tot -5.891153e+00 -33.91633914 -2.499933e+00 -1.611600e+05
## gmat_qpc 6.001979e-01 -11.37186171 6.646346e-01 -3.335823e+04
## gmat_vpc -3.267667e+00 -3.61816529 -2.114569e+00 -5.273852e+03
## gmat_tpc -1.292372e+00 -7.85751718 -4.663244e-01 3.522750e+03
## s_avg -3.223721e-01 0.15926392 -1.671372e-02 2.831601e+03
## f_avg -2.608088e-01 -0.06628700 -6.260260e-03 7.876560e+02
## quarter 1.232119e+00 -0.30866822 3.553381e-02 -9.296214e+03
## work_yrs -3.086682e-01 10.44882490 -2.898318e-02 1.486147e+03
## frstlang 3.553381e-02 -0.02898318 1.035266e-01 -1.419586e+03
## salary -9.296214e+03 1486.14704152 -1.419586e+03 2.596062e+09
## satis -5.227133e-03 -131.24080907 9.484532e+00 -6.347115e+06
## satis
## age -1.763499e+02
## sex -8.780808e+00
## gmat_tot 1.765263e+03
## gmat_qpc 3.348371e+02
## gmat_vpc 3.923563e+02
## gmat_tpc 4.842467e+02
## s_avg -4.628845e+00
## f_avg 2.125329e+00
## quarter -5.227133e-03
## work_yrs -1.312408e+02
## frstlang 9.484532e+00
## salary -6.347115e+06
## satis 1.380974e+05var(data.df)## age sex gmat_tot gmat_qpc
## age 1.376904e+01 -4.513248e-02 -3.115879e+01 -1.192655e+01
## sex -4.513248e-02 1.872677e-01 -1.328841e+00 -1.053769e+00
## gmat_tot -3.115879e+01 -1.328841e+00 3.310688e+03 6.200233e+02
## gmat_qpc -1.192655e+01 -1.053769e+00 6.200233e+02 2.210731e+02
## gmat_vpc -2.763643e+00 5.463758e-01 7.260006e+02 3.814826e+01
## gmat_tpc -8.839978e+00 -4.908960e-02 6.839911e+02 1.357997e+02
## s_avg 2.116874e-01 2.096227e-02 2.480257e+00 -1.691233e-01
## f_avg -3.399348e-02 2.082698e-02 3.154688e+00 5.753854e-01
## quarter -2.045935e-01 -6.414267e-02 -5.891153e+00 6.001979e-01
## work_yrs 1.029494e+01 -1.580172e-02 -3.391634e+01 -1.137186e+01
## frstlang 6.796610e-02 2.138980e-04 -2.499933e+00 6.646346e-01
## salary -1.183042e+04 1.518264e+03 -1.611600e+05 -3.335823e+04
## satis -1.763499e+02 -8.780808e+00 1.765263e+03 3.348371e+02
## gmat_vpc gmat_tpc s_avg f_avg
## age -2.7636427 -8.8399775 0.21168739 -0.03399348
## sex 0.5463758 -0.0490896 0.02096227 0.02082698
## gmat_tot 726.0006417 683.9910698 2.48025721 3.15468838
## gmat_qpc 38.1482581 135.7996845 -0.16912329 0.57538542
## gmat_vpc 284.2481217 157.4932488 1.31357023 0.67207000
## gmat_tpc 157.4932488 196.6057057 0.62710008 0.58698618
## s_avg 1.3135702 0.6271001 0.14521760 0.11016898
## f_avg 0.6720700 0.5869862 0.11016898 0.27567237
## quarter -3.2676666 -1.2923719 -0.32237213 -0.26080880
## work_yrs -3.6181653 -7.8575172 0.15926392 -0.06628700
## frstlang -2.1145691 -0.4663244 -0.01671372 -0.00626026
## salary -5273.8523836 3522.7500067 2831.60098580 787.65597177
## satis 392.3562739 484.2466779 -4.62884495 2.12532927
## quarter work_yrs frstlang salary
## age -2.045935e-01 10.29493864 6.796610e-02 -1.183042e+04
## sex -6.414267e-02 -0.01580172 2.138980e-04 1.518264e+03
## gmat_tot -5.891153e+00 -33.91633914 -2.499933e+00 -1.611600e+05
## gmat_qpc 6.001979e-01 -11.37186171 6.646346e-01 -3.335823e+04
## gmat_vpc -3.267667e+00 -3.61816529 -2.114569e+00 -5.273852e+03
## gmat_tpc -1.292372e+00 -7.85751718 -4.663244e-01 3.522750e+03
## s_avg -3.223721e-01 0.15926392 -1.671372e-02 2.831601e+03
## f_avg -2.608088e-01 -0.06628700 -6.260260e-03 7.876560e+02
## quarter 1.232119e+00 -0.30866822 3.553381e-02 -9.296214e+03
## work_yrs -3.086682e-01 10.44882490 -2.898318e-02 1.486147e+03
## frstlang 3.553381e-02 -0.02898318 1.035266e-01 -1.419586e+03
## salary -9.296214e+03 1486.14704152 -1.419586e+03 2.596062e+09
## satis -5.227133e-03 -131.24080907 9.484532e+00 -6.347115e+06
## satis
## age -1.763499e+02
## sex -8.780808e+00
## gmat_tot 1.765263e+03
## gmat_qpc 3.348371e+02
## gmat_vpc 3.923563e+02
## gmat_tpc 4.842467e+02
## s_avg -4.628845e+00
## f_avg 2.125329e+00
## quarter -5.227133e-03
## work_yrs -1.312408e+02
## frstlang 9.484532e+00
## salary -6.347115e+06
## satis 1.380974e+05Task 1b: Subset of dataset consisting of only those people who actually got a job
placed.df <- subset(data.df, salary>0 & salary!= 998 & salary!=999)
View(placed.df)Contingency Tables
mytable <- with(placed.df, table(sex))
mytable## sex
## 1 2
## 72 31mytable <- with(placed.df, table(frstlang))
mytable## frstlang
## 1 2
## 96 7aggregate(salary ~ sex, data=placed.df, mean)## sex salary
## 1 1 104970.97
## 2 2 98524.39aggregate(salary ~ frstlang, data=placed.df, mean)## frstlang salary
## 1 1 101748.6
## 2 2 120614.3T-Tests
t.test(salary ~ sex, data=placed.df)##
## Welch Two Sample t-test
##
## data: salary by sex
## t = 1.3628, df = 38.115, p-value = 0.1809
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -3128.55 16021.72
## sample estimates:
## mean in group 1 mean in group 2
## 104970.97 98524.39Comments: p-value=0.1809(>0.05)
t.test(salary ~ frstlang, data=placed.df)##
## Welch Two Sample t-test
##
## data: salary by frstlang
## t = -1.1202, df = 6.0863, p-value = 0.3049
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -59933.62 22202.25
## sample estimates:
## mean in group 1 mean in group 2
## 101748.6 120614.3Regression Model1:
fit <- lm(salary ~ work_yrs + gmat_tot + s_avg + f_avg, data = placed.df)
summary(fit)##
## Call:
## lm(formula = salary ~ work_yrs + gmat_tot + s_avg + f_avg, data = placed.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -36351 -8173 -1170 3864 87090
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 98635.48 22643.60 4.356 3.26e-05 ***
## work_yrs 2579.88 577.97 4.464 2.16e-05 ***
## gmat_tot -14.98 32.53 -0.460 0.646
## s_avg 2422.16 5033.78 0.481 0.631
## f_avg -1087.60 3889.90 -0.280 0.780
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16200 on 98 degrees of freedom
## Multiple R-squared: 0.2098, Adjusted R-squared: 0.1776
## F-statistic: 6.506 on 4 and 98 DF, p-value: 0.0001098Regression Model2:
fit <- lm(salary ~ work_yrs + age + s_avg + frstlang , data = placed.df)
summary(fit)##
## Call:
## lm(formula = salary ~ work_yrs + age + s_avg + frstlang, data = placed.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32957 -9005 -1362 4613 76947
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 34470.6 26189.2 1.316 0.1912
## work_yrs 746.2 1121.1 0.666 0.5072
## age 1833.3 1085.7 1.689 0.0945 .
## s_avg 2207.1 4233.5 0.521 0.6033
## frstlang 9270.9 6894.3 1.345 0.1818
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15630 on 98 degrees of freedom
## Multiple R-squared: 0.2647, Adjusted R-squared: 0.2347
## F-statistic: 8.818 on 4 and 98 DF, p-value: 4.008e-06Comments: Model 2 is a better model
Task 1b: Comparing the remaining subset of those people who did not get a job and compare them with those people who got a job
notplaced.df <- subset(data.df, salary==0)
View(notplaced.df)T-Test:
t.test(gmat_tot ~ frstlang, data=notplaced.df)##
## Welch Two Sample t-test
##
## data: gmat_tot by frstlang
## t = 0.51644, df = 7.9236, p-value = 0.6197
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -49.86769 78.58720
## sample estimates:
## mean in group 1 mean in group 2
## 615.6098 601.2500Comments: p-value=0.6197