MBA Starting Salaries
Surabhi Srivastava
23 January 2018
TASK 2(a)
Reading and describing the dataset
Salary.df<-read.csv(paste("MBA Starting Salaries Data.csv"))
View(Salary.df)summary(Salary.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. :998.0library(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 22.45Summary statistics of important variables
Data Types:
str(Salary.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 ...Mean of important variables:
mean(Salary.df$age)## [1] 27.35766mean(Salary.df$s_avg)## [1] 3.025401mean(Salary.df$f_avg)## [1] 3.061533mean(Salary.df$work_yrs)## [1] 3.872263mean(Salary.df$salary)## [1] 39025.69mean(Salary.df$satis)## [1] 172.1788Median of important variables:
median(Salary.df$age)## [1] 27median(Salary.df$s_avg)## [1] 3median(Salary.df$f_avg)## [1] 3median(Salary.df$work_yrs)## [1] 3median(Salary.df$salary)## [1] 999median(Salary.df$satis)## [1] 6Standard Deviation of important variables:
sd(Salary.df$age)## [1] 3.710666sd(Salary.df$s_avg)## [1] 0.3810743sd(Salary.df$f_avg)## [1] 0.5250451sd(Salary.df$work_yrs)## [1] 3.232464sd(Salary.df$salary)## [1] 50951.56sd(Salary.df$satis)## [1] 371.6146Visualising the dataset using boxplot
boxplot(Salary.df$age,horizontal=TRUE,main="Visualisation of age")
boxplot(Salary.df$gmat_tot,horizontal=TRUE,main="Visualisation of GMAT Total Score")
boxplot(Salary.df$work_yrs,horizontal=TRUE,main="Visualisation of number of work years")
boxplot(Salary.df$salary,horizontal=TRUE,main="Visualisation of salary")
Drawing Scatter Plot to indicate correlation
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitscatterplot.matrix(formula=~age+sex+gmat_tot+s_avg+f_avg+quarter+work_yrs+frstlang+salary+satis,cex=0.6,diagonal="histogram",data = Salary.df)## Warning: 'scatterplot.matrix' is deprecated.
## Use 'scatterplotMatrix' instead.
## See help("Deprecated") and help("car-deprecated").
Drawing Corrgram
library(corrgram)
corrgram(Salary.df, order = T, text.panel=panel.txt,
lower.panel = panel.shade,
upper.panel = panel.pie, main="Corrgram of all variables")
Creating a variance-covariance matrix
cov(Salary.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(Salary.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+05TASK2(b)
Forming the subset of those who got the job
placed <- Salary.df[ which(Salary.df$salary!=0),]Creating the contingency table
mytable1 <- xtabs(~salary+sex,data = placed)
mytable1## sex
## salary 1 2
## 998 37 9
## 999 30 5
## 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 1mytable2 <- xtabs(~salary+age,data = placed)
mytable2## age
## salary 22 23 24 25 26 27 28 29 30 31 32 33 34 39 40
## 998 0 0 2 15 11 11 4 0 1 2 0 0 0 0 0
## 999 0 0 2 6 5 7 3 5 3 2 2 0 0 0 0
## 64000 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
## 77000 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
## 78256 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82000 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
## 85000 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0
## 86000 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0
## 88000 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
## 88500 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
## 90000 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0
## 92000 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0
## 93000 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0
## 95000 0 0 1 5 0 0 0 1 0 0 0 0 0 0 0
## 96000 0 0 1 1 2 0 0 0 0 0 0 0 0 0 0
## 96500 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
## 97000 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0
## 98000 0 1 3 2 1 1 1 1 0 0 0 0 0 0 0
## 99000 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## 100000 0 1 4 1 1 1 0 0 0 1 0 0 0 0 0
## 100400 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
## 101000 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0
## 101100 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
## 101600 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
## 102500 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
## 103000 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
## 104000 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0
## 105000 0 1 1 2 3 1 0 0 1 1 0 0 1 0 0
## 106000 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0
## 107000 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
## 107300 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
## 107500 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
## 108000 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0
## 110000 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## 112000 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0
## 115000 0 0 1 1 0 3 0 0 0 0 0 0 0 0 0
## 118000 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
## 120000 0 0 0 0 0 1 1 0 2 0 0 0 0 0 0
## 126710 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
## 130000 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
## 145800 0 0 1 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 1
## 162000 0 0 0 1 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 1mytable3 <- xtabs(~gmat_tot+sex,data = placed)
mytable3## sex
## gmat_tot 1 2
## 450 0 1
## 460 1 0
## 500 2 1
## 520 0 1
## 530 1 1
## 540 2 0
## 550 4 0
## 560 9 4
## 570 9 2
## 580 8 3
## 590 5 1
## 600 14 3
## 610 7 2
## 620 12 4
## 630 14 3
## 640 4 2
## 650 7 4
## 660 8 3
## 670 8 5
## 680 7 2
## 690 4 0
## 700 2 1
## 710 5 1
## 720 1 1
## 730 1 0
## 740 3 0
## 790 1 0mytable4 <- xtabs(~work_yrs+sex,data = placed)
mytable4## sex
## work_yrs 1 2
## 0 2 0
## 1 8 4
## 2 41 19
## 3 34 8
## 4 28 6
## 5 6 3
## 6 7 3
## 7 4 0
## 8 4 1
## 9 1 0
## 10 1 0
## 15 1 1
## 16 2 0mytable5 <- xtabs(~salary+frstlang,data = placed)
mytable5## frstlang
## salary 1 2
## 998 38 8
## 999 26 9
## 64000 1 0
## 77000 1 0
## 78256 1 0
## 82000 1 0
## 85000 4 0
## 86000 2 0
## 88000 1 0
## 88500 1 0
## 90000 3 0
## 92000 3 0
## 93000 3 0
## 95000 7 0
## 96000 4 0
## 96500 1 0
## 97000 2 0
## 98000 8 2
## 99000 0 1
## 100000 9 0
## 100400 1 0
## 101000 2 0
## 101100 1 0
## 101600 1 0
## 102500 1 0
## 103000 1 0
## 104000 1 1
## 105000 11 0
## 106000 3 0
## 107000 1 0
## 107300 0 1
## 107500 1 0
## 108000 2 0
## 110000 1 0
## 112000 3 0
## 115000 5 0
## 118000 0 1
## 120000 4 0
## 126710 1 0
## 130000 1 0
## 145800 1 0
## 146000 1 0
## 162000 1 0
## 220000 0 1Running chi-square test
chisq.test(mytable1)## Warning in chisq.test(mytable1): Chi-squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: mytable1
## X-squared = 64.319, df = 43, p-value = 0.0192chisq.test(mytable2)## Warning in chisq.test(mytable2): Chi-squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: mytable2
## X-squared = 948.87, df = 602, p-value < 2.2e-16chisq.test(mytable3)## Warning in chisq.test(mytable3): Chi-squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: mytable3
## X-squared = 17.414, df = 26, p-value = 0.896chisq.test(mytable4)## Warning in chisq.test(mytable4): Chi-squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: mytable4
## X-squared = 8.2662, df = 12, p-value = 0.764chisq.test(mytable5)## Warning in chisq.test(mytable5): Chi-squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: mytable5
## X-squared = 48.273, df = 43, p-value = 0.2682Running the t-test
t.test(mytable1)##
## One Sample t-test
##
## data: mytable1
## t = 3.765, df = 87, p-value = 0.000302
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 0.9870773 3.1947409
## sample estimates:
## mean of x
## 2.090909t.test(mytable2)##
## One Sample t-test
##
## data: mytable2
## t = 6.6143, df = 659, p-value = 7.727e-11
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 0.1960245 0.3615512
## sample estimates:
## mean of x
## 0.2787879t.test(mytable3)##
## One Sample t-test
##
## data: mytable3
## t = 7.058, df = 53, p-value = 3.637e-09
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 2.439094 4.375721
## sample estimates:
## mean of x
## 3.407407t.test(mytable4)##
## One Sample t-test
##
## data: mytable4
## t = 3.2898, df = 25, p-value = 0.002979
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 2.646542 11.507304
## sample estimates:
## mean of x
## 7.076923t.test(mytable5)##
## One Sample t-test
##
## data: mytable5
## t = 3.7666, df = 87, p-value = 0.0003004
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 0.9875448 3.1942733
## sample estimates:
## mean of x
## 2.090909Regression model
reg <- lm(salary~age+sex+work_yrs,data = placed)
summary(reg)##
## Call:
## lm(formula = salary ~ age + sex + work_yrs, data = placed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -82407 -52377 22515 45293 117966
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 74699 62860 1.188 0.2363
## age -2005 2548 -0.787 0.4324
## sex 13777 8961 1.537 0.1259
## work_yrs 5673 2813 2.017 0.0452 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 51660 on 180 degrees of freedom
## Multiple R-squared: 0.04794, Adjusted R-squared: 0.03207
## F-statistic: 3.021 on 3 and 180 DF, p-value: 0.03112reg <- lm(salary~gmat_tot+sex+gmat_tot+frstlang+quarter,data = placed)
summary(reg)##
## Call:
## lm(formula = salary ~ gmat_tot + sex + gmat_tot + frstlang +
## quarter, data = placed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -90378 -48397 15960 40122 170419
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 206446.17 50007.22 4.128 5.6e-05 ***
## gmat_tot -174.55 69.37 -2.516 0.0127 *
## sex 10419.93 8725.34 1.194 0.2340
## frstlang -27618.09 11267.00 -2.451 0.0152 *
## quarter -8798.76 3360.58 -2.618 0.0096 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 50340 on 179 degrees of freedom
## Multiple R-squared: 0.1012, Adjusted R-squared: 0.08115
## F-statistic: 5.041 on 4 and 179 DF, p-value: 0.0007144reg <- lm(salary~age+work_yrs,data = placed)
summary(reg)##
## Call:
## lm(formula = salary ~ age + work_yrs, data = placed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -87007 -54400 27484 44513 126316
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 104828 59952 1.749 0.0821 .
## age -2534 2534 -1.000 0.3186
## work_yrs 6014 2815 2.137 0.0340 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 51860 on 181 degrees of freedom
## Multiple R-squared: 0.03543, Adjusted R-squared: 0.02478
## F-statistic: 3.325 on 2 and 181 DF, p-value: 0.0382By analysing the above models, we can see that the second model best fits.
TASK 2(c)
Comapring the subsets of those who didnot get the job to those who got the job
notplaced <- Salary.df[ which(Salary.df$salary==0),]
View(notplaced)Contingency table
mytable3 <- xtabs(~gmat_tot+sex,data = notplaced)
mytable3## sex
## gmat_tot 1 2
## 450 1 0
## 480 1 0
## 510 2 0
## 530 2 1
## 540 2 1
## 550 3 1
## 560 3 5
## 570 5 2
## 580 4 0
## 590 3 0
## 600 3 0
## 610 7 2
## 620 2 2
## 630 4 1
## 640 3 3
## 650 3 2
## 660 3 0
## 670 4 0
## 680 2 1
## 700 1 1
## 710 3 1
## 720 2 0
## 730 1 0
## 740 1 0
## 750 1 0
## 760 1 0mytable4 <- xtabs(~work_yrs+sex,data = notplaced)
mytable4## sex
## work_yrs 1 2
## 0 1 0
## 1 12 0
## 2 16 6
## 3 9 5
## 4 8 1
## 5 7 5
## 6 2 0
## 7 3 2
## 8 2 0
## 9 0 1
## 10 0 1
## 11 1 1
## 12 2 0
## 13 0 1
## 16 1 0
## 18 1 0
## 22 2 0We can compare the above contingency table with table corresponding to placed dataframe
Running chi-squared test
chisq.test(mytable3)## Warning in chisq.test(mytable3): Chi-squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: mytable3
## X-squared = 19.78, df = 25, p-value = 0.7583chisq.test(mytable4)## Warning in chisq.test(mytable4): Chi-squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: mytable4
## X-squared = 21.229, df = 16, p-value = 0.1699Running a logistic regression
setwd("C:/Users/SURABHI/Desktop/IIM INTERNSHIP")
Model.df<-read.csv(paste("MBA Starting Salaries Data.csv"),header=T,na.strings=c(""))
sapply(Model.df,function(x) sum(is.na(x)))## age sex gmat_tot gmat_qpc gmat_vpc gmat_tpc s_avg f_avg
## 0 0 0 0 0 0 0 0
## quarter work_yrs frstlang salary satis
## 0 0 0 0 0library(Amelia)## Loading required package: Rcpp## ##
## ## Amelia II: Multiple Imputation
## ## (Version 1.7.4, built: 2015-12-05)
## ## Copyright (C) 2005-2018 James Honaker, Gary King and Matthew Blackwell
## ## Refer to http://gking.harvard.edu/amelia/ for more information
## ##missmap(Model.df, main = "Missing values vs observed")
data <- subset(Model.df,select=c(1,2,3,4,5,6,7,8,9,10,11,12))
data$salary[data$salary>0] <- 1train <- data[1:800,]
test <- data[801:889,]model <- glm(salary~gmat_qpc,family=binomial(link='logit'),data=train)
summary(model)##
## Call:
## glm(formula = salary ~ gmat_qpc, family = binomial(link = "logit"),
## data = train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5893 -1.4189 0.8395 0.8976 1.0766
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.205952 0.693627 -0.297 0.767
## gmat_qpc 0.011480 0.008535 1.345 0.179
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 346.93 on 273 degrees of freedom
## Residual deviance: 345.13 on 272 degrees of freedom
## (526 observations deleted due to missingness)
## AIC: 349.13
##
## Number of Fisher Scoring iterations: 4