Analysis of starting MBA salaries
Sree Gowri Addepalli
January 24, 2018
This is an analysis of the Harvard Business case study " MBA starting salaries“. Here, we try to analyze various factors that lead to change in the salaries of MBA students. The dataset contains the following columns: age, sex, gmat_tot, gmat_qpc, gmat_vpc, gmat_tpc, s_avg, f_avg, quarter, work_yrs, frstlang, salary, satis.
TASK 2A: UNDERSTANDING THE DATASET AND THE RELATIONSHIP BETWEEN VARIOUS VARIABLES WITH RESPECT TO SALARY.
# Reading the dataset.
setwd("C:/Users/GOWRI/Desktop/iim_internship/week_4/Mini_project")
MBAdata <- read.csv(file="MBA_Starting_Salaries_Data.csv",head=TRUE,sep=",")
View(MBAdata)
# Reading the dataset without the missing or unanswered data and unplaced students.
MBAdataRef <- MBAdata[which(MBAdata$salary!=998 & MBAdata$salary !=999 & MBAdata$salary !=0),]
# Reading the dataset without the missing or unanswered data.
MBAdataFull <- MBAdata[which(MBAdata$salary!=998 & MBAdata$salary !=999),]Analysis of the dataset and subsets.
library(psych)
summaryOfMBAdata <- describe(MBAdataRef)
MBAdataSum <- summaryOfMBAdata[ c(3,4,5,8,9)]
MBAdataSum## mean sd median min max
## age 26.78 3.27 2.60e+01 22.0 40
## sex 1.30 0.46 1.00e+00 1.0 2
## gmat_tot 616.02 50.69 6.20e+02 500.0 720
## gmat_qpc 79.73 13.39 8.20e+01 39.0 99
## gmat_vpc 78.56 16.14 8.10e+01 30.0 99
## gmat_tpc 84.52 11.01 8.70e+01 51.0 99
## s_avg 3.09 0.38 3.10e+00 2.2 4
## f_avg 3.09 0.49 3.25e+00 0.0 4
## quarter 2.26 1.12 2.00e+00 1.0 4
## work_yrs 3.68 3.01 3.00e+00 0.0 16
## frstlang 1.07 0.25 1.00e+00 1.0 2
## salary 103030.74 17868.80 1.00e+05 64000.0 220000
## satis 5.88 0.78 6.00e+00 3.0 7# Summary of MBA salaries dataset.
summary(MBAdata)## 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. :998.0# Summary of the dataset without the missing or unanswered data and unplaced students.
summary(MBAdataRef)## age sex gmat_tot gmat_qpc
## Min. :22.00 Min. :1.000 Min. :500 Min. :39.00
## 1st Qu.:25.00 1st Qu.:1.000 1st Qu.:580 1st Qu.:72.00
## Median :26.00 Median :1.000 Median :620 Median :82.00
## Mean :26.78 Mean :1.301 Mean :616 Mean :79.73
## 3rd Qu.:28.00 3rd Qu.:2.000 3rd Qu.:655 3rd Qu.:89.00
## Max. :40.00 Max. :2.000 Max. :720 Max. :99.00
## gmat_vpc gmat_tpc s_avg f_avg
## Min. :30.00 Min. :51.00 Min. :2.200 Min. :0.000
## 1st Qu.:71.00 1st Qu.:78.00 1st Qu.:2.850 1st Qu.:2.915
## Median :81.00 Median :87.00 Median :3.100 Median :3.250
## Mean :78.56 Mean :84.52 Mean :3.092 Mean :3.091
## 3rd Qu.:92.00 3rd Qu.:93.50 3rd Qu.:3.400 3rd Qu.:3.415
## Max. :99.00 Max. :99.00 Max. :4.000 Max. :4.000
## quarter work_yrs frstlang salary
## Min. :1.000 Min. : 0.00 Min. :1.000 Min. : 64000
## 1st Qu.:1.000 1st Qu.: 2.00 1st Qu.:1.000 1st Qu.: 95000
## Median :2.000 Median : 3.00 Median :1.000 Median :100000
## Mean :2.262 Mean : 3.68 Mean :1.068 Mean :103031
## 3rd Qu.:3.000 3rd Qu.: 4.00 3rd Qu.:1.000 3rd Qu.:106000
## Max. :4.000 Max. :16.00 Max. :2.000 Max. :220000
## satis
## Min. :3.000
## 1st Qu.:5.000
## Median :6.000
## Mean :5.883
## 3rd Qu.:6.000
## Max. :7.000# Summary of the dataset without the missing or unanswered data.
summary(MBAdataFull)## age sex gmat_tot gmat_qpc
## Min. :22.00 Min. :1.00 Min. :450.0 Min. :28.00
## 1st Qu.:25.00 1st Qu.:1.00 1st Qu.:570.0 1st Qu.:72.00
## Median :27.00 Median :1.00 Median :610.0 Median :82.00
## Mean :27.59 Mean :1.28 Mean :615.2 Mean :79.35
## 3rd Qu.:29.00 3rd Qu.:2.00 3rd Qu.:650.0 3rd Qu.:91.00
## Max. :48.00 Max. :2.00 Max. :760.0 Max. :99.00
## gmat_vpc gmat_tpc s_avg f_avg
## Min. :22.00 Min. : 0.00 Min. :2.000 Min. :0.000
## 1st Qu.:71.00 1st Qu.:75.00 1st Qu.:2.800 1st Qu.:2.750
## Median :81.00 Median :87.00 Median :3.090 Median :3.000
## Mean :78.13 Mean :83.48 Mean :3.064 Mean :3.078
## 3rd Qu.:91.00 3rd Qu.:93.00 3rd Qu.:3.300 3rd Qu.:3.330
## Max. :99.00 Max. :99.00 Max. :4.000 Max. :4.000
## quarter work_yrs frstlang salary
## Min. :1.000 Min. : 0.000 Min. :1.000 Min. : 0
## 1st Qu.:1.000 1st Qu.: 2.000 1st Qu.:1.000 1st Qu.: 0
## Median :2.000 Median : 3.000 Median :1.000 Median : 85000
## Mean :2.394 Mean : 4.104 Mean :1.078 Mean : 54985
## 3rd Qu.:3.000 3rd Qu.: 5.000 3rd Qu.:1.000 3rd Qu.:100000
## Max. :4.000 Max. :22.000 Max. :2.000 Max. :220000
## satis
## Min. :3.000
## 1st Qu.:5.000
## Median :6.000
## Mean :5.762
## 3rd Qu.:6.000
## Max. :7.000Effect of Age on salary.
library(lattice)
boxplot(MBAdataRef$salary ~MBAdataRef$age ,
xlab = "Age", ylab ="salary", main = "Effect of Age on salary.")
# we can see a significant correlation between age and salary.Effect of Gender on salary.
library(lattice)
boxplot(MBAdataRef$salary ~MBAdataRef$sex ,
xlab = "Sex", ylab ="salary", main = "Effect of gender on salary.")
# There is not much effect of gender on salary.Effect of work years on Salary
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitscatterplot(MBAdataRef$salary~MBAdataRef$work_yrs,spread=FALSE, smoother.args=list(lty=2), pch=19,
main="Scatterplot of Salary vs. work years ",
xlab="Work years",
ylab="salary")
# There is a strong correlation between the number of work years and the salary.Effect of first Language on salary.
library(lattice)
boxplot(MBAdataRef$salary ~MBAdataRef$frstlang ,
xlab = "First Language", ylab ="salary", main = "Effect of first Language on salary.")
# There is no significant correlation between the first language and the salary.Effect of satisfaction on salary.
library(lattice)
boxplot(MBAdataRef$salary ~MBAdataRef$satis ,
xlab = "Satisfaction", ylab ="salary", main = "Effect of satisfaction on salary.")
# There is no significant correlation between satisfaction and salary.Effect of GMAT on Salary.
library(car)
scatterplotMatrix(formula = ~ salary + gmat_tot + gmat_qpc + gmat_vpc + gmat_tpc , cex=0.6,
data=MBAdataRef, main = " Effect of GMAT on Salary.")
Effect of spring_MBA, Fall_MBA and quartile ranking on Salary.
library(car)
scatterplotMatrix(formula = ~ salary + s_avg + f_avg + quarter, cex=0.6,
data=MBAdataRef, main = " Effect of spring_MBA, Fall_MBA and quartile ranking on Salary.")
Draw a Corrgram
library("corrgram") ## Warning: replacing previous import by 'magrittr::%>%' when loading
## 'dendextend'corrgram(MBAdataRef, order=FALSE, lower.panel=panel.shade,
upper.panel=panel.pie, text.panel=panel.txt,
main="Corrgram of MBA data variables")
Create a Variance-Covariance Matrix.
covMBAdatRef <-cov(MBAdataRef)
covMBAdatRef## age sex gmat_tot gmat_qpc
## age 10.7045498 -2.164477e-01 -1.305445e+01 -7.22796497
## sex -0.2164477 2.124500e-01 -4.568818e-01 -0.90757662
## gmat_tot -13.0544451 -4.568818e-01 2.569294e+03 452.14258519
## gmat_qpc -7.2279650 -9.075766e-01 4.521426e+02 179.18027794
## gmat_vpc 0.9505045 3.974872e-01 6.386360e+02 20.45849990
## gmat_tpc -3.4602132 -2.377689e-01 5.393623e+02 97.03607462
## s_avg 0.1938587 1.409575e-02 3.299562e+00 0.07838473
## f_avg -0.3462517 3.725395e-02 3.027432e+00 0.64252142
## quarter -0.4604988 -1.104131e-02 -6.005140e+00 0.18960594
## work_yrs 8.6728536 -1.281173e-01 -1.873882e+01 -7.36245955
## frstlang 0.2898344 8.756901e-03 -1.687607e+00 0.04806777
## salary 29210.5193223 -1.369577e+03 -8.212449e+04 3382.43784504
## satis 0.2776509 -3.321911e-02 2.570912e+00 -0.04178565
## gmat_vpc gmat_tpc s_avg f_avg
## age 9.505045e-01 -3.460213e+00 0.19385875 -3.462517e-01
## sex 3.974872e-01 -2.377689e-01 0.01409575 3.725395e-02
## gmat_tot 6.386360e+02 5.393623e+02 3.29956215 3.027432e+00
## gmat_qpc 2.045850e+01 9.703607e+01 0.07838473 6.425214e-01
## gmat_vpc 2.606602e+02 1.393882e+02 0.96945936 1.803303e-01
## gmat_tpc 1.393882e+02 1.211342e+02 0.58062916 3.785056e-01
## s_avg 9.694594e-01 5.806292e-01 0.14325138 8.231046e-02
## f_avg 1.803303e-01 3.785056e-01 0.08231046 2.378638e-01
## quarter -2.325528e+00 -1.227013e+00 -0.35620503 -2.356492e-01
## work_yrs -1.366838e+00 -4.389206e+00 0.18604797 -3.176271e-01
## frstlang -8.915858e-01 -4.575481e-01 -0.01319912 -6.243099e-03
## salary -3.964803e+04 -2.596339e+04 688.02042071 -9.241129e+02
## satis 1.879973e+00 1.002856e+00 -0.04256901 -4.498382e-02
## quarter work_yrs frstlang salary
## age -4.604988e-01 8.6728536 2.898344e-01 2.921052e+04
## sex -1.104131e-02 -0.1281173 8.756901e-03 -1.369577e+03
## gmat_tot -6.005140e+00 -18.7388159 -1.687607e+00 -8.212449e+04
## gmat_qpc 1.896059e-01 -7.3624595 4.806777e-02 3.382438e+03
## gmat_vpc -2.325528e+00 -1.3668380 -8.915858e-01 -3.964803e+04
## gmat_tpc -1.227013e+00 -4.3892062 -4.575481e-01 -2.596339e+04
## s_avg -3.562050e-01 0.1860480 -1.319912e-02 6.880204e+02
## f_avg -2.356492e-01 -0.3176271 -6.243099e-03 -9.241129e+02
## quarter 1.254140e+00 -0.4347992 3.102989e-02 -2.571117e+03
## work_yrs -4.347992e-01 9.0630116 1.494384e-01 2.445820e+04
## frstlang 3.102989e-02 0.1494384 6.396345e-02 1.206714e+03
## salary -2.571117e+03 24458.1995050 1.206714e+03 3.192940e+08
## satis 1.975062e-01 0.1485818 1.779935e-02 -5.606583e+02
## satis
## age 0.27765087
## sex -0.03321911
## gmat_tot 2.57091186
## gmat_qpc -0.04178565
## gmat_vpc 1.87997335
## gmat_tpc 1.00285551
## s_avg -0.04256901
## f_avg -0.04498382
## quarter 0.19750619
## work_yrs 0.14858176
## frstlang 0.01779935
## salary -560.65829050
## satis 0.61374453#Transform covariance to correlation matrix
covCorrMBAdataRef <- cov2cor(covMBAdatRef)
covCorrMBAdataRef## age sex gmat_tot gmat_qpc gmat_vpc
## age 1.00000000 -0.14352927 -0.07871678 -0.165039057 0.01799420
## sex -0.14352927 1.00000000 -0.01955548 -0.147099027 0.05341428
## gmat_tot -0.07871678 -0.01955548 1.00000000 0.666382266 0.78038546
## gmat_qpc -0.16503906 -0.14709903 0.66638227 1.000000000 0.09466541
## gmat_vpc 0.01799420 0.05341428 0.78038546 0.094665411 1.00000000
## gmat_tpc -0.09609156 -0.04686981 0.96680810 0.658650025 0.78443167
## s_avg 0.15654954 0.08079985 0.17198874 0.015471662 0.15865101
## f_avg -0.21699191 0.16572186 0.12246257 0.098418869 0.02290167
## quarter -0.12568145 -0.02139041 -0.10578964 0.012648346 -0.12862079
## work_yrs 0.88052470 -0.09233003 -0.12280018 -0.182701263 -0.02812182
## frstlang 0.35026743 0.07512009 -0.13164323 0.014198516 -0.21835333
## salary 0.49964284 -0.16628869 -0.09067141 0.014141299 -0.13743230
## satis 0.10832308 -0.09199534 0.06474206 -0.003984632 0.14863481
## gmat_tpc s_avg f_avg quarter work_yrs
## age -0.09609156 0.15654954 -0.21699191 -0.12568145 0.88052470
## sex -0.04686981 0.08079985 0.16572186 -0.02139041 -0.09233003
## gmat_tot 0.96680810 0.17198874 0.12246257 -0.10578964 -0.12280018
## gmat_qpc 0.65865003 0.01547166 0.09841887 0.01264835 -0.18270126
## gmat_vpc 0.78443167 0.15865101 0.02290167 -0.12862079 -0.02812182
## gmat_tpc 1.00000000 0.13938500 0.07051391 -0.09955033 -0.13246963
## s_avg 0.13938500 1.00000000 0.44590413 -0.84038355 0.16328236
## f_avg 0.07051391 0.44590413 1.00000000 -0.43144819 -0.21633018
## quarter -0.09955033 -0.84038355 -0.43144819 1.00000000 -0.12896722
## work_yrs -0.13246963 0.16328236 -0.21633018 -0.12896722 1.00000000
## frstlang -0.16437561 -0.13788905 -0.05061394 0.10955726 0.19627277
## salary -0.13201783 0.10173175 -0.10603897 -0.12848526 0.45466634
## satis 0.11630842 -0.14356557 -0.11773304 0.22511985 0.06299926
## frstlang salary satis
## age 0.35026743 0.49964284 0.108323083
## sex 0.07512009 -0.16628869 -0.091995338
## gmat_tot -0.13164323 -0.09067141 0.064742057
## gmat_qpc 0.01419852 0.01414130 -0.003984632
## gmat_vpc -0.21835333 -0.13743230 0.148634805
## gmat_tpc -0.16437561 -0.13201783 0.116308417
## s_avg -0.13788905 0.10173175 -0.143565573
## f_avg -0.05061394 -0.10603897 -0.117733043
## quarter 0.10955726 -0.12848526 0.225119851
## work_yrs 0.19627277 0.45466634 0.062999256
## frstlang 1.00000000 0.26701953 0.089834769
## salary 0.26701953 1.00000000 -0.040050600
## satis 0.08983477 -0.04005060 1.000000000TASK 2b: WHO GOT HOW MUCH SALARY?
# Articulate a Hypothesis that you could test using a Regression Model. Run T-Tests appropriate, to test your Hypotheses. Fit a Linear Regression Model using lm().
# Null Hypothesis- "The salary does not depend on Gender.
# T-Test to check correlation between salary and Gender.
t.test(MBAdataRef$salary ~ MBAdataRef$sex)##
## Welch Two Sample t-test
##
## data: MBAdataRef$salary by MBAdataRef$sex
## t = 1.3628, df = 38.115, p-value = 0.1809
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -3128.55 16021.72
## sample estimates:
## mean in group 1 mean in group 2
## 104970.97 98524.39# As p-value>0.05, accept the null hypothesis, So, there is a no siginficant difference starting salary of male and female MBAs as salary doesnt depend on gender.# Null Hypothesis- "The salary does not depend on First Language."
# T-Test to check correlation between salary and first language.
t.test(MBAdataRef$salary ~ MBAdataRef$frstlang)##
## Welch Two Sample t-test
##
## data: MBAdataRef$salary by MBAdataRef$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 120614.3# As p-value>0.05, accept the null hypothesis, So,there is no significant difference between starting salary of MBAs whose first language is english and others as salary doesnt depend on first language.Comparision of various Regression Model that predict starting salary.
# Model 1
MbaSalModel1<-lm(salary ~ age +gmat_tot + gmat_qpc + gmat_vpc + gmat_tpc + quarter + s_avg+ f_avg + satis + frstlang , data = MBAdataRef)
summary(MbaSalModel1)##
## Call:
## lm(formula = salary ~ age + gmat_tot + gmat_qpc + gmat_vpc +
## gmat_tpc + quarter + s_avg + f_avg + satis + frstlang, data = MBAdataRef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24137 -8244 -490 5313 68756
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 64622.144 49262.731 1.312 0.1929
## age 2501.003 559.182 4.473 2.2e-05 ***
## gmat_tot 8.337 177.818 0.047 0.9627
## gmat_qpc 827.849 491.659 1.684 0.0956 .
## gmat_vpc 530.807 498.305 1.065 0.2896
## gmat_tpc -1436.428 711.446 -2.019 0.0464 *
## quarter -2647.810 2692.668 -0.983 0.3280
## s_avg -1805.530 8145.604 -0.222 0.8251
## f_avg -2741.535 3852.548 -0.712 0.4785
## satis -925.938 2140.124 -0.433 0.6663
## frstlang 5156.619 6934.452 0.744 0.4590
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15370 on 92 degrees of freedom
## Multiple R-squared: 0.3328, Adjusted R-squared: 0.2603
## F-statistic: 4.589 on 10 and 92 DF, p-value: 2.778e-05# Model 2
MbaSalModel2<-lm(salary ~ age +gmat_tot + quarter +satis
+ frstlang , data = MBAdataRef)
summary(MbaSalModel2)##
## Call:
## lm(formula = salary ~ age + gmat_tot + quarter + satis + frstlang,
## data = MBAdataRef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28366 -9128 -892 5055 76836
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 50088.40 25880.10 1.935 0.0559 .
## age 2487.04 517.40 4.807 5.6e-06 ***
## gmat_tot -14.65 31.11 -0.471 0.6386
## quarter -1119.24 1462.40 -0.765 0.4459
## satis -1856.87 2056.96 -0.903 0.3689
## frstlang 8269.35 6644.88 1.244 0.2163
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15600 on 97 degrees of freedom
## Multiple R-squared: 0.2748, Adjusted R-squared: 0.2374
## F-statistic: 7.352 on 5 and 97 DF, p-value: 7.014e-06# Model 3
MbaSalModel3<-lm(salary ~ age +gmat_tot + gmat_qpc + gmat_vpc + gmat_tpc + satis
+ frstlang , data = MBAdataRef)
summary(MbaSalModel3)##
## Call:
## lm(formula = salary ~ age + gmat_tot + gmat_qpc + gmat_vpc +
## gmat_tpc + satis + frstlang, data = MBAdataRef)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27442 -9074 -26 5449 65805
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 51877.83 47122.04 1.101 0.2737
## age 2720.36 507.19 5.364 5.73e-07 ***
## gmat_tot -27.96 162.79 -0.172 0.8640
## gmat_qpc 841.99 471.63 1.785 0.0774 .
## gmat_vpc 567.02 477.05 1.189 0.2376
## gmat_tpc -1309.36 699.44 -1.872 0.0643 .
## satis -1688.22 2036.28 -0.829 0.4091
## frstlang 4176.03 6703.97 0.623 0.5348
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15270 on 95 degrees of freedom
## Multiple R-squared: 0.3198, Adjusted R-squared: 0.2697
## F-statistic: 6.38 on 7 and 95 DF, p-value: 3.716e-06# Seeing the R squared, the thid model looks more accurate.Comparision of subsets of data having placed and unplaced students.
# Compare job(placed) and no Job(Placed)
MBAdataFull <- MBAdata[which(MBAdata$salary!=998 & MBAdata$salary !=999),]
MBAdataFull$job[MBAdataFull$salary ==0] <- 0
MBAdataFull$job[MBAdataFull$salary !=0] <- 1
View(MBAdataFull)
# Null hypothesis: Gender and placement are independent
# ChiSquareTest
mbadataschi<-xtabs(~sex + job,data = MBAdataFull)
addmargins(mbadataschi)## job
## sex 0 1 Sum
## 1 67 72 139
## 2 23 31 54
## Sum 90 103 193chisq.test(mbadataschi)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: mbadataschi
## X-squared = 0.29208, df = 1, p-value = 0.5889# As p>0.05, null hypothesis is accepted, Gender and placement are independent.
# Null hypothesis: first Language and placement are independent
# ChiSquareTest
mbadataschi1<-xtabs(~frstlang + job, data = MBAdataFull)
addmargins(mbadataschi1)## job
## frstlang 0 1 Sum
## 1 82 96 178
## 2 8 7 15
## Sum 90 103 193chisq.test(mbadataschi1)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: mbadataschi1
## X-squared = 0.074127, df = 1, p-value = 0.7854# As p>0.05, null hypothesis is accepted, language and placement are independent.LOGISTIC REGRESSION TO PREDICT WHETHER THE STUDENT WILL GET PLACED OR NOT.
# Reading the dataset
MBATrainingdata <- read.csv(file="MBA_Starting_Salaries_Data.csv",head=TRUE,sep=",")
View(MBATrainingdata)
# Adding a column of placed and unplaced students.
MBATrainingdataFull <- MBATrainingdata[which(MBATrainingdata$salary!=998 & MBATrainingdata$salary !=999),]
MBATrainingdataFull$job[MBATrainingdataFull$salary ==0] <- 0
MBATrainingdataFull$job[MBATrainingdataFull$salary !=0] <- 1
# Making a subset of the data with relevant columns.
Data <- subset(MBATrainingdataFull,select=c(1,2,3,7,8,9,10,11,12,13,14))
View(Data)
# Splitting into train and test data.
train <- Data[1:160,]
test <- Data[161:193,]
# Logistic regression Model on the job column, to predict whether the student will get the job or not based on the various factors selected.
LRmodel <- glm(job ~.,family=binomial(link='logit'),data=train)## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurredsummary(LRmodel)##
## Call:
## glm(formula = job ~ ., family = binomial(link = "logit"), data = train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.083e-05 -1.354e-06 2.110e-08 2.110e-08 1.671e-05
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.235e+01 1.291e+06 0.000 1.000
## age 3.776e-02 1.660e+04 0.000 1.000
## sex 2.759e+00 6.361e+04 0.000 1.000
## gmat_tot -9.237e-03 5.430e+02 0.000 1.000
## s_avg -1.328e-02 2.842e+05 0.000 1.000
## f_avg -2.992e-01 9.099e+04 0.000 1.000
## quarter 1.701e-01 9.579e+04 0.000 1.000
## work_yrs -5.826e-01 2.222e+04 0.000 1.000
## frstlang -2.021e+00 2.808e+05 0.000 1.000
## salary 5.840e-04 6.096e-01 0.001 0.999
## satis 1.429e-01 3.472e+04 0.000 1.000
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2.2141e+02 on 159 degrees of freedom
## Residual deviance: 1.3566e-09 on 149 degrees of freedom
## AIC: 22
##
## Number of Fisher Scoring iterations: 25anova(LRmodel, test="Chisq")## Warning: glm.fit: algorithm did not converge
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred## Analysis of Deviance Table
##
## Model: binomial, link: logit
##
## Response: job
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 159 221.41
## age 1 4.148 158 217.26 0.0416846 *
## sex 1 0.028 157 217.23 0.8682202
## gmat_tot 1 0.074 156 217.16 0.7859236
## s_avg 1 14.565 155 202.59 0.0001354 ***
## f_avg 1 0.082 154 202.51 0.7746748
## quarter 1 0.482 153 202.03 0.4874415
## work_yrs 1 0.819 152 201.21 0.3654938
## frstlang 1 0.020 151 201.19 0.8870032
## salary 1 201.190 150 0.00 < 2.2e-16 ***
## satis 1 0.000 149 0.00 0.9999987
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#predictive model
fitted.results <- predict(LRmodel,newdata=test,type='response')
fitted.results <- ifelse(fitted.results > 0.5,1,0)
misClasificError <- mean(fitted.results != test$job)
print(paste('Accuracy',1-misClasificError))## [1] "Accuracy 1"library(ROCR)## Warning: package 'ROCR' was built under R version 3.2.5## Loading required package: gplots## Warning: package 'gplots' was built under R version 3.2.5##
## Attaching package: 'gplots'## The following object is masked from 'package:stats':
##
## lowesspr <- prediction(fitted.results, test$job)
prf <- performance(pr, measure = "tpr", x.measure = "fpr")
plot(prf)
auc <- performance(pr, measure = "auc")
auc <- auc@y.values[[1]]
auc## [1] 1