This project analyses the factors affecting the starting salaries of MBA graduates of an institute and the likeliness to enroll in an MBA programme in that instutute.

Reading data into the file:

mba<-read.csv(paste("MBA Starting Salaries Data.csv"),)

Summary Statistics

summary(mba)

##       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

library(psych)

## 
## Attaching package: 'psych'

## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha

## The following object is masked from 'package:car':
## 
##     logit

describe(mba)

##          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

 there are missing salaries in the given data.

To make the data direct toward the ones who were placed and gave the review and the ones who did not get placed, its better to create two sub tables.

To improve readablity, its better to convert sex and Language into factor variables.

mba$sex[mba$sex==1]<- "Male"
mba$sex[mba$sex==2]<- "Female"
mba$sex<-factor(mba$sex)
mba$frstlang[mba$frstlang==1]<- "English"
mba$frstlang[mba$frstlang==2]<- "Other"
mba$frstlang<-factor(mba$frstlang)

str(mba)

## 'data.frame':    274 obs. of  13 variables:
##  $ age     : int  23 24 24 24 24 24 25 25 25 25 ...
##  $ sex     : Factor w/ 2 levels "Female","Male": 1 2 2 2 1 2 2 1 2 2 ...
##  $ 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: Factor w/ 2 levels "English","Other": 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 ...

Table for those who got Placed and Gave the survey

placed<-mba[which(mba$salary>1000),]
some(placed)

##     age    sex gmat_tot gmat_qpc gmat_vpc gmat_tpc s_avg f_avg quarter
## 36   27 Female      700       94       98       98   3.3  3.25       1
## 46   23 Female      650       93       81       93   3.4  3.00       1
## 118  25   Male      670       95       89       95   3.2  3.50       2
## 120  24   Male      560       52       81       72   3.2  3.25       2
## 133  34   Male      550       72       58       69   3.0  3.00       2
## 190  25   Male      610       89       74       87   2.7  2.75       3
## 200  24   Male      710       99       92       99   2.9  3.00       3
## 208  28   Male      570       56       84       75   2.9  3.00       3
## 272  25   Male      540       79       45       65   2.6  2.50       4
## 273  26   Male      550       72       58       69   2.6  2.75       4
##     work_yrs frstlang salary satis
## 36         2  English  85000     6
## 46         2  English 100000     7
## 118        2  English  95000     6
## 120        2  English  96000     7
## 133       16  English 105000     5
## 190        4  English  93000     6
## 200        3  English 100000     6
## 208        4  English 108000     6
## 272        3  English 115000     5
## 273        3  English 126710     6

Table for those who did not get Placed

notplaced<-mba[which(mba$salary==0),]
some(notplaced)

##     age    sex gmat_tot gmat_qpc gmat_vpc gmat_tpc s_avg f_avg quarter
## 2    24   Male      610       90       71       87  3.50  4.00       1
## 33   42 Female      650       75       98       93  3.38  3.00       1
## 107  30   Male      680       97       87       96  3.00  3.00       2
## 150  25   Male      550       72       58       69  2.90  3.00       3
## 165  27 Female      550       66       63       69  2.90  3.00       3
## 184  34   Male      610       82       78       86  2.70  3.00       3
## 218  25   Male      700       99       87       98  2.00  2.00       4
## 230  27   Male      580       84       58       78  2.70  2.75       4
## 237  28   Male      570       69       71        0  2.30  2.50       4
## 253  32   Male      510       79       22       54  2.30  2.25       4
##     work_yrs frstlang salary satis
## 2          2  English      0     6
## 33        13  English      0     5
## 107        4  English      0     5
## 150        3  English      0     6
## 165        3  English      0     4
## 184       12  English      0     5
## 218        1  English      0     7
## 230        1  English      0     5
## 237        5  English      0     5
## 253        5    Other      0     5

Analysis of those got placed and gave the survey

summary(placed)

##       age            sex        gmat_tot      gmat_qpc        gmat_vpc    
##  Min.   :22.00   Female:31   Min.   :500   Min.   :39.00   Min.   :30.00  
##  1st Qu.:25.00   Male  :72   1st Qu.:580   1st Qu.:72.00   1st Qu.:71.00  
##  Median :26.00               Median :620   Median :82.00   Median :81.00  
##  Mean   :26.78               Mean   :616   Mean   :79.73   Mean   :78.56  
##  3rd Qu.:28.00               3rd Qu.:655   3rd Qu.:89.00   3rd Qu.:92.00  
##  Max.   :40.00               Max.   :720   Max.   :99.00   Max.   :99.00  
##     gmat_tpc         s_avg           f_avg          quarter     
##  Min.   :51.00   Min.   :2.200   Min.   :0.000   Min.   :1.000  
##  1st Qu.:78.00   1st Qu.:2.850   1st Qu.:2.915   1st Qu.:1.000  
##  Median :87.00   Median :3.100   Median :3.250   Median :2.000  
##  Mean   :84.52   Mean   :3.092   Mean   :3.091   Mean   :2.262  
##  3rd Qu.:93.50   3rd Qu.:3.400   3rd Qu.:3.415   3rd Qu.:3.000  
##  Max.   :99.00   Max.   :4.000   Max.   :4.000   Max.   :4.000  
##     work_yrs        frstlang      salary           satis      
##  Min.   : 0.00   English:96   Min.   : 64000   Min.   :3.000  
##  1st Qu.: 2.00   Other  : 7   1st Qu.: 95000   1st Qu.:5.000  
##  Median : 3.00                Median :100000   Median :6.000  
##  Mean   : 3.68                Mean   :103031   Mean   :5.883  
##  3rd Qu.: 4.00                3rd Qu.:106000   3rd Qu.:6.000  
##  Max.   :16.00                Max.   :220000   Max.   :7.000

describe(placed)

##           vars   n      mean       sd   median   trimmed     mad     min
## age          1 103     26.78     3.27 2.60e+01     26.30    2.97    22.0
## sex*         2 103      1.70     0.46 2.00e+00      1.75    0.00     1.0
## gmat_tot     3 103    616.02    50.69 6.20e+02    615.90   59.30   500.0
## gmat_qpc     4 103     79.73    13.39 8.20e+01     81.05   13.34    39.0
## gmat_vpc     5 103     78.56    16.14 8.10e+01     80.33   16.31    30.0
## gmat_tpc     6 103     84.52    11.01 8.70e+01     85.60   11.86    51.0
## s_avg        7 103      3.09     0.38 3.10e+00      3.10    0.44     2.2
## f_avg        8 103      3.09     0.49 3.25e+00      3.13    0.37     0.0
## quarter      9 103      2.26     1.12 2.00e+00      2.20    1.48     1.0
## work_yrs    10 103      3.68     3.01 3.00e+00      3.11    1.48     0.0
## frstlang*   11 103      1.07     0.25 1.00e+00      1.00    0.00     1.0
## salary      12 103 103030.74 17868.80 1.00e+05 101065.06 7413.00 64000.0
## satis       13 103      5.88     0.78 6.00e+00      5.89    1.48     3.0
##              max    range  skew kurtosis      se
## age           40     18.0  1.92     4.90    0.32
## sex*           2      1.0 -0.86    -1.28    0.05
## gmat_tot     720    220.0  0.01    -0.69    4.99
## gmat_qpc      99     60.0 -0.81     0.17    1.32
## gmat_vpc      99     69.0 -0.87     0.21    1.59
## gmat_tpc      99     48.0 -0.84     0.19    1.08
## s_avg          4      1.8 -0.13    -0.61    0.04
## f_avg          4      4.0 -2.52    13.86    0.05
## quarter        4      3.0  0.27    -1.34    0.11
## work_yrs      16     16.0  2.48     6.83    0.30
## frstlang*      2      1.0  3.38     9.54    0.02
## salary    220000 156000.0  3.18    17.16 1760.67
## satis          7      4.0 -0.40     0.44    0.08

Salary distribution

library(lattice)
histogram(placed$salary,main="Salary Distribution of Placed",xlab="Salary",ylab="Percent of Total",col="grey")

# Variation of different variables with Sex

aggregate(cbind(salary,work_yrs,age)~sex,data = placed,mean)

##      sex    salary work_yrs      age
## 1 Female  98524.39 3.258065 26.06452
## 2   Male 104970.97 3.861111 27.08333

Variation of Salary with Sex

boxplot(salary~sex,data = placed,horizontal=TRUE, col=c("blue3","red2"),main="Salary vs Sex",xlab="Salary",ylab="Sex")

Variation of Salary with Work experience

scatterplot(salary~work_yrs,data = placed,main="Distribution of Salary vs Work experience",ylab="Salary",xlab="Work Years")

Distribution of Salary with GMAT score

scatterplot(salary~gmat_tot,data = placed,main="Distribution of Salary vs GMAT Scores",ylab="Salary",xlab="GMAT Scores")

Scatterplot Matrix

scatterplot.matrix(~salary+s_avg+f_avg,data=placed)

Effect of Age onn Salary

Average salary of the placed MBA graduates of different age groups

aggregate(salary~age,data = placed ,mean)

##    age    salary
## 1   22  85000.00
## 2   23  91651.20
## 3   24 101518.75
## 4   25  99086.96
## 5   26 101665.00
## 6   27 102214.29
## 7   28 103625.00
## 8   29 102083.33
## 9   30 109916.67
## 10  31 100500.00
## 11  32 107300.00
## 12  33 118000.00
## 13  34 105000.00
## 14  39 112000.00
## 15  40 183000.00

boxplot(salary~age,data=placed,horizontal=TRUE,main="Distribution of Salary vs Age",ylab="Age",xlab="Salary")

Distribution of Salary based on satisfaction

This is the average of only those graduates who got placed.

aggregate(salary~satis,data = placed , mean)

##   satis    salary
## 1     3  95000.00
## 2     4  95000.00
## 3     5 102974.34
## 4     6 105364.20
## 5     7  98531.82

boxplot(salary~satis,data=placed,horizontal=TRUE,main="Distribution of Salary vs Satisfaction",ylab="Satisfaction",xlab="Salary")

Effect of language on Salaries

boxplot(salary~frstlang,data=placed,horizontal=TRUE,main="Distribution of Salary vs Language",ylab="Language",xlab="Salary")

Correlation of the variables

This correlation includes the correlation with all the graduates irrespective of whether they were placed or not.

cor(mba[,c(1,3:10,12,13)])

##                  age    gmat_tot    gmat_qpc    gmat_vpc     gmat_tpc
## age       1.00000000 -0.14593840 -0.21616985 -0.04417547 -0.169903066
## gmat_tot -0.14593840  1.00000000  0.72473781  0.74839187  0.847799647
## gmat_qpc -0.21616985  0.72473781  1.00000000  0.15218014  0.651377538
## gmat_vpc -0.04417547  0.74839187  0.15218014  1.00000000  0.666216035
## gmat_tpc -0.16990307  0.84779965  0.65137754  0.66621604  1.000000000
## s_avg     0.14970402  0.11311702 -0.02984873  0.20445365  0.117362449
## f_avg    -0.01744806  0.10442409  0.07370455  0.07592225  0.079732099
## quarter  -0.04967221 -0.09223903  0.03636638 -0.17460736 -0.083035351
## work_yrs  0.85829810 -0.18235434 -0.23660827 -0.06639049 -0.173361859
## salary   -0.06257355 -0.05497188 -0.04403293 -0.00613934  0.004930901
## satis    -0.12788825  0.08255770  0.06060004  0.06262375  0.092934266
##                s_avg       f_avg       quarter     work_yrs       salary
## age       0.14970402 -0.01744806 -4.967221e-02  0.858298096 -0.062573547
## gmat_tot  0.11311702  0.10442409 -9.223903e-02 -0.182354339 -0.054971880
## gmat_qpc -0.02984873  0.07370455  3.636638e-02 -0.236608270 -0.044032933
## gmat_vpc  0.20445365  0.07592225 -1.746074e-01 -0.066390490 -0.006139340
## gmat_tpc  0.11736245  0.07973210 -8.303535e-02 -0.173361859  0.004930901
## s_avg     1.00000000  0.55062139 -7.621166e-01  0.129292714  0.145836062
## f_avg     0.55062139  1.00000000 -4.475064e-01 -0.039056921  0.029443027
## quarter  -0.76211664 -0.44750637  1.000000e+00 -0.086026406 -0.164369865
## work_yrs  0.12929271 -0.03905692 -8.602641e-02  1.000000000  0.009023407
## salary    0.14583606  0.02944303 -1.643699e-01  0.009023407  1.000000000
## satis    -0.03268664  0.01089273 -1.267198e-05 -0.109255286 -0.335217114
##                  satis
## age      -1.278882e-01
## gmat_tot  8.255770e-02
## gmat_qpc  6.060004e-02
## gmat_vpc  6.262375e-02
## gmat_tpc  9.293427e-02
## s_avg    -3.268664e-02
## f_avg     1.089273e-02
## quarter  -1.267198e-05
## work_yrs -1.092553e-01
## salary   -3.352171e-01
## satis     1.000000e+00

To see how the salaries of the placed graduates are correlated:

cor(placed[,c(1,3:10,12,13)])

##                  age    gmat_tot     gmat_qpc    gmat_vpc    gmat_tpc
## age       1.00000000 -0.07871678 -0.165039057  0.01799420 -0.09609156
## gmat_tot -0.07871678  1.00000000  0.666382266  0.78038546  0.96680810
## gmat_qpc -0.16503906  0.66638227  1.000000000  0.09466541  0.65865003
## gmat_vpc  0.01799420  0.78038546  0.094665411  1.00000000  0.78443167
## gmat_tpc -0.09609156  0.96680810  0.658650025  0.78443167  1.00000000
## s_avg     0.15654954  0.17198874  0.015471662  0.15865101  0.13938500
## f_avg    -0.21699191  0.12246257  0.098418869  0.02290167  0.07051391
## quarter  -0.12568145 -0.10578964  0.012648346 -0.12862079 -0.09955033
## work_yrs  0.88052470 -0.12280018 -0.182701263 -0.02812182 -0.13246963
## salary    0.49964284 -0.09067141  0.014141299 -0.13743230 -0.13201783
## satis     0.10832308  0.06474206 -0.003984632  0.14863481  0.11630842
##                s_avg       f_avg     quarter    work_yrs      salary
## age       0.15654954 -0.21699191 -0.12568145  0.88052470  0.49964284
## gmat_tot  0.17198874  0.12246257 -0.10578964 -0.12280018 -0.09067141
## gmat_qpc  0.01547166  0.09841887  0.01264835 -0.18270126  0.01414130
## gmat_vpc  0.15865101  0.02290167 -0.12862079 -0.02812182 -0.13743230
## gmat_tpc  0.13938500  0.07051391 -0.09955033 -0.13246963 -0.13201783
## s_avg     1.00000000  0.44590413 -0.84038355  0.16328236  0.10173175
## f_avg     0.44590413  1.00000000 -0.43144819 -0.21633018 -0.10603897
## quarter  -0.84038355 -0.43144819  1.00000000 -0.12896722 -0.12848526
## work_yrs  0.16328236 -0.21633018 -0.12896722  1.00000000  0.45466634
## salary    0.10173175 -0.10603897 -0.12848526  0.45466634  1.00000000
## satis    -0.14356557 -0.11773304  0.22511985  0.06299926 -0.04005060
##                 satis
## age       0.108323083
## gmat_tot  0.064742057
## gmat_qpc -0.003984632
## gmat_vpc  0.148634805
## gmat_tpc  0.116308417
## s_avg    -0.143565573
## f_avg    -0.117733043
## quarter   0.225119851
## work_yrs  0.062999256
## salary   -0.040050600
## satis     1.000000000

Visualising The Correlations

library(gplots)

## 
## Attaching package: 'gplots'

## The following object is masked from 'package:stats':
## 
##     lowess

library(corrgram)
 corrgram(placed, order=FALSE, lower.panel=panel.shade,
          upper.panel=panel.pie, text.panel=panel.txt,
          main="Corrgram of store variables")

Regressional Analysis

Model1

salary= b + b1work_yrs + b2age + b3gmat_qpc + b4gmat_vpc + b5s_avg + b6f_avg + b7sex +b8frstlang + e

mod1<-lm(salary~work_yrs + age + gmat_qpc + gmat_vpc + s_avg + f_avg + sex +frstlang,data = placed)
summary(mod1)

## 
## Call:
## lm(formula = salary ~ work_yrs + age + gmat_qpc + gmat_vpc + 
##     s_avg + f_avg + sex + frstlang, data = placed)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -28098  -8994  -1771   4642  79218 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept)    39633.2    29871.9   1.327   0.1878  
## work_yrs         663.6     1144.3   0.580   0.5634  
## age             1890.4     1135.5   1.665   0.0993 .
## gmat_qpc         120.1      121.0   0.993   0.3234  
## gmat_vpc        -146.6      101.8  -1.439   0.1535  
## s_avg           4006.6     4968.5   0.806   0.4220  
## f_avg          -1055.5     3808.8  -0.277   0.7823  
## sexMale         3737.4     3575.7   1.045   0.2986  
## frstlangOther   7851.5     7340.9   1.070   0.2876  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15570 on 94 degrees of freedom
## Multiple R-squared:  0.3006, Adjusted R-squared:  0.2411 
## F-statistic: 5.051 on 8 and 94 DF,  p-value: 3.102e-05

As can be seen by the above analysis the p-values of all the independent variables are greater than 0.05.

This can also be checked:

mod1$coefficients

##   (Intercept)      work_yrs           age      gmat_qpc      gmat_vpc 
##    39633.1612      663.5975     1890.4183      120.1321     -146.5648 
##         s_avg         f_avg       sexMale frstlangOther 
##     4006.6062    -1055.5165     3737.3708     7851.5333

Visualising the coefficients

coefplot(mod1)

As can be seen all the coefficients pass zero.

Conclusion

Model1 is not a good model for regression.

Model2

salary= b + b1work_yrs + b2satis + b3sex +b4frstlang + e

mod2<-lm(salary~work_yrs + satis + sex +frstlang,data = placed)
summary(mod2)

## 
## Call:
## lm(formula = salary ~ work_yrs + satis + sex + frstlang, data = placed)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -30492  -8055  -1744   5362  80436 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   102214.0    11827.8   8.642 1.06e-13 ***
## work_yrs        2409.4      526.1   4.579 1.37e-05 ***
## satis          -2244.4     1988.4  -1.129   0.2618    
## sexMale         5949.5     3392.2   1.754   0.0826 .  
## frstlangOther  14675.7     6274.0   2.339   0.0214 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15580 on 98 degrees of freedom
## Multiple R-squared:  0.2695, Adjusted R-squared:  0.2397 
## F-statistic: 9.038 on 4 and 98 DF,  p-value: 2.953e-06

There are some independent variables that have p-values less than 0.05 or may be considered significant.

To clarify this a look at the coefficients would be good

mod2$coefficients

##   (Intercept)      work_yrs         satis       sexMale frstlangOther 
##    102213.950      2409.391     -2244.425      5949.464     14675.672