MBA Starting Salaries Data

Setting Working Directory

setwd("E:/Internship/Tasks/Week 4/Week 4, Day 1 (Mon)")

Reading MBA Starting Salaries Data csv file

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

Viewing Data

View(MBA)
dim(MBA)

## [1] 274  13

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

Summary Statistics using Describe Command

library("psych", lib.loc="~/R/win-library/3.4")
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

Cleaning data, removing rows of students who didn’t answered the survey

surveyanswered <-MBA[which(MBA$salary!="998"),]
dim(surveyanswered)

## [1] 228  13

View(surveyanswered)

Visualizing in Boxplots

Boxplot showing variance of age and Mean Age is 27.57018

boxplot(surveyanswered$age,ylab="Age",ylim=c(20,35),xlim=c(1,1),main="Boxplot showing variance of age")

mean(surveyanswered$age)

## [1] 27.57018

Distribution of gender bias in students

table(surveyanswered$sex)## 1=Male,2=Female

## 
##   1   2 
## 169  59

Variation of GMAT scores

boxplot(surveyanswered$gmat_tot,ylim=c(550,700),xlim=c(1,1),main="Boxplot Showing Variation of GMAT Total Scores",ylab="GMAT Scores")

mean(surveyanswered$gmat_tot)

## [1] 617.3246

Variation of GMAT Quantitative Percentile

boxplot(surveyanswered$gmat_qpc,ylim=c(64,100),xlim=c(1,1),main="Boxplot Showing Variation of GMAT Quant Percentile",ylab="GMAT Quantitative Percentile")

mean(surveyanswered$gmat_qpc)

## [1] 80.23684

Variation of GMAT Verbal Percentile

boxplot(surveyanswered$gmat_vpc,ylim=c(60,100),xlim=c(1,1),main="Boxplot Showing Variation of GMAT Verbal Percentile",ylab="GMAT Verbal Percentile")

mean(surveyanswered$gmat_vpc)

## [1] 77.85088

Variation of GMAT Total Percentile

boxplot(surveyanswered$gmat_tpc,ylim=c(72,100),xlim=c(1,1),main="Boxplot Showing Variation of GMAT Total Percentile",ylab="GMAT Total Percentile")

mean(surveyanswered$gmat_tot)

## [1] 617.3246

Variation of MBA Spring Average

boxplot(surveyanswered$s_avg,ylim=c(),xlim=c(1,1),main="Boxplot Showing Variation of Spring MBA Average",ylab= "MBA Spring Average")

mean(surveyanswered$s_avg)

## [1] 3.031009

Variation of MBA Fall Average

boxplot(surveyanswered$f_avg,ylim=c(1.8,4),xlim=c(1,1),main="Boxplot Showing Variation of Fall MBA Average",ylab="MBA Fall Average")

mean(surveyanswered$f_avg)

## [1] 3.058947

Variation of Quartile Ranking among MBA students

boxplot(surveyanswered$quarter,ylim=c(0,4),xlim=c(1,1),main="Boxplot Showing Variation of Quartile Ranking Among Students",ylab="Quartile Ranking")

mean(surveyanswered$quarter)

## [1] 2.47807

Variation of Working Experience among MBA students

boxplot(surveyanswered$work_yrs,ylim=c(0,7),xlim=c(1,1),main="Boxplot Showing Variation of Work Experience Among Students",ylab="Years of Experience")

mean(surveyanswered$work_yrs)

## [1] 4.030702

Distribution of first language among students

table(surveyanswered$frstlang)## 1=English, 2=Others

## 
##   1   2 
## 204  24

Excluding data of students who have not filled survey or didn’t reported salary

salaryknown <-MBA[which(MBA$salary != '998'& MBA$salary != '999'),]
dim(salaryknown)

## [1] 193  13

View(salaryknown)

Variation of Salary among MBA students only whose salary are known

boxplot(salaryknown$salary,ylim=c(-100000,200000),xlim=c(1,1),main="Variation of Salary Among Students whose salary are known",ylab="Salary")

mean(salaryknown$salary)

## [1] 54985.32

Variation of Satisfaction Rate among MBA students

boxplot(surveyanswered$satis,ylim=c(2,10),xlim=c(1,1),main="Variation of Satisfaction Rate Among MBA Students")

mean(surveyanswered$satis)

## [1] 5.565789

Scatter Plot showing relation in Salary and GMAT Total Scores

plot(x=salaryknown$salary,y=salaryknown$gmat_tot,xlab="Salary",ylab="GMAT Total Score", main="Scatter Plot showing relation in Salary and GMAT Total Scores")

Scatter Plot showing relation in Salary and GMAT Quant Percentile

plot(x=salaryknown$salary,y=salaryknown$gmat_qpc,xlab="Salary",ylab="GMAT Quant Percentile", main="Scatter Plot showing relation in Salary and GMAT Quant Percentile")

Scatter Plot showing relation in Salary and GMAT Verbal Percentile

plot(x=salaryknown$salary,y=salaryknown$gmat_vpc,xlab="Salary",ylab="GMAT Verbal Percentile", main="Scatter Plot showing relation in Salary and GMAT Verbal Percentile")

Scatter Plot showing relation in Salary and GMAT Total Percentile

plot(x=salaryknown$salary,y=salaryknown$gmat_tpc,xlab="Salary",ylab="GMAT Total Percentile", main="Scatter Plot showing relation in Salary and GMAT Total Percentile")

Scatter Plot showing relation in Salary and Spring MBA Average

plot(x=salaryknown$salary,y=salaryknown$s_avg,xlab="Salary",ylab="Spring MBA Average", main="Scatter Plot showing relation in Salary and Spring MBA Average")

Scatter Plot showing relation in Salary and Fall MBA Average

plot(x=salaryknown$salary,y=salaryknown$f_avg,xlab="Salary",ylab="Fall MBA Average", main="Scatter Plot showing relation in Salary and Fall MBA Average")

Scatter Plot showing relation in Salary and Quartile Ranking

plot(y=salaryknown$salary,x=salaryknown$quarter,ylab="Salary",xlab="Quartile Ranking", main="Scatter Plot showing relation in Salary and Quartile Ranking")

Scatter Plot showing relation in Salary and Working Experience

plot(y=salaryknown$salary,x=salaryknown$work_yrs,ylab="Salary",xlab="Years of Working Experience", main="Scatter Plot showing relation in Salary and Working Experience")

Scatter Plot showing relation in Salary and Students First Language

plot(y=salaryknown$salary,x=salaryknown$frstlang,ylab="Salary",xlab="First Language,    1=English,  2=Other", main="Scatter Plot showing relation in Salary and Students First Language")

Scatter Plot showing relation in Salary and Students Satisfaction Rate

plot(y=salaryknown$salary,x=salaryknown$satis,ylab="Salary",xlab="Satisfaction Rating", main="Scatter Plot showing relation in Salary and Students Satisfaction Rate")

Covariance Correltion Table

cor(salaryknown,use="complete")

##                   age          sex      gmat_tot     gmat_qpc     gmat_vpc
## age       1.000000000 -0.031876273 -1.256220e-01 -0.220590341 -0.006721674
## sex      -0.031876273  1.000000000 -4.351109e-02 -0.167904888  0.099184398
## gmat_tot -0.125622047 -0.043511095  1.000000e+00  0.743099719  0.752906719
## gmat_qpc -0.220590341 -0.167904888  7.430997e-01  1.000000000  0.175497777
## gmat_vpc -0.006721674  0.099184398  7.529067e-01  0.175497777  1.000000000
## gmat_tpc -0.131681932 -0.012849186  8.791496e-01  0.690581939  0.688039929
## s_avg     0.164342257  0.073368077  1.435675e-01  0.019038162  0.190665307
## f_avg    -0.034290725  0.042895288  1.010821e-01  0.130285115  0.033106093
## quarter  -0.076614994 -0.086616877 -8.407099e-02  0.008601267 -0.139400223
## work_yrs  0.871679595 -0.023832548 -1.736909e-01 -0.241384675 -0.041357878
## frstlang  0.097619028 -0.008488358 -9.557089e-02  0.094537575 -0.295162826
## salary   -0.130198680  0.018516965 -5.685962e-05  0.028391635  0.003389965
## satis    -0.073500580 -0.061738773  7.981946e-02 -0.020006117  0.195134711
##             gmat_tpc       s_avg        f_avg      quarter     work_yrs
## age      -0.13168193  0.16434226 -0.034290725 -0.076614994  0.871679595
## sex      -0.01284919  0.07336808  0.042895288 -0.086616877 -0.023832548
## gmat_tot  0.87914961  0.14356746  0.101082103 -0.084070990 -0.173690863
## gmat_qpc  0.69058194  0.01903816  0.130285115  0.008601267 -0.241384675
## gmat_vpc  0.68803993  0.19066531  0.033106093 -0.139400223 -0.041357878
## gmat_tpc  1.00000000  0.18894788  0.109811857 -0.128533421 -0.166139876
## s_avg     0.18894788  1.00000000  0.520554250 -0.735421726  0.159136628
## f_avg     0.10981186  0.52055425  1.000000000 -0.382421186 -0.047951357
## quarter  -0.12853342 -0.73542173 -0.382421186  1.000000000 -0.126454286
## work_yrs -0.16613988  0.15913663 -0.047951357 -0.126454286  1.000000000
## frstlang -0.10789784 -0.12631935 -0.055830525  0.089504320 -0.002916547
## salary    0.06094464  0.09632412  0.008846655 -0.147257809 -0.053266846
## satis     0.13288434 -0.04639953 -0.114704819  0.067729421 -0.007722658
##              frstlang        salary        satis
## age       0.097619028 -1.301987e-01 -0.073500580
## sex      -0.008488358  1.851696e-02 -0.061738773
## gmat_tot -0.095570885 -5.685962e-05  0.079819458
## gmat_qpc  0.094537575  2.839164e-02 -0.020006117
## gmat_vpc -0.295162826  3.389965e-03  0.195134711
## gmat_tpc -0.107897839  6.094464e-02  0.132884339
## s_avg    -0.126319350  9.632412e-02 -0.046399534
## f_avg    -0.055830525  8.846655e-03 -0.114704819
## quarter   0.089504320 -1.472578e-01  0.067729421
## work_yrs -0.002916547 -5.326685e-02 -0.007722658
## frstlang  1.000000000  7.125825e-03 -0.135986251
## salary    0.007125825  1.000000e+00  0.156439455
## satis    -0.135986251  1.564395e-01  1.000000000

Corrogram of variables

library("corrgram", lib.loc="~/R/win-library/3.4")
corrgram(salaryknown,lower.panel="panel.shade",upper.panel="panel.pie",order=TRUE)

Creating a data frame placed in which all the stduents are placed and have salary > 0

placed <-MBA[which(MBA$salary != '998' & MBA$salary != '999' & MBA$salary != '0'),]
dim(placed)

## [1] 103  13

View(placed)

Trying to put salary as a function of age,sex,GMAT Performance,MBA Performance,Quartile Ranking, First Language,Years of experience and satisfaction rate

fit <-lm(salary ~ age + sex + gmat_tot + gmat_qpc + gmat_vpc + gmat_tpc + s_avg + f_avg + quarter + work_yrs + frstlang + satis, data=placed)
summary(fit)

## 
## Call:
## lm(formula = salary ~ age + sex + gmat_tot + gmat_qpc + gmat_vpc + 
##     gmat_tpc + s_avg + f_avg + quarter + work_yrs + frstlang + 
##     satis, data = placed)
## 
## 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_tot       16.19     178.85   0.090   0.9281  
## gmat_qpc      796.55     496.78   1.603   0.1123  
## gmat_vpc      546.31     501.97   1.088   0.2794  
## 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

residuals(fit)

##          35          36          37          38          39          40 
##  -9121.5225 -20118.7262 -13728.9064  -6280.8242 -16809.4288   2721.5554 
##          41          42          43          44          45          46 
##  -3952.2049    725.3372  -5859.1870   1394.0064   2241.5696   6115.4816 
##          47          48          49          50          51          52 
##  -2921.6198  -2001.7336    704.9329    659.7695    732.3905  -2844.2249 
##          53          54          55          56          57          58 
##   -534.7181 -12003.4297   1706.5455  -4392.9044   1255.9892   4667.3406 
##          59          60          61          62          63          64 
##   3922.0854 -19710.6524   9055.6028   5837.0849  -5387.1697  18008.9367 
##          65          66          67          68          69         115 
##   9186.2841   8030.4338   8460.4124   9113.9350  57397.8423 -13874.7383 
##         116         117         118         119         120         121 
##  -5637.0156 -24353.3417  -7167.8666  -4344.7667   3003.0343 -19900.4167 
##         122         123         124         125         126         127 
##   2364.4086  -3205.4685 -11265.6145 -11371.3216   6178.6477 -13592.0319 
##         128         129         130         131         132         133 
##   3362.9844  -1309.6841  -5427.5111   6009.2247    507.9454 -26489.1303 
##         134         135         136         137         138         139 
##   6321.1964   -372.7203  16875.4951  13667.7506  28394.4324  47101.2425 
##         186         187         188         189         190         191 
## -14818.5479 -13995.5905  -4419.4767  -7955.8161  -8175.1887  -8009.2493 
##         192         193         194         195         196         197 
##  -4244.9288  -5476.6101   9853.6854  13229.8943   5664.7847 -14385.6980 
##         198         199         200         201         202         203 
##  -4417.8343 -12646.6695    134.6264   3472.5678   8379.5480  -8914.1699 
##         204         205         206         207         208         209 
##  -5564.2811   4659.6177   3353.4934  -6712.7200   6300.2463  14927.9986 
##         256         257         258         259         260         261 
## -22668.1316 -12360.1760  -9852.8397 -11624.1880  -6634.7819 -15666.5153 
##         262         263         264         265         266         267 
##   2031.5837  -2034.1828  -1349.6857   2352.7517  11621.9035   7082.1372 
##         268         269         270         271         272         273 
##    405.4271   3234.9490 -21479.1925  12490.4345   8061.0812  23803.0101 
##         274 
##  70601.7162

Now putting salary as a function of only significant variable fromabove regression i.e age, GMAT Quant Percentile, GMAT Total Percentile, Quartile Ranking and First Language

fit <-lm(salary ~ age + gmat_qpc + gmat_tpc + quarter + frstlang, data=placed)
summary(fit )

## 
## Call:
## lm(formula = salary ~ age + gmat_qpc + gmat_tpc + quarter + frstlang, 
##     data = placed)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -25457  -8804   -679   4434  73624 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  38832.1    19296.8   2.012   0.0470 *  
## age           2641.4      510.2   5.177 1.22e-06 ***
## gmat_qpc       355.5      155.3   2.289   0.0242 *  
## gmat_tpc      -423.9      189.2  -2.240   0.0274 *  
## quarter      -1657.6     1383.5  -1.198   0.2338    
## frstlang      4402.0     6660.0   0.661   0.5102    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15220 on 97 degrees of freedom
## Multiple R-squared:  0.3099, Adjusted R-squared:  0.2743 
## F-statistic:  8.71 on 5 and 97 DF,  p-value: 7.51e-07

residuals(fit)

##           35           36           37           38           39 
##  -6842.41226 -19775.94616 -11852.13138  -9345.99118 -13487.03737 
##           40           41           42           43           44 
##  -4146.87982    432.00320   -580.73774  -4532.13518   -279.35436 
##           45           46           47           48           49 
##    170.48290   4025.72794  -3674.06248  -2040.29412   3031.91597 
##           50           51           52           53           54 
##    -98.19145   2360.76003   -278.65380  -1969.41583 -12268.22429 
##           55           56           57           58           59 
##    726.03459  -8258.84371    112.56121   6415.38278   1393.38325 
##           60           61           62           63           64 
## -23008.20649    119.66834   9868.50824  -3866.55137  18465.84608 
##           65           66           67           68           69 
##  12227.14786   7410.17151   8517.20412  12096.87957  61084.59218 
##          115          116          117          118          119 
## -17259.75340  -8720.38506 -22582.70211  -4462.75785  -5433.15646 
##          120          121          122          123          124 
##   4718.22360 -12503.21418   6063.43534  -2676.55670 -16272.23668 
##          125          126          127          128          129 
## -15304.05099   4150.48715 -15460.02872    279.61494  -5423.60805 
##          130          131          132          133          134 
##  -6024.76681   7230.74602   2688.98422 -21077.88008   3720.53216 
##          135          136          137          138          139 
##   3393.98305  18698.70334  15888.89465  29181.43018  48076.52092 
##          186          187          188          189          190 
## -11460.98108 -15134.41365  -8118.82068  -3237.42043  -6062.78410 
##          191          192          193          194          195 
## -12097.52458  -3366.18621  -7757.35340   7526.61334  10356.55704 
##          196          197          198          199          200 
##   1166.72773  -9353.20122  -9410.72784  -7964.05678   5109.47149 
##          201          202          203          204          205 
##   3562.66913   3730.85108  -5848.41599  -3821.54893   4763.81285 
##          206          207          208          209          256 
##   3741.99386  -9553.95248   7659.78845  17328.38310 -25457.07388 
##          257          258          259          260          261 
##  -8887.19671  -9807.65111 -10287.81666 -11352.77328 -10144.72826 
##          262          263          264          265          266 
##  -5569.73834   -695.77211  -5030.90272   3127.46446   8231.13668 
##          267          268          269          270          271 
##   1785.54091   -678.62417    760.08768 -19274.22963  17951.41429 
##          272          273          274 
##  11825.29562  25078.20488  73624.22237

We see that R-Squared value have reduced significantly but no much reduction in adjusted R-Square value

Now putting slary as a function of only age, GMAT Quant Percentile and GMAT Total Percentile

fit <-lm(salary ~ age + gmat_qpc + gmat_tpc , data=placed)
summary(fit )

## 
## Call:
## lm(formula = salary ~ age + gmat_qpc + gmat_tpc, data = placed)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -27913  -8913   -660   4973  72402 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  33975.5    18197.9   1.867   0.0649 .  
## age           2836.8      466.4   6.082 2.24e-08 ***
## gmat_qpc       363.0      150.8   2.407   0.0179 *  
## gmat_tpc      -424.1      181.7  -2.333   0.0217 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15200 on 99 degrees of freedom
## Multiple R-squared:  0.2979, Adjusted R-squared:  0.2766 
## F-statistic:    14 on 3 and 99 DF,  p-value: 1.117e-07

residuals(fit)

##           35           36           37           38           39 
##  -4190.23389 -18129.85104  -9763.63397  -7220.99720 -11855.77441 
##           40           41           42           43           44 
##  -2386.88954   2737.99372   1762.65180  -2176.05420   1867.88785 
##           45           46           47           48           49 
##   2290.52015   6460.02399  -1350.49439   -233.38058   5060.50091 
##           50           51           52           53           54 
##   2081.26589   4390.63665   1670.22977   -660.41158 -11245.20937 
##           55           56           57           58           59 
##   2035.81728  -7214.28841   1764.71013   8538.43065   2879.75701 
##           60           61           62           63           64 
## -23547.15050   1753.87132  11507.18727   1169.87750  20309.25620 
##           65           66           67           68           69 
##  13670.38742   8593.29700   9628.30953  11371.46905  63091.90193 
##          115          116          117          118          119 
## -17024.49104  -8306.07228 -23130.24132  -4091.38466  -5004.20613 
##          120          121          122          123          124 
##   5599.45166 -11818.69643   6993.53277  -2017.22722 -11683.40545 
##          125          126          127          128          129 
## -11031.15947   4884.56127 -16065.53428    693.92772  -5459.30825 
##          130          131          132          133          134 
##  -6095.86650   7488.45122   2772.13591 -22299.95223   3975.70742 
##          135          136          137          138          139 
##   3013.26265  19345.53600  16038.79107  29401.47116  48693.68926 
##          186          187          188          189          190 
## -11977.89434 -16753.74862  -9281.89426  -4376.49427  -7306.07228 
##          191          192          193          194          195 
## -13940.08783  -4925.99794  -9462.63816   6525.01262   9481.15369 
##          196          197          198          199          200 
##     47.76141  -6642.79331 -11240.52906 -10016.43186   3989.79732 
##          201          202          203          204          205 
##   2356.85057   2682.61315  -7886.73735  -5995.78652   3714.21264 
##          206          207          208          209          256 
##   1792.86007  -7717.50066   6072.57714  16230.56794 -27913.49061 
##          257          258          259          260          261 
## -11336.32137 -12758.11748 -13302.17918 -14418.85375 -13435.32870 
##          262          263          264          265          266 
##  -8543.23140  -3552.35939  -8113.17763    523.50457   5614.09614 
##          267          268          269          270          271 
##  -1324.45221  -4234.80864  -2387.37506 -18846.83822  15625.05460 
##          272          273          274 
##   8994.28583  22104.44662  72401.75896

We see that Multiple R-Squared value have reduced again little but adjusted R-Sqaure value is still same but we can conclude that salary of placed students depend much on age, GMAT Quant Percentile and GMAT Total Percentile more

Creating a data frame unplaced of students whose salary is equal to 0

unplaced <-MBA[which(MBA$salary =='0'),]
dim(unplaced)

## [1] 90 13

View(unplaced)

Introducing a new variable status_placed that whether a student is placed or not 1 represnt placed and 0 represent unplaced

salaryknown$status_placed <- ifelse( salaryknown$salary > 1, "1" , no = "0")

Contigency tale with status placement and Sex

table(salaryknown$status_placed,salaryknown$sex)

##    
##      1  2
##   0 67 23
##   1 72 31

prop.table(table(salaryknown$status_placed,salaryknown$sex),1)

##    
##             1         2
##   0 0.7444444 0.2555556
##   1 0.6990291 0.3009709

prop.table(table(salaryknown$status_placed,salaryknown$sex),2)

##    
##             1         2
##   0 0.4820144 0.4259259
##   1 0.5179856 0.5740741

The result shows that 57% of girls are placed contrary to 51% of boys placed, which related with companies look for gender diversity

mytable <-xtabs(~status_placed + sex, data=salaryknown)
chisq.test(mytable)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  mytable
## X-squared = 0.29208, df = 1, p-value = 0.5889

prop.table(mytable <-xtabs(~status_placed + sex, data=salaryknown))

##              sex
## status_placed         1         2
##             0 0.3471503 0.1191710
##             1 0.3730570 0.1606218

addmargins(mytable)

##              sex
## status_placed   1   2 Sum
##           0    67  23  90
##           1    72  31 103
##           Sum 139  54 193

prop.table(addmargins(mytable),2)*100

##              sex
## status_placed        1        2      Sum
##           0   24.10072 21.29630 23.31606
##           1   25.89928 28.70370 26.68394
##           Sum 50.00000 50.00000 50.00000

Higher P-value also support that placement and sex are related

Comparing Mean Age of all, placed and unplaced students

mean(salaryknown$age)

## [1] 27.58549

mean(salaryknown$age[salaryknown$salary != "0" ])

## [1] 26.7767

mean(salaryknown$age[salaryknown$salary == "0" ])

## [1] 28.51111

So average age of placed students is lowest while avaerge age of unplaced is the highest,which means lower age helps in placement

Comparing Mean GMAT Total of all, placed and unplaced students

mean(salaryknown$gmat_tot)

## [1] 615.2332

mean(salaryknown$gmat_tot[salaryknown$salary != "0" ])

## [1] 616.0194

mean(salaryknown$gmat_tot[salaryknown$salary == "0" ])

## [1] 614.3333

So clearly placed student have highest Average GMAT Total folloewd by allover Average GMAT total and at lowest the GMAT Total of unplaced students. So Higer the GMAT total more the chance of placement

Comparing Mean GMAT Quant Percentile of all, placed and unplaced students

mean(salaryknown$gmat_qpc)

## [1] 79.34715

mean(salaryknown$gmat_qpc[salaryknown$salary != "0" ])

## [1] 79.72816

mean(salaryknown$gmat_qpc[salaryknown$salary == "0" ])

## [1] 78.91111

Again placed student have highest Average GMATQunat Percentile folloewd by allover Average GMAT Quant Percentile and at lowest the GMAT Quant Percentile of unplaced students. So Higer the Quant Percentile more the chance of placement.

Comparing Mean GMAT Verbal Percentile of all, placed and unplaced students

mean(salaryknown$gmat_vpc)

## [1] 78.12953

mean(salaryknown$gmat_vpc[salaryknown$salary != "0" ])

## [1] 78.56311

mean(salaryknown$gmat_vpc[salaryknown$salary == "0" ])

## [1] 77.63333

Again placed student have highest Average GMAT Verabl Percentile folloewd by allover Average GMAT Verbal Percentile and at lowest the GMAT Verbal Percentile of unplaced students. So Higer the Verbal Percentile more the chance of placement.

Comparing Mean GMAT Total Percentile of all, placed and unplaced students

mean(surveyanswered$gmat_tpc)

## [1] 83.61404

mean(surveyanswered$gmat_tpc[surveyanswered$salary != "0" ])

## [1] 84.47826

mean(surveyanswered$gmat_tpc[surveyanswered$salary == "0" ])

## [1] 82.28889

Again placed student have highest Average GMAT total Percentile folloewd by allover Average GMAT Verbal Percentile and at lowest the GMAT total Percentile of unplaced students. So Higer the total Percentile more the chance of placement.

Comparing Mean Spring Average of all, placed and unplaced students

mean(salaryknown$s_avg)

## [1] 3.063834

mean(salaryknown$s_avg[salaryknown$salary != "0" ])

## [1] 3.09233

mean(salaryknown$s_avg[salaryknown$salary == "0" ])

## [1] 3.031222

Again placed student have highest Spring Average followed by allover Spring Average Percentile and at lowest the Spring Average of unplaced students. So Higer the spring Average more the chance of placement.

Comparing Mean Fall Average of all, placed and unplaced students

mean(salaryknown$f_avg)

## [1] 3.077668

mean(salaryknown$f_avg[salaryknown$salary != "0" ])

## [1] 3.090971

mean(salaryknown$f_avg[salaryknown$salary == "0" ])

## [1] 3.062444

Again placed student have highest Fall Average followed by allover Fall Average Percentile and at lowest the Fall Average of unplaced students. So Higer the Fall Average more the chance of placement.

Comparing Mean Quartile Ranking of all, placed and unplaced students

mean(salaryknown$quarter)

## [1] 2.393782

mean(salaryknown$quarter[salaryknown$salary != "0" ])

## [1] 2.262136

mean(salaryknown$quarter[salaryknown$salary == "0" ])

## [1] 2.544444

Again placed student havebetter ranking followed by allover Average ranking and at lowest the Average Quartile Ranking of unplaced students. So better the ranking better the chance of placement.

Comparing Mean Working Experience of all, placed and unplaced students

mean(salaryknown$work_yrs)

## [1] 4.103627

mean(salaryknown$work_yrs[salaryknown$salary != "0" ])

## [1] 3.679612

mean(salaryknown$work_yrs[salaryknown$salary == "0" ])

## [1] 4.588889

Here placed students have minimum avaerage work ex folowed by allover avaerage and lastly unplaced have maximum work experince, so less experience help in getting placed.

Comparing the effect of first language on all, placed and unplaced students

mytable <-xtabs(~ status_placed + frstlang, data=salaryknown)
mytable

##              frstlang
## status_placed  1  2
##             0 82  8
##             1 96  7

addmargins(mytable)

##              frstlang
## status_placed   1   2 Sum
##           0    82   8  90
##           1    96   7 103
##           Sum 178  15 193

chisq.test(mytable)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  mytable
## X-squared = 0.074127, df = 1, p-value = 0.7854

Higher P-Value shows that first language have effect on placement

Comparing satisfaction rate of all, placed and unplaced students

mean(salaryknown$satis)

## [1] 5.761658

mean(salaryknown$satis[salaryknown$salary != "0" ])

## [1] 5.883495

mean(salaryknown$satis[salaryknown$salary == "0" ])

## [1] 5.622222

So placed students have shown highest satisfaction while unplaced students have shown the lowest satisfaction

Assigning values to variable status_placed and converting it into numeric variable

salaryknown$status_placed <- ifelse( salaryknown$salary > 1, "1" , no = "0")
salaryknown$status_placed <- factor(salaryknown$status_placed)
salaryknown$status_placed <- factor(salaryknown$status_placed)

Challenge

Running logistic regression on dataset salary known to predict the status of placement of student

data <- subset(salaryknown, select=c(1,2,3,4,5,6,9,10,11,13,14))
train <-data[1:150,]
test  <-data[151:193,]
library("glm2", lib.loc="~/R/win-library/3.4")
model <- glm(status_placed ~.,family=binomial(link='logit'),data=train)
summary(model)

## 
## Call:
## glm(formula = status_placed ~ ., family = binomial(link = "logit"), 
##     data = train)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.9080  -1.1151   0.7427   1.0386   1.5244  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)  
## (Intercept)  3.625855   4.846925   0.748   0.4544  
## age         -0.143999   0.101420  -1.420   0.1557  
## sex         -0.099873   0.392916  -0.254   0.7994  
## gmat_tot    -0.004329   0.014667  -0.295   0.7679  
## gmat_qpc    -0.055383   0.052299  -1.059   0.2896  
## gmat_vpc    -0.047847   0.050862  -0.941   0.3469  
## gmat_tpc     0.127970   0.078713   1.626   0.1040  
## quarter     -0.488002   0.224710  -2.172   0.0299 *
## work_yrs     0.037768   0.110118   0.343   0.7316  
## frstlang    -0.101547   0.692551  -0.147   0.8834  
## satis        0.281737   0.235374   1.197   0.2313  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 206.64  on 149  degrees of freedom
## Residual deviance: 191.72  on 139  degrees of freedom
## AIC: 213.72
## 
## Number of Fisher Scoring iterations: 4

Annova Test

anova(model, test="Chisq")

## Analysis of Deviance Table
## 
## Model: binomial, link: logit
## 
## Response: status_placed
## 
## Terms added sequentially (first to last)
## 
## 
##          Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                       149     206.64           
## age       1   4.9691       148     201.67  0.02580 *
## sex       1   0.0012       147     201.66  0.97186  
## gmat_tot  1   0.0452       146     201.62  0.83169  
## gmat_qpc  1   0.1837       145     201.44  0.66819  
## gmat_vpc  1   0.3484       144     201.09  0.55502  
## gmat_tpc  1   3.1229       143     197.97  0.07720 .
## quarter   1   4.4985       142     193.47  0.03393 *
## work_yrs  1   0.2539       141     193.21  0.61432  
## frstlang  1   0.0460       140     193.17  0.83009  
## satis     1   1.4471       139     191.72  0.22900  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Finding Accuracy of the model

fitted.results <- predict(model,newdata=subset(test,select=c(1,2,3,4,5,6,7,8,9,10,11)),type='response')
fitted.results <- ifelse(fitted.results > 0.5,1,0)

misClasificError <- mean(fitted.results != test$status_placed)
print(paste('Accuracy',1-misClasificError))

## [1] "Accuracy 0.581395348837209"

58% is the accuracy of the above model

Final conclusions Factors Affecting placements are lower age,female biased, higher GMAT Total, higher GMAT Quant Percentile, higher GMAT Verable Perecntile, highre GMAT total percentile, higher Sprong Average, higher Fall Average, low work experience and higher satisfaction rating are factors which improve chances of placement.

Higher salary is more influenced by age, GMAT Quant Percentile and GMAT total percentile