setwd("C:/Users/Taiyyab Ali/Desktop/R language")
MBASalary <- read.csv(paste("MBAStartingSalariesData.csv",sep=""))
  1. Creating a data with actually placed MBAs
placedMBA <- MBASalary[which(MBASalary$salary > 999),]

2.Salary dependent variables in MBAs

model1 <- salary ~ age + sex + work_yrs + gmat_tot + f_avg + s_avg + quarter + satis
fit1 <-lm (model1, data = placedMBA)
summary(fit1)
## 
## Call:
## lm(formula = model1, data = placedMBA)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -24191  -7715  -1892   5226  84183 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 77506.24   41331.20   1.875   0.0639 .
## age          2378.24    1030.48   2.308   0.0232 *
## sex         -4021.37    3518.14  -1.143   0.2559  
## work_yrs      327.98    1118.32   0.293   0.7700  
## gmat_tot      -16.54      32.10  -0.515   0.6077  
## f_avg        -245.64    3870.72  -0.063   0.9495  
## s_avg       -2688.53    8041.77  -0.334   0.7389  
## quarter     -1691.87    2676.79  -0.632   0.5289  
## satis       -1877.21    2099.06  -0.894   0.3734  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15840 on 94 degrees of freedom
## Multiple R-squared:  0.276,  Adjusted R-squared:  0.2144 
## F-statistic:  4.48 on 8 and 94 DF,  p-value: 0.0001243

Excepet age all variable seems statistically insignificant.

library(leaps)
leap1 <- regsubsets(model1, data = placedMBA, nbest=1)
# summary(leap1)
plot(leap1, scale="adjr2")

All the variable have very less significance in salary.

3.Lets exclude MBA score

model2 <- salary ~ age + sex + work_yrs + gmat_tot + quarter + satis
fit2 <- lm(model2, data = placedMBA)
summary(fit2)
## 
## Call:
## lm(formula = model2, data = placedMBA)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -26282  -7776  -2189   5475  84544 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 68433.67   32014.97   2.138   0.0351 *
## age          2378.81    1017.95   2.337   0.0215 *
## sex         -4221.88    3423.82  -1.233   0.2206  
## work_yrs      313.32    1100.36   0.285   0.7765  
## gmat_tot      -18.49      31.33  -0.590   0.5564  
## quarter      -889.75    1456.19  -0.611   0.5426  
## satis       -1930.23    2073.30  -0.931   0.3542  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15680 on 96 degrees of freedom
## Multiple R-squared:  0.275,  Adjusted R-squared:  0.2297 
## F-statistic:  6.07 on 6 and 96 DF,  p-value: 2.035e-05
library(coefplot)
## Loading required package: ggplot2
coefplot(fit2, intercept= FALSE, outerCI=1.96,coefficients=c("age","sex","work_yrs", "gmat_tot","quarter","satis"))
## Warning: Ignoring unknown aesthetics: xmin, xmax

fit3 <- lm(salary ~ age + work_yrs + gmat_tot, data = placedMBA)
summary(fit3)
## 
## Call:
## lm(formula = salary ~ age + work_yrs + gmat_tot, data = placedMBA)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -32657  -8150  -2117   4705  78974 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 46876.35   29418.14   1.593   0.1142  
## age          2448.62    1002.87   2.442   0.0164 *
## work_yrs      319.93    1094.82   0.292   0.7707  
## gmat_tot      -17.19      30.92  -0.556   0.5795  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15680 on 99 degrees of freedom
## Multiple R-squared:  0.2529, Adjusted R-squared:  0.2303 
## F-statistic: 11.17 on 3 and 99 DF,  p-value: 2.228e-06
fit4 <- lm(salary ~ age + gmat_tot, data = placedMBA)
summary(fit4)
## 
## Call:
## lm(formula = salary ~ age + gmat_tot, data = placedMBA)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -32536  -8423  -1802   4955  79066 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 41776.16   23573.16   1.772   0.0794 .  
## age          2706.59     473.72   5.713 1.15e-07 ***
## gmat_tot      -18.21      30.58  -0.596   0.5528    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15600 on 100 degrees of freedom
## Multiple R-squared:  0.2523, Adjusted R-squared:  0.2373 
## F-statistic: 16.87 on 2 and 100 DF,  p-value: 4.859e-07

It seems like starting salary is mostly depend on other variable like how they presented self in interview or other aptitude test which are not covered in data because intercept is very high and statistically significant. Although age, sex, and other score matter because everytime reducing variable R-square and adjusted R-squre deceases.