mba_salary
Ayushi
26 December 2017
model <- read.csv(paste("MBA Starting Salaries Data.csv",sep=""))
View(model)summary(model)## 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(model)## 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 22.45Visualizing the distribution of each variable independently
Age:
hist(model$age,xlab="age in years",main="age distribution",col="skyblue",breaks=10)
Gender distribution
hist(model$sex,xlab="gender",main="gender distribution",col="lightblue")
1 represents male and 2 represents female
Gmat total score distribution
hist(model$gmat_tot,xlab="total gmat score", main="gmat score frequency distribution",col="lightblue",breaks=20)
hist(model$gmat_qpc,xlab = "quantitative GMAT percentile",main="quantitative distribution", col="lightblue")
Spring mba average
hist(model$s_avg,xlab="spring mba average", main="spring mba average frequency distribution", col="lightblue",breaks=20)
Fall mba average
hist(model$f_avg,xlab="fall mba average", main="fall mba average frequency distribution", col="lightblue",breaks=20)
Work experience distribution
hist(model$work_yrs,xlab="work experience in years",main="work expreience frequency distribution", col="lightblue",breaks=20)
First language distribution
hist(model$frstlang,xlab="first language",main="first lamguage frequency distribution",col="lightblue")
Salary distribution
model1<-model[which(model$salary!='998' & model$salary!='999'& model$salary!='0'),]
hist(model1$salary,xlab="starting salary",main="first salary frequency distribution",col="lightblue")
degree of satisfaction with MBA program (1= low, 7 = high satisfaction)
new <- model[which(model$satis<='7'),]
hist(new$satis,xlab="degree of satisfaction with MBA program",main="frequency distribution of degree of satisfaction",col="lightblue",breaks=5)
Scatterplot between salary and age
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitscatterplot(salary~age, data=model1,
main="Scatter plot of salary vs age",
xlab="age",
ylab="salary")
Scatterplot between salary and sex
library(car)
scatterplot(salary~sex,data=model1,
spread=FALSE,
main="scatterplot of salary and sex",ylab="salary",xlab="sex")
Scatterplot of salary and first language
scatterplot(salary~frstlang, data=model1,
main="scatterplot of first language and salary",xlab="first language",ylab="salary")
scatterplot of gmat total and salary
scatterplot(salary~gmat_tot, data=model1,
main="scatterplot of gmat total score and salary",xlab="gmat total score",ylab="salary")
Scatterplot of salary and work experience
scatterplot(salary~work_yrs, data=model1,
main="scatterplot of work experience and salary",xlab="work experience in years",ylab="salary")
Scatterplot of salary and satisfaction
scatterplot(salary~satis, data=model1,
main="scatterplot of satisfaction and salary",xlab="satisfaction",ylab="salary")
Corrgram of the variables from the data set of the people who got jobs
library(corrgram)
corrgram(model1, order=TRUE, lower.panel=panel.shade,
upper.panel=panel.pie, text.panel=panel.txt,
main="MBA starting salary analysis Correlogram")
cor(model[, c(1:13)]) ## age sex gmat_tot gmat_qpc gmat_vpc
## age 1.00000000 -0.028106442 -0.14593840 -0.21616985 -0.04417547
## sex -0.02810644 1.000000000 -0.05336820 -0.16377435 0.07488782
## gmat_tot -0.14593840 -0.053368202 1.00000000 0.72473781 0.74839187
## gmat_qpc -0.21616985 -0.163774346 0.72473781 1.00000000 0.15218014
## gmat_vpc -0.04417547 0.074887816 0.74839187 0.15218014 1.00000000
## gmat_tpc -0.16990307 -0.008090213 0.84779965 0.65137754 0.66621604
## s_avg 0.14970402 0.127115144 0.11311702 -0.02984873 0.20445365
## f_avg -0.01744806 0.091663891 0.10442409 0.07370455 0.07592225
## quarter -0.04967221 -0.133533171 -0.09223903 0.03636638 -0.17460736
## work_yrs 0.85829810 -0.011296374 -0.18235434 -0.23660827 -0.06639049
## frstlang 0.05692649 0.001536205 -0.13503402 0.13892774 -0.38980465
## salary -0.06257355 0.068858628 -0.05497188 -0.04403293 -0.00613934
## satis -0.12788825 -0.054602220 0.08255770 0.06060004 0.06262375
## gmat_tpc s_avg f_avg quarter work_yrs
## age -0.169903066 0.14970402 -0.01744806 -4.967221e-02 0.858298096
## sex -0.008090213 0.12711514 0.09166389 -1.335332e-01 -0.011296374
## gmat_tot 0.847799647 0.11311702 0.10442409 -9.223903e-02 -0.182354339
## gmat_qpc 0.651377538 -0.02984873 0.07370455 3.636638e-02 -0.236608270
## gmat_vpc 0.666216035 0.20445365 0.07592225 -1.746074e-01 -0.066390490
## gmat_tpc 1.000000000 0.11736245 0.07973210 -8.303535e-02 -0.173361859
## s_avg 0.117362449 1.00000000 0.55062139 -7.621166e-01 0.129292714
## f_avg 0.079732099 0.55062139 1.00000000 -4.475064e-01 -0.039056921
## quarter -0.083035351 -0.76211664 -0.44750637 1.000000e+00 -0.086026406
## work_yrs -0.173361859 0.12929271 -0.03905692 -8.602641e-02 1.000000000
## frstlang -0.103362747 -0.13631308 -0.03705695 9.949226e-02 -0.027866747
## salary 0.004930901 0.14583606 0.02944303 -1.643699e-01 0.009023407
## satis 0.092934266 -0.03268664 0.01089273 -1.267198e-05 -0.109255286
## frstlang salary satis
## age 0.056926486 -0.062573547 -1.278882e-01
## sex 0.001536205 0.068858628 -5.460222e-02
## gmat_tot -0.135034017 -0.054971880 8.255770e-02
## gmat_qpc 0.138927742 -0.044032933 6.060004e-02
## gmat_vpc -0.389804653 -0.006139340 6.262375e-02
## gmat_tpc -0.103362747 0.004930901 9.293427e-02
## s_avg -0.136313080 0.145836062 -3.268664e-02
## f_avg -0.037056954 0.029443027 1.089273e-02
## quarter 0.099492259 -0.164369865 -1.267198e-05
## work_yrs -0.027866747 0.009023407 -1.092553e-01
## frstlang 1.000000000 -0.086592096 7.932264e-02
## salary -0.086592096 1.000000000 -3.352171e-01
## satis 0.079322637 -0.335217114 1.000000e+00Correlation of salary with other variables
cor(model1$salary, model1)## age sex gmat_tot gmat_qpc gmat_vpc gmat_tpc
## [1,] 0.4996428 -0.1662887 -0.09067141 0.0141413 -0.1374323 -0.1320178
## s_avg f_avg quarter work_yrs frstlang salary satis
## [1,] 0.1017317 -0.106039 -0.1284853 0.4546663 0.2670195 1 -0.0400506contingency tables showing the affect of various factors on the salary
mytable <-xtabs(~salary+sex,data=model1)
mytable## sex
## salary 1 2
## 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 1 mytable1 <-xtabs(~salary+work_yrs+frstlang,data=model1)
mytable1## , , frstlang = 1
##
## work_yrs
## salary 0 1 2 3 4 5 6 7 8 10 15 16
## 64000 0 0 1 0 0 0 0 0 0 0 0 0
## 77000 0 0 1 0 0 0 0 0 0 0 0 0
## 78256 0 1 0 0 0 0 0 0 0 0 0 0
## 82000 0 1 0 0 0 0 0 0 0 0 0 0
## 85000 0 1 2 1 0 0 0 0 0 0 0 0
## 86000 0 0 1 1 0 0 0 0 0 0 0 0
## 88000 0 0 0 1 0 0 0 0 0 0 0 0
## 88500 0 0 0 1 0 0 0 0 0 0 0 0
## 90000 0 0 2 0 0 1 0 0 0 0 0 0
## 92000 0 0 3 0 0 0 0 0 0 0 0 0
## 93000 0 0 0 0 1 1 0 0 1 0 0 0
## 95000 1 1 2 2 0 1 0 0 0 0 0 0
## 96000 0 1 2 0 1 0 0 0 0 0 0 0
## 96500 0 0 1 0 0 0 0 0 0 0 0 0
## 97000 0 0 0 1 1 0 0 0 0 0 0 0
## 98000 0 0 6 0 1 0 0 1 0 0 0 0
## 99000 0 0 0 0 0 0 0 0 0 0 0 0
## 100000 0 0 6 1 1 0 1 0 0 0 0 0
## 100400 0 0 0 1 0 0 0 0 0 0 0 0
## 101000 0 0 2 0 0 0 0 0 0 0 0 0
## 101100 0 0 0 0 0 0 0 0 1 0 0 0
## 101600 0 0 0 1 0 0 0 0 0 0 0 0
## 102500 0 0 0 0 0 0 1 0 0 0 0 0
## 103000 0 0 0 1 0 0 0 0 0 0 0 0
## 104000 0 0 0 0 1 0 0 0 0 0 0 0
## 105000 0 0 4 4 0 1 1 0 0 0 0 1
## 106000 0 0 0 0 0 0 2 0 1 0 0 0
## 107000 0 0 1 0 0 0 0 0 0 0 0 0
## 107300 0 0 0 0 0 0 0 0 0 0 0 0
## 107500 0 0 0 1 0 0 0 0 0 0 0 0
## 108000 0 0 0 1 1 0 0 0 0 0 0 0
## 110000 0 0 0 0 0 0 1 0 0 0 0 0
## 112000 0 0 1 0 0 0 1 0 0 0 0 1
## 115000 0 2 0 1 2 0 0 0 0 0 0 0
## 118000 0 0 0 0 0 0 0 0 0 0 0 0
## 120000 0 0 0 1 0 2 0 0 1 0 0 0
## 126710 0 0 0 1 0 0 0 0 0 0 0 0
## 130000 0 0 0 0 1 0 0 0 0 0 0 0
## 145800 0 0 1 0 0 0 0 0 0 0 0 0
## 146000 0 0 0 0 0 0 0 0 0 0 1 0
## 162000 0 1 0 0 0 0 0 0 0 0 0 0
## 220000 0 0 0 0 0 0 0 0 0 0 0 0
##
## , , frstlang = 2
##
## work_yrs
## salary 0 1 2 3 4 5 6 7 8 10 15 16
## 64000 0 0 0 0 0 0 0 0 0 0 0 0
## 77000 0 0 0 0 0 0 0 0 0 0 0 0
## 78256 0 0 0 0 0 0 0 0 0 0 0 0
## 82000 0 0 0 0 0 0 0 0 0 0 0 0
## 85000 0 0 0 0 0 0 0 0 0 0 0 0
## 86000 0 0 0 0 0 0 0 0 0 0 0 0
## 88000 0 0 0 0 0 0 0 0 0 0 0 0
## 88500 0 0 0 0 0 0 0 0 0 0 0 0
## 90000 0 0 0 0 0 0 0 0 0 0 0 0
## 92000 0 0 0 0 0 0 0 0 0 0 0 0
## 93000 0 0 0 0 0 0 0 0 0 0 0 0
## 95000 0 0 0 0 0 0 0 0 0 0 0 0
## 96000 0 0 0 0 0 0 0 0 0 0 0 0
## 96500 0 0 0 0 0 0 0 0 0 0 0 0
## 97000 0 0 0 0 0 0 0 0 0 0 0 0
## 98000 0 0 1 1 0 0 0 0 0 0 0 0
## 99000 0 0 0 0 0 1 0 0 0 0 0 0
## 100000 0 0 0 0 0 0 0 0 0 0 0 0
## 100400 0 0 0 0 0 0 0 0 0 0 0 0
## 101000 0 0 0 0 0 0 0 0 0 0 0 0
## 101100 0 0 0 0 0 0 0 0 0 0 0 0
## 101600 0 0 0 0 0 0 0 0 0 0 0 0
## 102500 0 0 0 0 0 0 0 0 0 0 0 0
## 103000 0 0 0 0 0 0 0 0 0 0 0 0
## 104000 0 0 0 0 1 0 0 0 0 0 0 0
## 105000 0 0 0 0 0 0 0 0 0 0 0 0
## 106000 0 0 0 0 0 0 0 0 0 0 0 0
## 107000 0 0 0 0 0 0 0 0 0 0 0 0
## 107300 0 0 1 0 0 0 0 0 0 0 0 0
## 107500 0 0 0 0 0 0 0 0 0 0 0 0
## 108000 0 0 0 0 0 0 0 0 0 0 0 0
## 110000 0 0 0 0 0 0 0 0 0 0 0 0
## 112000 0 0 0 0 0 0 0 0 0 0 0 0
## 115000 0 0 0 0 0 0 0 0 0 0 0 0
## 118000 0 0 0 0 0 0 0 0 0 1 0 0
## 120000 0 0 0 0 0 0 0 0 0 0 0 0
## 126710 0 0 0 0 0 0 0 0 0 0 0 0
## 130000 0 0 0 0 0 0 0 0 0 0 0 0
## 145800 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
## 162000 0 0 0 0 0 0 0 0 0 0 0 0
## 220000 0 0 0 0 0 0 0 0 0 0 1 0Chi-square test
t.test(model1$salary,model1$sex)##
## Welch Two Sample t-test
##
## data: model1$salary and model1$sex
## t = 58.517, df = 102, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 99537.17 106521.71
## sample estimates:
## mean of x mean of y
## 1.030307e+05 1.300971e+00Since, p-value <0.05. So, there is a significant difference between salaries of men and women.
chisq.test(mytable)## Warning in chisq.test(mytable): Chi-squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: mytable
## X-squared = 52.681, df = 41, p-value = 0.1045Regression models
m1<-lm(salary ~ age+sex+gmat_tot+gmat_tpc+gmat_qpc+gmat_vpc+frstlang+quarter, data=model1)
summary(m1)##
## Call:
## lm(formula = salary ~ age + sex + gmat_tot + gmat_tpc + gmat_qpc +
## gmat_vpc + frstlang + quarter, data = model1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25167 -7550 -1109 5163 71055
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 50739.508 44276.926 1.146 0.2547
## age 2458.718 525.702 4.677 9.73e-06 ***
## sex -3456.252 3458.815 -0.999 0.3202
## gmat_tot 6.807 159.950 0.043 0.9661
## gmat_tpc -1429.300 693.662 -2.061 0.0421 *
## gmat_qpc 796.902 474.955 1.678 0.0967 .
## gmat_vpc 533.123 473.264 1.126 0.2628
## frstlang 5868.789 6789.285 0.864 0.3896
## quarter -1820.645 1392.015 -1.308 0.1941
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15200 on 94 degrees of freedom
## Multiple R-squared: 0.3333, Adjusted R-squared: 0.2766
## F-statistic: 5.875 on 8 and 94 DF, p-value: 4.368e-06p-values of age and overall gmat percentile are less than 0.05. Hence salary depends on these two factors.
m2<- lm(salary~s_avg+f_avg+work_yrs+satis, data=model1)
summary(m2)##
## Call:
## lm(formula = salary ~ s_avg + f_avg + work_yrs + satis, data = model1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -33329 -7748 -853 3885 87689
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 101048.7 20095.5 5.028 2.23e-06 ***
## s_avg 1588.0 4987.7 0.318 0.751
## f_avg -1186.1 3885.5 -0.305 0.761
## work_yrs 2649.6 572.3 4.630 1.12e-05 ***
## satis -1531.7 2075.3 -0.738 0.462
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16180 on 98 degrees of freedom
## Multiple R-squared: 0.2125, Adjusted R-squared: 0.1804
## F-statistic: 6.611 on 4 and 98 DF, p-value: 9.407e-05p-value of work experience is less than0.05. So, salary depends on it.
m3<- lm(salary~work_yrs+age+gmat_tpc+sex,data=model1)
summary(m3)##
## Call:
## lm(formula = salary ~ work_yrs + age + gmat_tpc + sex, data = model1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -31132 -8216 -1918 5863 80378
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 57425.9 27148.6 2.115 0.0369 *
## work_yrs 371.1 1090.4 0.340 0.7343
## age 2300.2 1005.4 2.288 0.0243 *
## gmat_tpc -143.1 141.9 -1.008 0.3158
## sex -4039.5 3400.0 -1.188 0.2377
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15600 on 98 degrees of freedom
## Multiple R-squared: 0.2678, Adjusted R-squared: 0.2379
## F-statistic: 8.962 on 4 and 98 DF, p-value: 3.282e-06First model is the best one.
Comparing people with job and without job
nojob <- model[which(model$salary!='998' & model$salary!='999' & model$salary=='0'),]
model1<- model1[1:90,]
chisq.test(nojob$age,model1$age)## Warning in chisq.test(nojob$age, model1$age): Chi-squared approximation may
## be incorrect##
## Pearson's Chi-squared test
##
## data: nojob$age and model1$age
## X-squared = 229.27, df = 252, p-value = 0.8449chisq.test(nojob$sex,model1$sex)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: nojob$sex and model1$sex
## X-squared = 0.11711, df = 1, p-value = 0.7322chisq.test(nojob$work_yrs,model1$work_yrs)## Warning in chisq.test(nojob$work_yrs, model1$work_yrs): Chi-squared
## approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: nojob$work_yrs and model1$work_yrs
## X-squared = 117.66, df = 176, p-value = 0.9998chisq.test(nojob$quarter,model1$quarter)## Warning in chisq.test(nojob$quarter, model1$quarter): Chi-squared
## approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: nojob$quarter and model1$quarter
## X-squared = 110.98, df = 9, p-value < 2.2e-16chisq.test(nojob$gmat_tot,model1$gmat_tot)## Warning in chisq.test(nojob$gmat_tot, model1$gmat_tot): Chi-squared
## approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: nojob$gmat_tot and model1$gmat_tot
## X-squared = 496.72, df = 500, p-value = 0.533chisq.test(nojob$gmat_qpc,model1$gmat_qpc)## Warning in chisq.test(nojob$gmat_qpc, model1$gmat_qpc): Chi-squared
## approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: nojob$gmat_qpc and model1$gmat_qpc
## X-squared = 1305.3, df = 1221, p-value = 0.04635chisq.test(nojob$gmat_tpc,model1$gmat_tpc)## Warning in chisq.test(nojob$gmat_tpc, model1$gmat_tpc): Chi-squared
## approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: nojob$gmat_tpc and model1$gmat_tpc
## X-squared = 776.54, df = 784, p-value = 0.5683chisq.test(nojob$gmat_vpc,model1$gmat_vpc)## Warning in chisq.test(nojob$gmat_vpc, model1$gmat_vpc): Chi-squared
## approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: nojob$gmat_vpc and model1$gmat_vpc
## X-squared = 716.3, df = 625, p-value = 0.006476chisq.test(nojob$frstlang,model1$frstlang)## Warning in chisq.test(nojob$frstlang, model1$frstlang): Chi-squared
## approximation may be incorrect##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: nojob$frstlang and model1$frstlang
## X-squared = 0.0080703, df = 1, p-value = 0.9284chisq.test(nojob$satis,model1$satis)## Warning in chisq.test(nojob$satis, model1$satis): Chi-squared approximation
## may be incorrect##
## Pearson's Chi-squared test
##
## data: nojob$satis and model1$satis
## X-squared = 7.502, df = 12, p-value = 0.8227The factors that are relevant are quartile, quantitativepercentile and verbal percentile in gmat.