Primary Variables for salary variation
GMAT Score, Gender, Age, WorkExperience
MBA Starting Salaries
Poornachandra Rao
December 26, 2017
PART 2
The RMD file contains the Data Analysis of “MBA Starting Salaries” case study.
Possible questions before joining the Particular B-School
Whether to enroll in the MBA program at this particular school? About starting salaries, whether gender and/or age made a difference? Whether students liked this particular program?? Whether her GMAT score made a difference in marks?
More chances of Enrollment
Better Salary, More Satisfaction Rating
Reading the Data in to R
MBA_Data <- read.csv(paste("MBA Starting Salaries Data.csv",sep=""))
dim(MBA_Data)## [1] 274 13View(MBA_Data)Creating summary statistics (e.g. mean, standard deviation, median, mode) for the important variables in the dataset.
library(psych)
describe(MBA_Data)## 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 22.45Structure of Data
str(MBA_Data)## 'data.frame': 274 obs. of 13 variables:
## $ age : int 23 24 24 24 24 24 25 25 25 25 ...
## $ sex : int 2 1 1 1 2 1 1 2 1 1 ...
## $ 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: int 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 ...Converting the data type of some columns
Sex
MBA_Data$sex[MBA_Data$sex==1] <- "Male"
MBA_Data$sex[MBA_Data$sex==2] <- "Female"
MBA_Data$sex= factor(MBA_Data$sex)First Language
MBA_Data$frstlang[MBA_Data$frstlang==1] <- "English"
MBA_Data$frstlang[MBA_Data$frstlang==2] <- "Other"
MBA_Data$frstlang= factor(MBA_Data$frstlang)Structure of the Dataset.
str(MBA_Data)## '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 ...Contingency Tables for MBA_Data Dataframe
Sex & FirstLanguage
sex_Flang <- xtabs(~MBA_Data$sex+MBA_Data$frstlang)
addmargins(sex_Flang)## MBA_Data$frstlang
## MBA_Data$sex English Other Sum
## Female 60 8 68
## Male 182 24 206
## Sum 242 32 274Satisfaction value
satisfaction <- xtabs(~MBA_Data$satis)
addmargins(satisfaction)## MBA_Data$satis
## 1 2 3 4 5 6 7 998 Sum
## 1 1 5 17 74 97 33 46 274prop.table(satisfaction)*100## MBA_Data$satis
## 1 2 3 4 5 6
## 0.3649635 0.3649635 1.8248175 6.2043796 27.0072993 35.4014599
## 7 998
## 12.0437956 16.7883212We can clearly see that morethan 74% of students have mentioned a satisfaction value of more than four. (i.e,>4).
Mean of all MBA Students as per Gender.
AllSalaryMean <- aggregate(MBA_Data$salary,list(Gender=MBA_Data$sex),mean)
AllSalaryMean## Gender x
## 1 Female 45121.07
## 2 Male 37013.62Mean of all MBA Students as per Age.
AllSalaryMean2 <- aggregate(MBA_Data$salary,list(Gender=MBA_Data$age),mean)
AllSalaryMean2## Gender x
## 1 22 42500.00
## 2 23 57282.00
## 3 24 49342.24
## 4 25 43395.55
## 5 26 35982.07
## 6 27 31499.37
## 7 28 39809.00
## 8 29 28067.95
## 9 30 55291.25
## 10 31 40599.40
## 11 32 13662.25
## 12 33 118000.00
## 13 34 26250.00
## 14 35 0.00
## 15 36 0.00
## 16 37 0.00
## 17 39 56000.00
## 18 40 183000.00
## 19 42 0.00
## 20 43 0.00
## 21 48 0.00998 = did not answer the survey
999 = answered the survey but did not disclose salary data
0: Not Yet Placed
Salary Value = Who are Placed
DataFrame-1
NotAnsweredSurvey <- MBA_Data[which(MBA_Data$salary=='998'),]
dim(NotAnsweredSurvey)## [1] 46 13DataFrame-2
NotdisclosedSalary <- MBA_Data[which(MBA_Data$salary=='999'),]
NotdisclosedSalary## age sex gmat_tot gmat_qpc gmat_vpc gmat_tpc s_avg f_avg quarter
## 5 24 Female 710 93 98 98 3.60 3.75 1
## 9 25 Male 630 79 91 89 3.30 3.25 1
## 21 27 Female 570 65 82 77 3.30 3.25 1
## 26 30 Male 620 82 84 87 3.40 2.80 1
## 30 32 Male 570 71 71 0 3.50 3.50 1
## 78 25 Male 690 87 98 98 3.00 3.00 2
## 87 26 Male 680 92 93 97 3.00 3.00 2
## 91 27 Male 740 99 98 99 3.10 3.50 2
## 99 28 Male 660 95 85 96 3.10 3.25 2
## 101 29 Male 580 91 50 80 3.10 2.67 2
## 105 29 Male 590 68 84 81 3.10 3.00 2
## 108 31 Male 670 83 98 96 3.20 3.40 2
## 145 24 Male 650 89 84 93 2.70 3.25 3
## 152 25 Male 660 95 84 94 2.70 3.00 3
## 158 26 Male 640 87 84 91 2.70 3.20 3
## 161 26 Male 600 97 45 83 2.70 3.00 3
## 166 27 Male 730 95 99 99 2.90 3.33 3
## 170 27 Female 620 97 54 87 2.70 2.75 3
## 179 28 Male 500 46 54 52 2.90 2.75 3
## 181 29 Male 560 57 74 73 2.80 3.00 3
## 212 25 Male 600 53 95 84 2.50 3.00 4
## 214 25 Female 650 87 91 93 2.50 2.50 4
## 217 25 Male 590 97 41 81 2.50 2.75 4
## 221 26 Male 560 87 45 72 2.60 3.00 4
## 223 26 Male 570 82 58 75 2.50 2.75 4
## 226 27 Male 660 97 81 94 2.50 2.50 4
## 228 27 Male 790 99 99 99 2.40 2.50 4
## 231 27 Male 620 85 85 89 3.30 3.00 4
## 235 28 Male 620 93 71 87 2.40 2.75 4
## 239 29 Male 690 99 87 97 2.30 2.25 4
## 240 29 Male 630 87 84 89 2.90 2.80 4
## 245 30 Male 550 79 45 69 2.45 2.75 4
## 246 30 Female 600 99 46 86 2.80 3.00 4
## 251 31 Male 640 79 92 92 2.70 2.75 4
## 252 32 Male 570 89 41 75 2.60 2.50 4
## work_yrs frstlang salary satis
## 5 2 English 999 5
## 9 2 Other 999 4
## 21 4 English 999 4
## 26 5 English 999 6
## 30 4 English 999 4
## 78 3 English 999 5
## 87 3 English 999 1
## 91 2 English 999 4
## 99 4 English 999 3
## 101 4 Other 999 4
## 105 6 English 999 5
## 108 4 English 999 6
## 145 1 English 999 5
## 152 3 English 999 6
## 158 4 English 999 5
## 161 4 Other 999 6
## 166 0 English 999 5
## 170 2 Other 999 2
## 179 9 English 999 6
## 181 4 English 999 5
## 212 2 English 999 4
## 214 3 English 999 7
## 217 2 Other 999 4
## 221 3 Other 999 3
## 223 3 English 999 6
## 226 4 English 999 4
## 228 4 English 999 6
## 231 1 English 999 5
## 235 3 English 999 4
## 239 7 English 999 5
## 240 3 English 999 4
## 245 5 Other 999 4
## 246 6 Other 999 4
## 251 7 English 999 3
## 252 4 Other 999 3DataFrame-3
NotPlaced <- MBA_Data[which(MBA_Data$salary=='0'),]
NotPlaced## age sex gmat_tot gmat_qpc gmat_vpc gmat_tpc s_avg f_avg quarter
## 1 23 Female 620 77 87 87 3.40 3.00 1
## 2 24 Male 610 90 71 87 3.50 4.00 1
## 3 24 Male 670 99 78 95 3.30 3.25 1
## 4 24 Male 570 56 81 75 3.30 2.67 1
## 6 24 Male 640 82 89 91 3.90 3.75 1
## 7 25 Male 610 89 74 87 3.40 3.50 1
## 8 25 Female 650 88 89 92 3.30 3.75 1
## 22 27 Male 740 99 96 99 3.50 3.50 1
## 23 27 Male 750 99 98 99 3.40 3.50 1
## 24 28 Female 540 75 50 65 3.60 4.00 1
## 25 29 Male 580 56 87 78 3.64 3.33 1
## 27 31 Female 560 60 78 72 3.30 3.75 1
## 28 32 Male 760 99 99 99 3.40 3.00 1
## 29 32 Male 640 79 91 91 3.60 3.75 1
## 31 34 Female 620 75 89 87 3.30 3.00 1
## 32 37 Female 560 43 87 72 3.40 3.50 1
## 33 42 Female 650 75 98 93 3.38 3.00 1
## 34 48 Male 590 84 62 81 3.80 4.00 1
## 70 22 Male 600 95 54 83 3.00 3.00 2
## 71 23 Male 640 89 87 92 3.00 3.00 2
## 72 24 Male 550 73 63 69 3.10 3.00 2
## 73 24 Male 570 82 58 75 3.09 3.50 2
## 74 24 Male 620 82 84 87 3.10 3.50 2
## 75 25 Female 570 61 81 76 3.00 3.25 2
## 76 25 Male 660 94 84 94 3.27 3.75 2
## 77 25 Male 680 94 92 97 3.17 3.50 2
## 88 26 Female 560 64 71 72 3.20 3.25 2
## 89 26 Male 560 87 41 72 3.00 3.00 2
## 90 26 Male 530 68 54 62 3.09 3.17 2
## 92 27 Male 720 99 95 99 3.10 3.25 2
## 93 27 Male 590 60 87 81 3.00 2.75 2
## 97 28 Male 620 81 90 89 3.20 3.00 2
## 98 28 Female 610 85 78 86 3.10 3.00 2
## 100 29 Male 660 94 87 94 3.00 3.00 2
## 102 29 Male 510 57 50 55 3.27 3.40 2
## 103 29 Female 640 90 84 92 3.20 3.00 2
## 104 29 Male 610 91 62 86 3.10 3.67 2
## 106 29 Male 580 79 67 78 3.00 3.25 2
## 107 30 Male 680 97 87 96 3.00 3.00 2
## 109 32 Female 610 64 89 86 3.25 0.00 2
## 110 35 Male 540 43 78 65 3.20 3.25 2
## 111 35 Male 630 66 95 90 3.08 3.25 2
## 112 36 Female 530 48 71 62 3.00 2.50 2
## 113 36 Male 650 87 89 93 3.00 3.20 2
## 114 43 Male 630 82 87 89 3.10 3.00 2
## 140 23 Male 720 95 98 99 2.80 2.50 3
## 141 24 Female 640 94 78 92 2.90 3.25 3
## 142 24 Male 710 96 97 99 2.80 2.75 3
## 143 24 Male 670 94 89 96 2.70 3.00 3
## 144 24 Female 710 97 97 99 2.80 3.00 3
## 146 24 Male 600 89 62 83 2.90 3.00 3
## 147 24 Female 640 96 71 91 2.70 2.50 3
## 150 25 Male 550 72 58 69 2.90 3.00 3
## 151 25 Male 710 99 91 98 2.90 3.25 3
## 159 26 Male 560 56 81 72 2.80 3.25 3
## 160 26 Male 540 52 71 65 2.70 2.75 3
## 162 26 Female 570 48 89 75 2.82 2.50 3
## 163 26 Male 610 82 81 86 2.90 2.75 3
## 164 27 Male 650 89 84 93 2.90 3.00 3
## 165 27 Female 550 66 63 69 2.90 3.00 3
## 167 27 Male 610 97 45 86 2.70 2.50 3
## 168 27 Female 630 82 89 89 2.70 3.25 3
## 169 27 Female 560 61 74 73 2.80 3.25 3
## 180 29 Male 590 92 58 81 2.80 2.75 3
## 182 32 Male 550 52 78 71 2.70 2.75 3
## 183 34 Male 610 79 81 86 2.80 3.00 3
## 184 34 Male 610 82 78 86 2.70 3.00 3
## 185 43 Male 480 49 41 45 2.90 3.25 3
## 213 25 Male 730 98 96 99 2.40 2.75 4
## 218 25 Male 700 99 87 98 2.00 2.00 4
## 219 26 Male 660 93 87 95 2.60 2.00 4
## 220 26 Male 450 28 46 34 2.10 2.00 4
## 222 26 Male 600 75 78 83 2.20 2.25 4
## 227 27 Female 560 59 74 73 2.40 2.50 4
## 229 27 Male 630 93 78 91 2.10 2.50 4
## 230 27 Male 580 84 58 78 2.70 2.75 4
## 232 27 Male 670 89 91 95 3.60 3.25 4
## 233 27 Male 580 74 70 78 3.40 3.25 4
## 234 28 Male 560 74 67 73 3.60 3.60 4
## 236 28 Male 710 94 98 99 3.40 3.75 4
## 237 28 Male 570 69 71 0 2.30 2.50 4
## 238 29 Male 530 35 81 62 3.30 2.75 4
## 241 29 Male 670 91 91 95 3.30 3.25 4
## 242 29 Male 630 99 50 89 2.90 3.25 4
## 243 29 Female 680 89 96 96 2.80 3.00 4
## 244 30 Male 650 88 92 93 3.45 3.83 4
## 250 31 Male 570 75 62 75 2.80 3.00 4
## 253 32 Male 510 79 22 54 2.30 2.25 4
## 254 35 Male 570 72 71 75 3.30 4.00 4
## 255 39 Female 700 89 98 98 3.30 3.25 4
## work_yrs frstlang salary satis
## 1 2 English 0 7
## 2 2 English 0 6
## 3 2 English 0 6
## 4 1 English 0 7
## 6 2 English 0 6
## 7 2 English 0 5
## 8 2 English 0 6
## 22 3 English 0 6
## 23 1 Other 0 5
## 24 5 English 0 5
## 25 3 English 0 5
## 27 10 English 0 7
## 28 5 English 0 5
## 29 7 English 0 6
## 31 7 English 0 6
## 32 9 English 0 6
## 33 13 English 0 5
## 34 22 English 0 6
## 70 1 English 0 5
## 71 2 English 0 7
## 72 0 Other 0 5
## 73 2 English 0 6
## 74 1 English 0 5
## 75 3 English 0 4
## 76 2 English 0 5
## 77 2 English 0 6
## 88 3 English 0 6
## 89 3 English 0 6
## 90 4 Other 0 5
## 92 5 English 0 5
## 93 3 English 0 6
## 97 4 English 0 6
## 98 5 English 0 6
## 100 1 English 0 6
## 102 5 English 0 5
## 103 3 English 0 5
## 104 7 English 0 5
## 106 4 English 0 6
## 107 4 English 0 5
## 109 11 English 0 7
## 110 8 English 0 5
## 111 12 English 0 5
## 112 7 English 0 5
## 113 18 English 0 6
## 114 16 English 0 5
## 140 1 English 0 5
## 141 2 Other 0 4
## 142 2 English 0 7
## 143 2 English 0 7
## 144 2 English 0 7
## 146 1 English 0 6
## 147 2 English 0 6
## 150 3 English 0 6
## 151 1 English 0 6
## 159 4 English 0 6
## 160 2 English 0 6
## 162 3 English 0 5
## 163 3 English 0 6
## 164 2 English 0 6
## 165 3 English 0 4
## 167 4 Other 0 5
## 168 5 English 0 6
## 169 5 English 0 6
## 180 3 Other 0 5
## 182 7 English 0 6
## 183 11 English 0 6
## 184 12 English 0 5
## 185 22 English 0 5
## 213 2 English 0 6
## 218 1 English 0 7
## 219 2 English 0 5
## 220 4 English 0 6
## 222 2 English 0 6
## 227 2 English 0 5
## 229 4 English 0 5
## 230 1 English 0 5
## 232 5 English 0 6
## 233 3 English 0 6
## 234 5 English 0 5
## 236 6 English 0 6
## 237 5 English 0 5
## 238 6 English 0 7
## 241 3 English 0 5
## 242 1 Other 0 4
## 243 4 English 0 5
## 244 2 English 0 6
## 250 1 English 0 6
## 253 5 Other 0 5
## 254 8 English 0 6
## 255 5 English 0 5DataFrame-4
Placed <- MBA_Data[which(MBA_Data$salary>999),]
dim(Placed)## [1] 103 13subset of Placed DataFrame.
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitsome(Placed)## age sex gmat_tot gmat_qpc gmat_vpc gmat_tpc s_avg f_avg quarter
## 38 25 Female 650 82 91 93 3.4 3.25 1
## 41 24 Male 670 84 96 95 3.3 3.25 1
## 120 24 Male 560 52 81 72 3.2 3.25 2
## 122 23 Male 590 72 81 81 3.2 3.25 2
## 125 28 Female 580 83 58 79 3.1 3.00 2
## 193 28 Male 580 72 71 78 2.8 3.00 3
## 196 25 Female 580 72 71 78 2.8 3.25 3
## 199 29 Male 710 93 98 99 2.9 3.25 3
## 200 24 Male 710 99 92 99 2.9 3.00 3
## 201 25 Female 630 84 87 89 2.8 2.75 3
## work_yrs frstlang salary satis
## 38 3 English 88000 7
## 41 0 English 95000 4
## 120 2 English 96000 7
## 122 2 English 98000 6
## 125 5 Other 99000 6
## 193 3 English 97000 6
## 196 2 English 98000 6
## 199 7 English 98000 5
## 200 3 English 100000 6
## 201 2 English 100000 6Mean of Placed MBA Students as per Gender.
PlacedSalaryMean <- aggregate(Placed$salary,list(Gender=Placed$sex),mean)
PlacedSalaryMean## Gender x
## 1 Female 98524.39
## 2 Male 104970.97Mean of Placed MBA Students as per Age.
AgeSalaryMean <- aggregate(Placed$salary,list(Gender=Placed$age),mean)
AgeSalaryMean## Gender x
## 1 22 85000.00
## 2 23 91651.20
## 3 24 101518.75
## 4 25 99086.96
## 5 26 101665.00
## 6 27 102214.29
## 7 28 103625.00
## 8 29 102083.33
## 9 30 109916.67
## 10 31 100500.00
## 11 32 107300.00
## 12 33 118000.00
## 13 34 105000.00
## 14 39 112000.00
## 15 40 183000.00Merging Placed, NotDisclosedSalary and NotPlaced to give KnownMBA_Data
KnownMBA_DATA <- rbind(Placed,NotdisclosedSalary,NotPlaced)
View(KnownMBA_DATA)Creating Dummy Variable “Got Placed” which is populated with ‘0’(didn’t got a Job) or ‘1’(Got a Job)
KnownMBA_DATA$GotPlaced <- (KnownMBA_DATA$salary>1000)
View(KnownMBA_DATA)Structure of the KnownMBA_DATA DataFrame
str(KnownMBA_DATA)## 'data.frame': 228 obs. of 14 variables:
## $ age : int 22 27 25 25 27 28 24 25 25 25 ...
## $ sex : Factor w/ 2 levels "Female","Male": 1 1 1 1 2 1 2 1 1 2 ...
## $ gmat_tot : int 660 700 680 650 710 620 670 560 530 650 ...
## $ gmat_qpc : int 90 94 87 82 96 52 84 52 50 79 ...
## $ gmat_vpc : int 92 98 96 91 96 98 96 81 62 93 ...
## $ gmat_tpc : int 94 98 96 93 98 87 95 72 61 93 ...
## $ s_avg : num 3.5 3.3 3.5 3.4 3.3 3.4 3.3 3.3 3.6 3.3 ...
## $ f_avg : num 3.75 3.25 2.67 3.25 3.5 3.75 3.25 3.5 3.67 3.5 ...
## $ quarter : int 1 1 1 1 1 1 1 1 1 1 ...
## $ work_yrs : int 1 2 2 3 2 5 0 1 3 1 ...
## $ frstlang : Factor w/ 2 levels "English","Other": 1 1 1 1 1 1 1 1 1 1 ...
## $ salary : int 85000 85000 86000 88000 92000 93000 95000 95000 95000 96000 ...
## $ satis : int 5 6 5 7 6 5 4 5 3 7 ...
## $ GotPlaced: logi TRUE TRUE TRUE TRUE TRUE TRUE ...No.of Males & Females.
table(KnownMBA_DATA$sex)##
## Female Male
## 59 169Contingency Tables for KnownMBA_DATA DataFrame
table1 <- xtabs(~GotPlaced,data=KnownMBA_DATA)
addmargins(table1)## GotPlaced
## FALSE TRUE Sum
## 125 103 228prop.table(table1)## GotPlaced
## FALSE TRUE
## 0.5482456 0.4517544table2 <- xtabs(~GotPlaced+sex,data=KnownMBA_DATA)
addmargins(table2)## sex
## GotPlaced Female Male Sum
## FALSE 28 97 125
## TRUE 31 72 103
## Sum 59 169 228prop.table(table2,2)## sex
## GotPlaced Female Male
## FALSE 0.4745763 0.5739645
## TRUE 0.5254237 0.4260355table3 <- xtabs(~GotPlaced+frstlang,data=KnownMBA_DATA)
addmargins(table3)## frstlang
## GotPlaced English Other Sum
## FALSE 108 17 125
## TRUE 96 7 103
## Sum 204 24 228prop.table(table3,2)## frstlang
## GotPlaced English Other
## FALSE 0.5294118 0.7083333
## TRUE 0.4705882 0.2916667Correlation & Visualization Matrix
Data <- KnownMBA_DATA[,c(1,10,3:9,12,13)]
CorrMatrix <- cor(Data)
round(CorrMatrix,2)## age work_yrs gmat_tot gmat_qpc gmat_vpc gmat_tpc s_avg f_avg
## age 1.00 0.86 -0.14 -0.21 -0.03 -0.16 0.16 -0.04
## work_yrs 0.86 1.00 -0.19 -0.25 -0.06 -0.17 0.14 -0.06
## gmat_tot -0.14 -0.19 1.00 0.72 0.74 0.83 0.11 0.10
## gmat_qpc -0.21 -0.25 0.72 1.00 0.14 0.65 -0.04 0.09
## gmat_vpc -0.03 -0.06 0.74 0.14 1.00 0.63 0.21 0.07
## gmat_tpc -0.16 -0.17 0.83 0.65 0.63 1.00 0.11 0.08
## s_avg 0.16 0.14 0.11 -0.04 0.21 0.11 1.00 0.54
## f_avg -0.04 -0.06 0.10 0.09 0.07 0.08 0.54 1.00
## quarter -0.07 -0.12 -0.07 0.05 -0.18 -0.07 -0.76 -0.41
## salary -0.11 -0.03 -0.03 -0.03 0.02 0.04 0.16 0.04
## satis -0.07 0.03 0.03 -0.10 0.19 0.09 0.06 -0.04
## quarter salary satis
## age -0.07 -0.11 -0.07
## work_yrs -0.12 -0.03 0.03
## gmat_tot -0.07 -0.03 0.03
## gmat_qpc 0.05 -0.03 -0.10
## gmat_vpc -0.18 0.02 0.19
## gmat_tpc -0.07 0.04 0.09
## s_avg -0.76 0.16 0.06
## f_avg -0.41 0.04 -0.04
## quarter 1.00 -0.19 -0.03
## salary -0.19 1.00 0.28
## satis -0.03 0.28 1.00corrplot of various variables
library(corrplot)## corrplot 0.84 loadedcorrplot(corr = cor(Data),method="circle")
Scatterplots based on Age, Sex, Work_yrs , First Language
library(car)
scatterplotMatrix(~KnownMBA_DATA$age+KnownMBA_DATA$sex+KnownMBA_DATA$work_yrs+KnownMBA_DATA$frstlang+KnownMBA_DATA$salary)
Salary based on GMAT Score
scatterplotMatrix(~KnownMBA_DATA$gmat_tot+KnownMBA_DATA$gmat_qpc+KnownMBA_DATA$gmat_vpc+KnownMBA_DATA$gmat_tpc+KnownMBA_DATA$salary)
Salary based on Academic Performance (s_avg,f_avg,Quarter Ranking)
scatterplotMatrix(~KnownMBA_DATA$s_avg+KnownMBA_DATA$f_avg+KnownMBA_DATA$quarter+KnownMBA_DATA$salary)
Hypothesis Statement
For Test 1 <- table2 H1: THe percentage of Females placed is higher than the percentage of Males Placed.
For Test 2 <- table3 H2: THe percentage of Students placed in English is higher than the percentage of Students Placed in other languages.
Pearson’s Chi-square test
chisq.test(table2)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: table2
## X-squared = 1.366, df = 1, p-value = 0.2425chisq.test(table3)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: table3
## X-squared = 2.1002, df = 1, p-value = 0.1473t-tests
t.test(table2)##
## One Sample t-test
##
## data: table2
## t = 3.4156, df = 3, p-value = 0.04198
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 3.89032 110.10968
## sample estimates:
## mean of x
## 57t.test(table3)##
## One Sample t-test
##
## data: table3
## t = 2.1776, df = 3, p-value = 0.1176
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -26.30272 140.30272
## sample estimates:
## mean of x
## 57Selecting a Regression model as, as y = f(x) where the vector of variables x may be different in different models
colnames(KnownMBA_DATA)## [1] "age" "sex" "gmat_tot" "gmat_qpc" "gmat_vpc"
## [6] "gmat_tpc" "s_avg" "f_avg" "quarter" "work_yrs"
## [11] "frstlang" "salary" "satis" "GotPlaced"Model: salary ~ age + sex + gmat_tot + work_yrs + frstlang
Model1 <- salary ~ work_yrs + s_avg + frstlang
fit <- lm(Model1,data=Placed)
summary(fit)##
## Call:
## lm(formula = Model1, data = Placed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -35244 -8500 -360 4263 78532
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 84104.3 13063.3 6.438 4.36e-09 ***
## work_yrs 2409.9 539.7 4.465 2.12e-05 ***
## s_avg 2948.6 4249.8 0.694 0.4894
## frstlangOther 13843.9 6399.1 2.163 0.0329 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15780 on 99 degrees of freedom
## Multiple R-squared: 0.2433, Adjusted R-squared: 0.2203
## F-statistic: 10.61 on 3 and 99 DF, p-value: 4.134e-06library(leaps)
leap <- regsubsets(Model1, data = Placed, nbest=1)
summary(leap)## Subset selection object
## Call: regsubsets.formula(Model1, data = Placed, nbest = 1)
## 3 Variables (and intercept)
## Forced in Forced out
## work_yrs FALSE FALSE
## s_avg FALSE FALSE
## frstlangOther FALSE FALSE
## 1 subsets of each size up to 3
## Selection Algorithm: exhaustive
## work_yrs s_avg frstlangOther
## 1 ( 1 ) "*" " " " "
## 2 ( 1 ) "*" " " "*"
## 3 ( 1 ) "*" "*" "*"plot(leap,scale="adjr")
Model2: salary ~ age + sex + gmat_tot work_yrs + frstlang +
Model2 <- salary ~ sex + gmat_qpc + gmat_vpc + gmat_tpc + work_yrs + frstlang +s_avg + f_avg + satis
fit2 <- lm(Model2,data=Placed)
summary(fit2)##
## Call:
## lm(formula = Model2, data = Placed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -31321 -8562 -877 5606 72768
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 97896.6 21628.0 4.526 1.77e-05 ***
## sexMale 5150.9 3479.3 1.480 0.142137
## gmat_qpc 834.5 361.0 2.311 0.023022 *
## gmat_vpc 646.9 358.4 1.805 0.074333 .
## gmat_tpc -1514.7 701.3 -2.160 0.033364 *
## work_yrs 2273.7 575.5 3.951 0.000152 ***
## frstlangOther 13158.0 6527.4 2.016 0.046704 *
## s_avg 5790.8 4948.5 1.170 0.244906
## f_avg -2288.3 3772.0 -0.607 0.545551
## satis -1340.1 2037.2 -0.658 0.512291
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15440 on 93 degrees of freedom
## Multiple R-squared: 0.3191, Adjusted R-squared: 0.2532
## F-statistic: 4.843 on 9 and 93 DF, p-value: 2.592e-05library(leaps)
leap2 <- regsubsets(Model2,data=Placed,nbest=1)
summary(leap2)## Subset selection object
## Call: regsubsets.formula(Model2, data = Placed, nbest = 1)
## 9 Variables (and intercept)
## Forced in Forced out
## sexMale FALSE FALSE
## gmat_qpc FALSE FALSE
## gmat_vpc FALSE FALSE
## gmat_tpc FALSE FALSE
## work_yrs FALSE FALSE
## frstlangOther FALSE FALSE
## s_avg FALSE FALSE
## f_avg FALSE FALSE
## satis FALSE FALSE
## 1 subsets of each size up to 8
## Selection Algorithm: exhaustive
## sexMale gmat_qpc gmat_vpc gmat_tpc work_yrs frstlangOther s_avg
## 1 ( 1 ) " " " " " " " " "*" " " " "
## 2 ( 1 ) " " " " " " " " "*" "*" " "
## 3 ( 1 ) "*" " " " " " " "*" "*" " "
## 4 ( 1 ) " " "*" "*" "*" "*" " " " "
## 5 ( 1 ) " " "*" "*" "*" "*" "*" " "
## 6 ( 1 ) "*" "*" "*" "*" "*" "*" " "
## 7 ( 1 ) "*" "*" "*" "*" "*" "*" "*"
## 8 ( 1 ) "*" "*" "*" "*" "*" "*" "*"
## f_avg satis
## 1 ( 1 ) " " " "
## 2 ( 1 ) " " " "
## 3 ( 1 ) " " " "
## 4 ( 1 ) " " " "
## 5 ( 1 ) " " " "
## 6 ( 1 ) " " " "
## 7 ( 1 ) " " " "
## 8 ( 1 ) " " "*"plot(leap2,scale="adjr2")
CONCLUSION
Model 2 has the best fit compared with Model 1 (Greater R-value). So the Explanatory Variables for Salary variation account for sexMale, gmat_qpc, gmat_vpc, gmat_tpc, work_yrs, frstlangOther, s_avg, f_avg, satis