Mubarak Mojoyinola Week 4 Assignment

Question 1

Predictor variable = GMAT Total Score

Question 2

Criterion variable= MBA GPA

Question 3

Relationship between the Variables

(SYX <- cor(GMATdata_revised$`GMAT Total Score`, GMATdata_revised$`MBA GPA`))

## [1] 0.6212698

The correlation between GMAT score and MBA GPA is 0.62
\(r^2\) = 0.3859762

Question 4

Mean and Standard Deviation of GMAT Total Score

(Mean_GMAT <- round(mean(GMATdata_revised$`GMAT Total Score`), digits = 2))

## [1] 578.5

(SD_GMAT <- round(sd(GMATdata_revised$`GMAT Total Score`), digits = 2))

## [1] 97.6

Mean and Standard Deviation of MBA GPA

(Mean_GPA <- round(mean(GMATdata_revised$`MBA GPA`), digits = 2))

## [1] 3.19

(SD_GPA <- round(sd(GMATdata_revised$`MBA GPA`), digits = 2))

## [1] 0.63

Table of mean and standard deviation

Mean <- c(Mean_GMAT, Mean_GPA)
Standard_Deviation <- c(SD_GMAT, SD_GPA)
Tab2 <- data.frame(Mean,Standard_Deviation, row.names=(c("GMAT", "MBA GPA")))
colnames(Tab2) <- c("Mean", "Standard Deviation")
Tab2

Question 5

Standard error of estimate of criterion variable

(SEE <- SD_GPA*(sqrt(1-(SYX)^2)))

## [1] 0.4936659

Question 6

Summary Statement
Given the degree of correlation between GMAT Score and first year GPA, it is valid to use GMAT score to predict future GPA of applicants seeking admission into the special program.The value \(r^2\) = 0.3859762 means GMAT Score is accounting for 38.6% of variation in MBA GPA. Although, our error estimate of 0.49 seems low, but GPA scale also has a short range which gives our prediction the potential to place student between \(\pm\)0.99 of their true GPA 95% of the time. This range is quite wide for a measurement like GPA and the admission committee should consider the use of additional material to GMAT score in making admission decison.