Suppose you are a data scientist working for a university. During the summer, the university considers potential learners to partake in a summer program. The following dataset represents the data collected by the university as well as the "Admit" label $($with $0$ as do not admit and $1$ as admit$).$

Consider the following dataset and the visualization $($created in R using corrplot$).$ The visualization illustrates the r value $($correlation$)$ between each pair of variables in the dataset.

Note: The code used to generate the correlation plot is:

library$($corrplot$)$

library$($RColorBrewer$)$

$($AdmitData$5$D$\_$Bi $<-$ read.csv$("$AdmissionDataForLogReg$5$D$.$csv$"))$

$($CorrelationMatrix $<-$ cor$($AdmitData$5$D$\_$Bi$))$

corrplot$($CorrelationMatrix$,$ method$=$"number", order$=$"hclust",

diag $=$ FALSE, type$=$"lower",cl$.$pos $=\text{'}$n$\text{'},$

col$=$brewer.pal$($n$=10,$ name$=$"Blues"$))$

Admit GPA Prescore VolunteerHours Height

$02\mathrm{.}55165$

$01\mathrm{.}84\mathrm{.}5070$

$13\mathrm{.}78\mathrm{.}3866$

$13\mathrm{.}49\mathrm{.}2573$

$02\mathrm{.}54\mathrm{.}9262$

$13\mathrm{.}87\mathrm{.}91167$

$13\mathrm{.}38\mathrm{.}8874$

$02\mathrm{.}23\mathrm{.}2175$

$01\mathrm{.}26376$

$13\mathrm{.}59\mathrm{.}2571$

Height

Admit $0\mathrm{.}07$ Admit

PreScore $0\mathrm{.}10\mathrm{.}94$ PreScore

GPA $-0\mathrm{.}290\mathrm{.}90\mathrm{.}76$ GPA

VolunteerHours $-0\mathrm{.}040\mathrm{.}860\mathrm{.}780\mathrm{.}79$

Choose the statement that is most accurate.

Question $4$ options:

a$)$ Because the dependent variable $($the label called Admit$)$ is binomial $(0$ or $1),$ you would likely elect to apply multiple linear regression to create a model for whether students might be admitted to the program or not.

b$)$ The linear correlation between PreScore and Admit is $\mathrm{.}10$ and similarly the linear correlation between VolunteerHours and Height is $\mathrm{.}79.$

c$)$ You know, as a data scientist, that one way to reduce the complexity of a model is to increase the dimensionality $($the number of columns or variables$)$ in a dataset.

d$)$ To improve the model and reduce the complexity of the model you elect to eliminate Height from the dataset as the best variable to remove.

e$)$ By looking at the correlation matrix visualization, you can see that all of the independent variables are strongly correlated with the dependent variable "Admit".