$8.$ This exercise relates to the College data set, which can be found in

the fle College.csv on the book website. It contains a number of

variables for $777$ diferent universities and colleges in the US$.$ The

variables are

$$ Private : Public$/$private indicator

$$ Apps : Number of applications received

$$ Accept : Number of applicants accepted

$$ Enroll : Number of new students enrolled

$$ Top$10$perc : New students from top $10\%$ of high school class

$$ Top$25$perc : New students from top $25\%$ of high school class

$$ F$.$Undergrad : Number of full$-$time undergraduates

$$ P$.$Undergrad : Number of part$-$time undergraduates

$2\mathrm{.}4$ Exercises $55$

$$ Outstate : Out$-$of$-$state tuition

$$ Room.Board : Room and board costs

$$ Books : Estimated book costs

$$ Personal : Estimated personal spending

$$ PhD : Percent of faculty with Ph$.$D$.$s

$$ Terminal : Percent of faculty with terminal degree

$$ S$.$F$.$Ratio : Student$/$faculty ratio

$$ perc.alumni : Percent of alumni who donate

$$ Expend : Instructional expenditure per student

$$ Grad.Rate : Graduation rate

Before reading the data into R$,$ it can be viewed in Excel or a text

editor.

$($a$)$ Use the read.csv$()$ function to read the data into R$.$ Call the

loaded data college. Make sure that you have the directory set

to the correct location for the data.

$($b$)$ Look at the data using the View$()$ function. You should notice

that the frst column is just the name of each university. We don$$t

really want R to treat this as data. However, it may be handy to

have these names for later. Try the following commands:

$>$ rownames$($college$)<-$ college$[,1]$

$>$ View$($college$)$

You should see that there is now a row.names column with the

name of each university recorded. This means that R has given

each row a name corresponding to the appropriate university. R

will not try to perform calculations on the row names. However,

we still need to eliminate the frst column in the data where the

names are stored. Try

$>$ college $<-$ college$[,-1]$

$>$ View$($college$)$

Now you should see that the frst data column is Private. Note

that another column labeled row.names now appears before the

Private column. However, this is not a data column but rather

the name that R is giving to each row.

$($c$)$ i$.$ Use the summary$()$ function to produce a numerical summary

of the variables in the data set.

ii$.$ Use the pairs$()$ function to produce a scatterplot matrix of

the frst ten columns or variables of the data. Recall that

you can reference the frst ten columns of a matrix A using

A$[,1$:$10].$

$562.$ Statistical Learning

iii. Use the plot$()$ function to produce side$-$by$-$side boxplots of

Outstate versus Private.

iv$.$ Create a new qualitative variable, called Elite, by binning

the Top$10$perc variable. We are going to divide universities

into two groups based on whether or not the proportion

of students coming from the top $10\%$ of their high school

classes exceeds $50\%.$

$>$ Elite $<-$ rep$("$No$",$ nrow$($college$))$

$>$ Elite$[$college$Top$10$perc $>50]<-$ "Yes"

$>$ Elite $<-$ as$.$factor$($Elite$)$

$>$ college $<-$ data.frame$($college$,$ Elite$)$

Use the summary$()$ function to see how many elite universities there are. Now use the plot$()$ function to produce

side$-$by$-$side boxplots of Outstate versus Elite.

v$.$ Use the hist$()$ function to produce some histograms with

difering numbers of bins for a few of the quantitative variables. You may fnd the command par$($mfrow $=$ c$(2,2))$

useful: it will divide the print window into four regions so

that four plots can be made simultaneously. Modifying the

arguments to this function will divide the screen in other

ways.

vi$.$ Continue exploring the data, and provide a brief summary

of what you discover