For questions requiring R code, provide screenshots of both the input $($code$)$ and

the resulting output. Alternatively, directly copy and paste the R code along

with its output from the Console after executing the code.

The following questions are based on the Carseats dataset in R$,$ which comprises sales data

for children$$s car seats. This dataset is available in the ISLR package.

$2\mathrm{.}1$ Load the ISLR package, import the Carseats dataset and assign it to the variable

data carseats. $[2]$

$2\mathrm{.}2$ Run the data carseats dataset summary and get the descriptive statistics for each

variable in the dataset. $[1]$

$2\mathrm{.}3$ Based on the summary output in question $2\mathrm{.}2.$ One of the eleven variables of the

data carseats is ShelveLoc, which represents the quality of the shelving location for

car seats at each store.

$2\mathrm{.}3\mathrm{.}1$ What is the class of the variable ShelveLoc? $[1]$

$2\mathrm{.}3\mathrm{.}2$ How many stores have Bad shelf locations and how many stores have Medium shelf

locations? $[2]$

$2\mathrm{.}3\mathrm{.}3$ Write R code to count the frequency of each unique value in the ShelveLoc

variable and display it in a table format. $[3]$

$2\mathrm{.}3\mathrm{.}4$ Write R code to retrieve the counts for Good and Bad in the ShelveLoc variable

and save them in variables good count and bad count. $[2]$

$2\mathrm{.}3\mathrm{.}5$ Plot a bar graph of ShelveLoc to show the distribution of shelf locations $($ShelveLoc$)$

in the data carseats and provide labels. $[3]$

$2\mathrm{.}3\mathrm{.}6$ Interpret the bar graph in question $2\mathrm{.}3\mathrm{.}5[3]$

$2$

$2\mathrm{.}4$ Apply the lm$()$ function in R to fit a multiple regression model to predict Sales using

Price, Urban and US$.$ Assign results to the variable carseats lm fit. $[3]$

$2\mathrm{.}5$ Apply the summary$()$ function to provide a summary of the multiple regression model

stored in carseats lm fit. $[2]$

$2\mathrm{.}6$ Provide an interpretation of each coefficient in the carseats lm fit regression model. $[7]$

$2\mathrm{.}7$ Write out the model in equation form specifying values to two places after the decimal

point. Hint: Be careful to handle the factor variables. $[2]$

$2\mathrm{.}8$ For which of the predictors; can you reject the null hypothesis H$0$ : j $=0?[2]$

$2\mathrm{.}9$ On the basis of your response to the previous question, use R to fit a smaller model that

only uses the predictors for which there is evidence of association with the outcome. $[3]$

$2\mathrm{.}10$ How well do the models in $(2\mathrm{.}4)$ and $(2\mathrm{.}9)$ fit the data? $[2]$

$2\mathrm{.}11$ Calculate $95\%$ confidence intervals for the coefficient$($s$)$ derived from the model described

in question $(2\mathrm{.}9)$ and interpret the output. $[3]$

$2\mathrm{.}12$ Does the model from $(2\mathrm{.}9)$ show indications of high leverage observations or outliers? $[4]$