In this problem, you will develop a model to predict whether a given car gets high or

low gas mileage based on the Auto data set.

$($a$)$ Create a binary variable, $mpg{01}_{?}$ that contains a $1$ if $mpg$ contains a value above

its median, and a $0$ if $mpg$ contains a value below its median. You can compute the

median using the median$()$ function. Note you may find it helpful to use the

dataframe $0$ function to create a single data set containing both $mpg01$ and the

other Auto variables.

$($b$)$ Explore the data graphically in order to investigate the association between

mpg $01$ and the other features. Which of the other features seem most likely to be

useful in predicting $mpg01?$ Scatterplots and boxplots may be useful tools to

answer this question. Describe your findings.

$($c$)$ Split the data randomly into a training set $(70\%)$ and a test set $(30\%).$ Make sure

to use set seed$(1),$ for reproducible results.

$($d$)$ Perform KNN on the training data, with several values of $K,$ in order to predict

mpg$01.$ Use only the variables that seemed most associated with mpg$01$ in $($b$).$

What test errors do you obtain? Which value of $K$ seems to perform the best on

this data set?

$($e$)$ Are the predictors you included into KNN model on the same scale? Proceed to

scale the train & test data from parts $(c)-(d)$ as we did in the lab. Only use the

predictors that you claimed to be useful in explaining $mpg01.$ Repeat part $(d)$ for

the scaled data.