$2.$ This problem involves the OJ data set which is part of the ISLR package and also available on Canvas.

$($a$)$ Create a training set containing a random sample of $800$ observations, and a test set containing the remaining observations.

$($b$)$ Fit a tree to the training data, with Purchase as the response and the other variables as predictors. Use the summary$)$ function to produce summary statistics about the tree, and describe the results obtained. What is the training error rate? How many terminal nodes does the tree have?

$($c$)$ Create a plot of the tree, and interpret the results.

$($d$)$ Predict the response on the test data, and produce a confusion matrix comparing the test labels to the predicted test labels. What is the test error rate?

$($e$)$ Create a pruned tree with four terminal nodes.

$($f$)$ Compare the test error rates between the pruned and unpruned trees. Which is higher?