Using RStudio

Problem $1(10$ pts$)$

This problem will use the OJ dataset which is part of the ISLR$2$ package. The data is tracking two kinds of orange juice purchases. Run the following commands to make this dataset available for use in RStudio.

$>$ install.packages$($ISLR$2)$

$>$ library$($ISLR$2)$

$>$ install.packages$($tree$)$

$>$ library$($tree$)$

$>$ attach$($OJ$)$

$>$ View$($OJ$)$

$>$ set.seed$(1)$

a$.(2$ pts$)$ Show the command to create a random sample of $800$ observations and the command to fit a classifier tree with Purchase as the response variable using the sample as training data.

b$.(3$ pts$)$ Show the summary for the tree created. What is the training error rate?

c$.(3$ pts$)$ Plot the tree, showing the text for each branch.

d$.(2$ pts$)$ Which predictor is the most important in the tree?

In this problem, continue to work with the OJ dataset to answer the questions below.

$>$ set.seed$(1)$

a$.(4$ pts$)$ Using the test data from problem $1,$ predict the response on the test data. Produce a confusion matrix using the table function for the prediction vs$.$ the actual Purchase data. What is the test error rate?

b$.(3$ pts$)$ Use the cv$.$tree$()$ function for the test tree to determine the optimal tree size.

c$.(3$ pts$)$ Create a plot with the tree size on the x$-$axis and the cross$-$validated deviance on the y$-$axis. Show the plot here.

Problem $3(10$ pts$)$

This problem will continue from the trees made on training and test data from the above problems.

$>$ set.seed$(1)$

a$.(3$ pts$)$ Prune the tree made from training data in problem $1$ using $8$ nodes in the prune.misclass function. Show the summary.

b$.(2$ pts$)$ Plot the pruned tree with text and paste it here.

c$.(3$ pts$)$ Prune the tree made from test data in problem $2$ using $2$ nodes in the prune.misclass function. Show the summary.

d$.(2$ pts$)$ Plot the pruned tree with text and paste it here

Problem $4(10$ pts$)$

This problem will examine components and concepts related to neural networks.

a$.(2$ pts$)$ What are the layers that make up a neural network?

b$.(2$ pts$)$ What is the purpose of the input layer? What form can the inputs take?

c$.(2$ pts$)$ What is the purpose of the output layer?

d$.(2$ pts$)$ What is the purpose of the hidden layer?

e$.(2$ pts$)$ Why is the hidden layer named so$?$

Problem $5(10$ pts$)$

This problem will focus on deep learning and neural network concepts.

a$.(3$ pts$)$ What is the purpose of a convolutional neural network? What does it do$?$

b$.(3$ pts$)$ What is the purpose of a recurrent neural network? What does it do$?$

c$.(4$ pts$)$ What are the four key ingredients for deep learning? Define each one.