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**HW06Cover Sheet**

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Q1 Textbook Examples

Chapter 8 – Tree-Based Methods

- 8.1.1 Regression Trees
- 8.1.2 Classification Trees
- Lab: 8.3.1 Fitting Classification Trees
- Lab: 8.3.2 Fitting Regression Trees
- Lab: 8.3.3 Bagging and Random Forests
- Lab: 8.3.4 Boosting

Datasets –

Hitters.csv

Heart.csv

Carseats.csv

Boston.csv

OJ.csv

Caravan.csv

Hint use: https://botlnec.github.io/islp/

Q2 Textbook Exercises

8.8 (page 333) In the lab, a classification tree was applied to the Carseats data set after converting Sales into a qualitative response variable. Now we will seek to predict Sales using regression trees and related approaches, treating the response as a quantitative variable.

(a) Split the data set into a training set and a test set.

(b) Fit a regression tree to the training set. Plot the tree and interpret the results. What test MSE do you obtain?

(c) Use cross-validation in order to determine the optimal level of tree complexity. Does pruning the tree improve the test MSE?

(d) Use the bagging approach in order to analyze this data. What test MSE do you obtain? Determine which variables are most important.

(e) Use random forests to analyze this data. What test MSE do you obtain? Determine which variables are most important. Describe the effect of m, the number of variables considered at each split, on the error rate obtained.

9. This problem involves the OJ data set which is part of the ISLR package.

(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. 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) Type in the name of the tree object in order to get a detailed text output. Pick one of the terminal nodes, and interpret the information displayed.

(d) Create a plot of the tree and interpret the results.

(e) 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?

(f) Use training set in order to determine the optimal tree size.

(g) Produce a plot with tree size on the x-axis and cross-validated classification error rate on the y-axis.

(h) Which tree size corresponds to the lowest cross-validated classification error rate?Produce a pruned tree corresponding to the optimal tree size obtained using cross-validation. If cross-validation does not lead to selection of a pruned tree, then create a pruned tree with five terminal nodes.

(j) Compare the training error rates between the pruned and unpruned trees. Which is higher?

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

10. We now use boosting to predict Salary in the Hitters data set.

(a) Remove the observations for whom the salary information is unknown, and then log-transform the salaries. 8.4 Exercises 335

(b) Create a training set consisting of the first 200 observations, and a test set consisting of the remaining observations.

(c) Perform boosting on the training set with 1,000 trees for a range of values of the shrinkage parameter λ. Produce a plot with different shrinkage values on the x-axis and the corresponding training set MSE on the y-axis.

(d) Produce a plot with different shrinkage values on the x-axis and the corresponding test set MSE on the y-axis.

(e) Compare the test MSE of boosting to the test MSE that results from applying two of the regression approaches seen in Chapters 3 and 6.

(f) Which variables appear to be the most important predictors in the boosted model?

(g) Now apply bagging to the training set. What is the test set MSE for this approach?

Hint – use https://botlnec.github.io/islp/

Or