Description
1. Consider the Hitters dataset from the previous project. It consists of 20 variables measured on
263 major league baseball players (after removing those with missing data). Take log(Salary) as
response (due to skewness in Salary) and the remaining 19 variables as predictors. All data will
be taken as training data. For all the models below, use leave-one-out cross-validation (LOOCV) to
compute the estimated test MSE.
(a) Fit a tree to the data. Summarize the results. Unless the number of terminal nodes is large,
display the tree graphically and explicitly describe the regions corresponding to the terminal
nodes that provide a partition of the predictor space (i.e., provide expressions for the regions
R1, . . . , RJ ). Report its estimated test MSE.
(b) Use LOOCV to determine whether pruning is helpful and determine the optimal size for the
pruned tree. Compare the best pruned and un-pruned trees. Report estimated test MSE for
the best pruned tree. Which predictors seem to be the most important?
(c) Use a bagging approach to analyze the data with B = 1000. Compute the estimated test MSE.
Which predictors seem to be the most important?
(d) Use a random forest approach to analyze the data with B = 1000 and m ≈ p/3. Compute the
estimated test MSE. Which predictors seem to be the most important?
(e) Use a boosting approach to analyze the data with B = 1000, d = 1, and λ = 0.01. Compute
the estimated test MSE. Which predictors seem to be the most important?
(f) Compare the results from the various methods. Which method would you recommend? How
does your recommendation compare with the method you recommended in the previous project?
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2. Consider the diabetes dataset from Mini Projects 3 and 4. As there, we will take Outcome as the
binary response, the remaining 8 variables as predictors, and all the data as training data. For all
the models below, use 10-fold cross-validation to compute the estimated test error rates and also to
tune any hyperparameter that requires tuning.
(a) Fit a support vector classifier to the data with cost parameter chosen optimally. Summarize key
features of the fit. Compute its estimated test error rate.
(b) Fit a support vector machine with a polynomial kernel of degree two and cost parameter chosen
optimally. Summarize key features of the fit. Compute its estimated test error rate.
(c) Fit a support vector machine with a radial kernel with both γ and cost parameter chosen
optimally. Summarize key features of the fit. Compute its estimated test error rate.
(d) Compare results from the above three methods and also from the method you recommended for
these data in Mini Projects 3 and 4. Which method would you recommend now?
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