(a) Sketch the tree corresponding to the CART partition given below. The word in each box...

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(a) Sketch the tree corresponding to the CART partition given below. The word in each box indicates the class label for that region. X2 1 0 Cat Dog Sheep Cat Rabbit 3 4 6 X (b) Create a diagram similar to that given in part (a) using the CART tree below. Indicate the class label in each region of the partitioned feature space. X1 <1 X2 <0 Apple Pear X2 <1 X2 <2 X1 <2 Banana Orange Grapes Apple (c) The predictive performance of a single tree can be substantially improved by aggregating many decision trees. i. Briefly explain the random forest method for classification. ii. Should pruned or un-pruned trees be used in random forests? Explain. iii. Briefly explain the of out-of-bag error rate for random forests. (d) Briefly explain how K-fold cross-validation can be used to approximate a test- ing error rate. Describe one advantage of cross-validation over the validation set approach. (a) Sketch the tree corresponding to the CART partition given below. The word in each box indicates the class label for that region. X2 1 0 Cat Dog Sheep Cat Rabbit 3 4 6 X (b) Create a diagram similar to that given in part (a) using the CART tree below. Indicate the class label in each region of the partitioned feature space. X1 <1 X2 <0 Apple Pear X2 <1 X2 <2 X1 <2 Banana Orange Grapes Apple (c) The predictive performance of a single tree can be substantially improved by aggregating many decision trees. i. Briefly explain the random forest method for classification. ii. Should pruned or un-pruned trees be used in random forests? Explain. iii. Briefly explain the of out-of-bag error rate for random forests. (d) Briefly explain how K-fold cross-validation can be used to approximate a test- ing error rate. Describe one advantage of cross-validation over the validation set approach.