Question 2 20 pts
Suppose we fit a classification tree to a given data set and construct the following tree: The question/decision rule corresponding to the first split is, "If X1<12.89 is true then go left, otherwise go right." If we go left, we end at a leaf node with 6123 training observations in class 0 and 88 training observations in class 1. Hence new observations that end at this leaf node would be predicted to be in class 0 with posterior probability 6123/(6123+88) = 0.98583159. If we go right we have another question/decision rule, "If X2<12.79 is true then go left, otherwise go right." And so on. Match the following data observations with their predicted class and posterior probabilities based on this decision tree:
(X1, X2, X3, X4, X5) = (13, 14, ­0.3, 0.9, 0.2) [ Choose ] (X1, X2, X3, X4, X5) = (14, 14, 0.1, 0.1, 0.1) [ Choose ] (X1, X2, X3, X4, X5) = (13, 14, 0.3, 1.1, 0.1) [ Choose ] Flag this Question Question 3 10 pts
For the scenario in Question 2, which one of the following describes the characteristics of an observation that has predicted class 0 and posterior probability 44/47 = 0.936? a) X1 < 12.89, X2 < 12.79, and X4 < 0.1449
b) X1 < 12.89, X2 ≥ 12.79, and 0.1449 ≤ X4 < 0.1809
c) X1 ≥ 12.89, X2 < 12.79, and 0.1449 ≤ X4 < 0.1809
d) X1 ≥ 12.89, X2 ≥ 12.79, and 0.1449 ≤ X4 < 0.1809
e) X1 ≥ 12.89, X2 ≥ 12.79, and X4 ≥ 0.1809 Flag this Question Question 4 10 pts
For the scenario in Question 2, consider the bottom right question/decision rule, "X1≥13.32," which, if true, leads to a leaf node with 33 training observations in class 0 and 7 training observations in class 1 and, if false, leads to a leaf node with 6 training observations in class 0 and 19 training observations in class 1. Suppose an alternative question/decision rule existed at this node, which, if true, leads to a leaf node with 34 training observations in class 0 and 11 training observations in class 1 and, if false, leads to a leaf node with 5 training observations in class 0 and 15 training observations in class 1. True or false: this alternative question/decision rule is preferable to the original question/decision rule? (Remember that the idea behind classification trees is to create "purer" child nodes.) True
False Flag this Question Question 5 10 pts
For the scenario in Question 2, X5 is not used at any of the splits. What single feature of classification trees does this best illustrate? a) Robustness to outliers and misclassified observations in the training set. b) Invariance under monotone transformations of quantitative predictors.
c) Automatic dimension reduction (variable selection).
d) Ease of interpretation via simple decision rules.
e) Provision of estimates of misclassification rates for test observations.

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