We have just put out a special promotion and would like to determine who responded to the mailing. We have a sample of consumers, including both purchasers and non-purchasers (all received the promotion), and would like to predict who is a purchaser. For each consumer, we have their age (bucketed into ranges), their income (bucketed into ranges), and whether or not they responded to last year's mailing. Purchase? Age Income Last Year? Yes Young Low No Yes Middle Low Yes Yes Old Middle Yes Yes Young Low Yes Yes Young Middle Yes Yes Middle Low No No Old High Yes No Middle Middle No No Young High Yes No Middle Middle Yes No Old High No Please show your calculations in the following questions, (a) Using the 1-rule method discussed in class, find the relevant sets of classification rules for the target variable by testing each of the input attributes. Which of these sets of rules has the lowest misclassification rate? (b) Now, we want to construct a decision tree using this data set. What is the entropy measure of the entire data set? (c) What is the information gain for splitting on age? On income? On last year? Which should be the initial split variable? (d) Draw the tree after the initial split using the information gain. What is the decision at each terminal node? (e) What is the accuracy of your decision tree on this data set? Explain your answer. (f) What would your tree predict for a Middle aged person with Middle income who did not purchase last year? Justify your answer. (g) What are the support and confidence of the rules - If Last Year = Yes, then Yes. - If Age = Middle, and Income = Low, then Yes. (h) Construct the entire decsion tree that uses Gini index as the impurity measure