HW1: Entropy, Information Gain, & Supervised Segmentation 1. Refer to the customer example in the notes on slides 7-9. If you were to segment the 12 customers by the variable "head shape," what would be the entropy for the two subgroups (square and circular head)? 2. Refer to the accompanying Excel file. A riding-mower manufacturer would like to find a way of classifying families in a city into those likely to purchase a riding mower and those not likely to buy one. A pilot random sample is undertaken that includes 12 owners and 12 nonowners in the city and includes the variables income and lot size. a. Convert income to categories of low high income with a cutoff of $60,000, and convert lot size to categories of small/large lot with a cutoff of 20,000 f?. b. If you could only use one variable to segment the data, which would be better? Why? 3. A bank would like to predict which customers will accept a loan offer. It uses historic data to construct a classification tree to classify records as either "non-acceptors" (blue orange) or acceptors" (orange blue). The variables include family income (S1000s), family size, and a categorical variable for education, where indicates a high school diploma, 1 indicates a bachelor's degree, and 2 indicates a graduate degree. All arrows to the left indicate the condition in the splitting node is "true;" all arrows to the right indicate the condition is "false." In addition to the splitting condition, nodes contain the total number of records in the subgroup and the number in each target category. (non-acceptors, acceptors). Construct the logical if then statements that correspond to nodes a, b, and e. For each node, also indicate the estimated probability that the predicted class is correct. Income s 110.5 samples = 3000 value = (2713, 287] True False 2363 Education s 1.5 637 (2326, 371 (387, 250 Node a Family 2.5 400 [357, 43) Income s 116.5 237 [30,207] 355 (355, 0] 45 [2, 43] 44 [30, 14) 193 [0.193) Nodeb Nodec HW1: Entropy, Information Gain, & Supervised Segmentation 1. Refer to the customer example in the notes on slides 7-9. If you were to segment the 12 customers by the variable "head shape," what would be the entropy for the two subgroups (square and circular head)? 2. Refer to the accompanying Excel file. A riding-mower manufacturer would like to find a way of classifying families in a city into those likely to purchase a riding mower and those not likely to buy one. A pilot random sample is undertaken that includes 12 owners and 12 nonowners in the city and includes the variables income and lot size. a. Convert income to categories of low high income with a cutoff of $60,000, and convert lot size to categories of small/large lot with a cutoff of 20,000 f?. b. If you could only use one variable to segment the data, which would be better? Why? 3. A bank would like to predict which customers will accept a loan offer. It uses historic data to construct a classification tree to classify records as either "non-acceptors" (blue orange) or acceptors" (orange blue). The variables include family income (S1000s), family size, and a categorical variable for education, where indicates a high school diploma, 1 indicates a bachelor's degree, and 2 indicates a graduate degree. All arrows to the left indicate the condition in the splitting node is "true;" all arrows to the right indicate the condition is "false." In addition to the splitting condition, nodes contain the total number of records in the subgroup and the number in each target category. (non-acceptors, acceptors). Construct the logical if then statements that correspond to nodes a, b, and e. For each node, also indicate the estimated probability that the predicted class is correct. Income s 110.5 samples = 3000 value = (2713, 287] True False 2363 Education s 1.5 637 (2326, 371 (387, 250 Node a Family 2.5 400 [357, 43) Income s 116.5 237 [30,207] 355 (355, 0] 45 [2, 43] 44 [30, 14) 193 [0.193) Nodeb Nodec