Chapter 17, Problem 8PS

Undergraduate students at Miami University in Oxford, Ohio, were surveyed in order to evaluate the effect of price on the purchase of a pizza Hut. The students were asked to suppose that they were going to have a large two-topping delivered to their residence. Then they were asked to select from either Pizza Hut or another pizzeria of their choice. The price they would have to pay to get a Pizza Hut pizza differed from survey to survey. For example, some surveys used the price $\text{\$11}\text{.49}$ . Other prices investigated were $\text{\$8}\text{.49, }\text{\$9}\text{.49,}\text{\$10}\text{.49, \$12}\text{.49, \$13}\text{.49}\text{.}$ and $\text{\$14}\text{.49}\text{.}$ The dependent variable for this study is whether or not a student will select Pizza Hut. The independent variables are the price of a Pizza Hut pizza and the gender of the student $(1=\text{male,}\text{0}=\text{female}).$

a. Using half the data as the training sample and the other half of the data as the validation sample, develop a classification tree model to predict the probability the student will select Pizza Hut based on the price of a Pizza Hut pizza and the gender of the student.

b. What conclusions can you reach about the probability the student will select Pizza Hut?