Undergraduate students at Miami University in Oxford, Ohio, were surveyed in order to evaluate the effect of price on the purchase of a pizza from Pizza Hut. The students were asked to suppose that they were going to have a large two-topping pizza 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 $$\$ 11.49$$. Other prices investigated were $$\$ 8.49, \$ 9.49, \$ 10.49, \$ 12.49, \$ 13.49$$, and $$\$ 14.49$$. The dependent variable for this study is whether or not a student will select Pizza Hut. Possible independent variables are the price of a Pizza Hut pizza and the gender of the student. The data set PizzaHut has 220 observations and three variables:
Gender $(1=$ male, $0=$ female $)$
Price $(8.49,9.49,10.49,11.49,12.49,13.49$, or 14.49$)$
Purchase ( $1=$ the student selected Pizza Hut, $0=$ the student selected another pizzeria)
a. Develop a logistic regression model to predict the probability that a student selects Pizza Hut based on the price of the pizza. Is price an important indicator of purchase selection?
b. Develop a logistic regression model to predict the probability that a student selects Pizza Hut based on the price of the pizza and the gender of the student. Is price an important indicator of purchase selection? Is gender an important indicator of purchase selection?
c. Compare the results from (a) and (b). Which model would you choose? Discuss.
d. Using the model selected in (c), predict the probability that a student will select Pizza Hut if the price is $$\$8.99$$.
e. Using the model selected in (c), predict the probability that a student will select Pizza Hut if the price is $$\$ 11.49$$.
f. Using the model selected in (c), predict the probability that a student will select Pizza Hut if the price is $$\$13.99$$.