For the following five exercises, you will need to construct indicator variables to use categorical variables as explanatory variables in logistic regression. Be sure to review the material in Chapter 11 on models with categorical explanatory variables (pages 571-575) before attempting these exercises.

Question 17.38

17.38 Student athletes and gambling.

A survey of student athletes that asked questions about gambling behavior classified students according to the National Collegiate Athletic Association (NCAA) division.13 For male student athletes, the percent who reported wagering on collegiate sports are given here along with the numbers of respondents in each division:

Division
I II III
Percent 17.2% 21.0% 24.4%
Number 5619 2957 4089
  1. Using the numbers and percents given, calculate the numbers of students who gamble and those who do not for each NCAA division.
  2. Use two indicator variables to code the explanatory variable, NCAA division. Let the first one be 1 for Division II and 0 otherwise; let the second be 1 for Division III and 0 otherwise. With this coding, the logistic regression model will use the intercept for Division I, the intercept plus the coefficient of the first indicator variable for Division II, and the intercept plus the coefficient of the second indicator variable for Division III.
  3. Run the multiple logistic regression and summarize the results.