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 17.39

17.39 Is there a trend?

Refer to the previous exercise. The coding of the indicator variables suggests a way to code models when you expect a pattern in the response that is based on some kind of ordering of the explanatory variable. In some settings this is called detecting a dose response.

  1. Use the model to give the estimated log odds for each NCAA division.
  2. Plot these estimates versus division and summarize the results. Does there appear to be a pattern in the results?
  3. How would you model the pattern that you described in part (b)?

17.39

(a) For Division . For Division . For Division . (b) The plot shows that log(odds) of gambling increases as Division increases. (c) Because the relationship is quite linear, we could use a regression analysis.