Popkin (1991) presented the data shown in Table 13.17 for number of auto crashes and number of alcohol-related (A/R) auto crashes for young drivers in North Carolina. You are interested in whether the probability a crash will be A/R is related to age and gender.
(a) Construct a profile plot (similar to those for the two-way ANOVA) for the ln (odds) that a crash will be alcohol-related, using the age category on the horizontal axis and separate symbols for gender. Discuss the apparent effects. Is there a graphical suggestion of an interaction?
(b) Construct a profile plot in the same way as for part (a), using the empirical probability that a crash will be alcohol-related. Is there a graphical suggestion of an interaction? How does it compare to that from the graph in part (a)?
(c) Construct a dummy variable system for the age category and gender, and fit a logistic regression that only includes main effects. Interpret the main effects, using the profile plot from part (a).
(d) Fit a logistic regression that includes main effects and interactions.
(e) Construct a likelihood ratio test for the null hypothesis that none of the interactions are significant. Interpret the results.
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