Table 7.5, also available at www.stat.ufl.edu/~aa/glm/data, summarizes responses of 1308 subjects to the question: within the past 12 months, how many people have you known personally that were victims of homicide?

The table shows responses by race, for those who identified their race as white or as black.

a. Let yi denote the response for subject i and let xi = 1 for blacks and xi = 0 for whites. Fit the Poisson GLM log ????i = ????0 + ????xi and interpret ????̂.

b. Describe factors of heterogeneity such that a Poisson GLM may be inadequate. Fit the corresponding negative binomial GLM, and estimate how the variance depends on the mean. What evidence does this model fit provide that the Poisson GLM had overdispersion? (Table 7.5 also shows the fits for these two models.)

c. Show that the Wald 95% confidence interval for the ratio of means for blacks and whites is (4.2, 7.5) for the Poisson GLM but (3.5, 9.0)

for the negative binomial GLM. Which do you think is more reliable?

Why?