For the Sexual Health pilot study, consider modeling the number of unprotected vaginal sex behaviors during the three month period of the study as a function of three predictors, HIV knowledge, depression, and baseline number of unprotected vaginal sex (VAGWOCT1).

(a) Fit the Poisson log-linear model.

(b) Use the deviance and Pearson statistics to examine whether there is overdispersion in the data.

(c) Does the model have an inflated zero issue?