Using data originally from Mullahy (1997) on smoking consumption (cigarettes smoked per day) by \(\mathrm{n}=807\) subjects, assess the suitability of a Poisson regression using a posterior predictive \(p\)-test to assess overdispersion. Focal response points, especially at one pack per day \((y=20)\), may cast doubt on the Poisson assumption. The predictors are years of education, logarithm of income, logarithm of cigarette price, restaurant ban (binary), white or nonwhite (binary) and age. As discussed above, one option involves comparing \(D=0.5 \sum_{i=1}^{n}\left\{\left(y_{i}-\mu_{i}\right)^{2}-y_{i}\right\}\) with its replicate data counterpart \(D_{\text {rep }}=0.5 \sum_{i=1}^{n}\left\{\left(y_{\text {rep }, i}-\mu_{i}\right)^{2}-y_{\text {rep }, i}\right\}\).