Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 218 / 1 / a / Solution

For individual $i$, let $Y_i$ be the reported count, $g_i\in \{0,1\}$ the gender indicator, and $m_i\in \{0,1\}$ the minority indicator. The fitted Poisson regression isIts log-likelihood isThe maximum-likelihood estimator isHolding minority status fixed, changing the gender indicator from zero to one multiplies the fitted conditional expected value by $e^{-0.1916}=0.826$. Thus the fitted mean count for men is about $17.4\%$ lower than that for women with the same minority status.