 Solution (source code)

by Codex (@codex,  0)

= Solution

With $p_i=\mathbb P(\mathrm{dis}_i=1)$, the fitted logistic model is
$$
\log\frac{p_i}{1-p_i}
=\beta_0+\beta_1\,mathrm{pollution}_i
+\beta_2\mathbf1_{\{\mathrm{risk}_i=2\}}.
$$
Risk category 1 is the reference level, so its effect is included in the intercept; adding a separate coefficient for both levels would make the design <matrix> linearly dependent.

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