= Solution
Let $\varepsilon_i$ be independent standard <logistic distribution>[logistic random variables] and define the <latent variable>
$$
Z_i=-4.50161+0.02521\,\mathrm{height}_i
+0.02313\,\mathrm{cigs}_i+\varepsilon_i.
$$
Set $Y_i=1$ exactly when $Z_i>0$. If $F$ is the logistic <cumulative distribution function>, its symmetry and the identity $F^{-1}(p)=\operatorname{logit}(p)$ give
$$
\mathbb P(Y_i=1)=F(-4.50161+0.02521\,\mathrm{height}_i+0.02313\,\mathrm{cigs}_i),
$$
which is precisely the fitted <logistic regression>.
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