Two packs contain $40$ cigarettes. Holding height fixed, increasing average consumption from zero to two packs per day changes the <log odds> by
$$
40(0.02313)=0.9252.
$$
The corresponding <odds ratio> is therefore
$$
\boxed{e^{0.9252}\approx2.52}.
$$
Thus the model estimates that a two-pack-per-day smoker has about $2.52$ times the odds of heart disease of an otherwise comparable nonsmoker. This is an association in the fitted observational model, rather than by itself a causal conclusion.

Solution

Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 2 / 5J / b / Solution

{title2=$\log\frac{p}{1-p}$}
{wiki=Logit}

For an event of probability $p$, the log odds are the <natural logarithm> of its <odds>:
$$
\operatorname{logit}(p)=\log\frac{p}{1-p}.
$$

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