Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 218 / 3 / a / Solution

For word-count vector $x$, the fitted logistic model isHolding other counts fixed, one additional occurrence of "dollar" multiplies the fitted spam odds by $e^{1.859318}$.

The logistic classifier isThe coefficients maximize the Bernoulli logistic-regression model likelihood over the training emails.