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No intercept should be included unless the ordering of the two teams has an external meaning such as home advantage. Ifthen reversing the teams gives ${\eta }_{k\ell ,ij}=-{\eta }_{ij,k\ell }$, so the logistic model automatically givesAn intercept would not change sign when the teams are swapped and would violate this required symmetry. Thus an intercept does not make sense in the stated model.

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.