 Solution

For independent patients, the Bernoulli logistic-regression model iswhere $d_i=1_{\{{\mathrm{frail}}_i=1\}}$ with nonfrail patients as the reference level in a regression factor. The fitted linear predictor isThe null model fits one intercept, so its 99 residual degrees of freedom imply 100 patients; the full model's $100-3=97$ confirms this. Unit weights correspond to individual binary responses, not grouped binomial counts.

The Akaike information criterion estimates expected relative out-of-sample discrepancy, using the maximized log-likelihood plus a complexity penalty:Here $k=3$, since the Bernoulli dispersion is fixed at one. The saturated model puts probability one on each observed binary outcome and has log likelihood zero, so the binomial deviance is $D=-2\ell (\hat{\beta })$. ConsequentlyThere is no estimated error-variance parameter to count. The printed name “Aikake” should be read as Akaike.