= Solution
For independent patients, the <Bernoulli logistic-regression model> is
$$
Y_i\sim\operatorname{Bernoulli}(p_i),\qquad
\log\frac{p_i}{1-p_i}=\beta_0+\beta_aa_i+\beta_fd_i,
$$
where $d_i=\mathbf1_{\{\mathrm{frail}_i=1\}}$ with nonfrail patients as the <reference level in a regression factor>. The fitted <linear predictor> is
$$
\boxed{\widehat\eta_i=4.25375-0.08942a_i-3.15336d_i,\qquad
\widehat p_i=\frac{e^{\widehat\eta_i}}{1+e^{\widehat\eta_i}}.}
$$
The null model fits one intercept, so its 99 <residual degrees of freedom> imply \b[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:
$$
\operatorname{AIC}=-2\ell(\widehat\beta)+2k,
\qquad
\ell(\beta)=\sum_{i=1}^{100}\left[y_i\eta_i-\log(1+e^{\eta_i})\right].
$$
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 $D=-2\ell(\widehat\beta)$. Consequently
$$
\boxed{\widehat{\operatorname{AIC}}=D+6=61.376+6=67.376.}
$$
There is no estimated error-variance parameter to count. The printed name “Aikake” should be read as Akaike.
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