Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 218 / 5 / d / Solution

There are three regression coefficients and $97$ residual degrees of freedom, so $n=100$. The reported residual standard error uses the unbiased divisor:Hence the maximum-likelihood variance estimate is ${\hat{\sigma }}^2=\mathrm{RSS}/100$. Substituting this, $n=100$, and the four fitted parameters—three coefficients plus ${\sigma }^2$—into the formula in part c(ii) gives the AIC.