At the maximum-likelihood estimates,
$$
\widehat\sigma_1^2=\frac1n\|Y-X\widehat\beta\|_2^2,
$$
so
$$
-2\ell(\widehat\beta,\widehat\sigma_1^2)
=n\{\log(2\pi\widehat\sigma_1^2)+1\}.
$$
There are $p$ regression coefficients and one variance parameter. Adding twice this parameter count gives
$$
\operatorname{AIC}(M_1)
=n\{\log(2\pi\widehat\sigma_1^2)+1\}+2(p+1).
$$


Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-218/5/c/ii/solution