Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 13J / iii / Solution

With $\widehat\sigma^2=\|Y-X\widehat\beta\|^2/(n-p)$, a simultaneous $(1-\alpha)$ confidence region for $\beta$ is
$$
(\beta-\widehat\beta)^TX^TX(\beta-\widehat\beta)
\leq p\widehat\sigma^2F_{p,n-p}(1-\alpha).
$$


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 Incoming links: Normal linear-model confidence ellipsoid