Question: In the simple linear model setting with (mu in mathcal{X}) and (Sigma propto I_{n}), show that the maximum value of the (log) likelihood is const

In the simple linear model setting with $\mu \in \mathcal{X}$ and $\Sigma \propto I_{n}$, show that the maximum value of the $\log$ likelihood is const $-n \log \|Q Y\|$, where $Q=I-P$ is the orthogonal projection with kernel $\mathcal{X}$, and the constant is independent of $\mathcal{X}$.

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