Consider a linear model $Y=X \beta+\sigma^{2} \varepsilon$ with $\varepsilon \sim N(0, I)$, where the design matrix $X$ is $n$ by $p$. Provide an expression for the $F$-statistic used to test the hypothesis $\beta_{p_{0}+1}=\beta_{p_{0}+2}=\cdots=\beta_{p}=0$ for $p_{0}<p$. Show that it is a monotone function of a log-likelihood ratio statistic.