In the setting of linear regression, when we want to test the hypothesis $H_0 : \beta_j = 0$, we can use either t-test or F-test, with test statistics $t = \frac{\hat{\beta_j}}{SE(\hat{\beta_j})}$ and $F = \frac{RSS(m) - RSS(m)}{RSS(M)/(N-P-1)}$ , where $RSS(M)$ is the RSS under the full model, and $RSS(m)$ is the RSS under the model that has $\beta_j = 0$. I know that $F = t^2$, but how to prove it?
Thanks!
