I have the model:
$y=X{\beta}+{\epsilon}$
I know $\hat{\beta}=(X'X)^{-1}X'y$ and that it is an unbiased estimator of ${\beta}$ and that $s^2=\hat{\epsilon}'\hat{\epsilon}/(n-k)$ and is an unbiased estimator of the variance.
How do I show that $\hat{\beta}$ and $s^2$ are independent?