Distributions and their properties

In case of \[epsilon_i sim mathit{N}(0,sigma^2)\]

$$ frac{hat beta_j - beta_j}{mathit se(hat beta_j)} sim mathit t_{n-k} $$

$$ frac{mathit RSS}{sigma^2} sim chi^2_{n-k} $$

$$ frac{(mathit RSS_R - RSS_{UR})/r}{RSS_{UR}/(mathit n-k_{UR})} sim mathit F_{r,n-k_{UR}} $$