Since β̂_{o}, β̂_{1}, ... β̂_{k} are independent of s^{2}, it follows that

l = a_{o}β̂_{o} + a_{1}β̂_{1} + ...... + a_{k}β̂_{k}

is independent of s^{2}. Use this fact and Theorems 11.2 and 11.3 to show that

has a Student’s T distribution with [n - (k + 1)] degrees of freedom.