Finding the distribution of the estimator of variance in this linear regression model
Hi everyone! I have an exam on Friday and this is a practice question.
I have been given a linear regression model where rvs Y1,...,Yn are given by
Yi = a + Bxi + Ei
Where a,B and x1,...,xk are constants with Sum(xi)=0 and E1,...,En are iid rvs each with the normal distribution with mean 0 and var o2.
I was asked to find the m.l.e for variance which I got as
o2' = 1/n*Sum((Yi - a' - B'xi)^2)
where a' and B' are the m.l.e for a and B and
a' = 1/n*Sum(Yi) , B' = (Sum(xi*Yi))/(Sum(xi^2))
I was then asked to find the distribution of a', B' and n*o2'/o2. I got that
a'~N(a,o2/n) and B'~N(B,o2/Sum(xi^2))
But I can't find the dist of no2'/o2! Has any got any ideas or can point me in the right direction? Many thanks!