
Estimators
For the linear regression model
Y=XB+e
(B= beta and e = epsilon)
ei~N(0,s^2) (s = sigma)
i = 1,...,n are independant, this model does not contain an intercept form
(E = sum of , ^B = beta hat)
i found that ^B = Ei xiyi / Ei xi^2
now i need to show that ^B is an unbiased estimator of B and that its variance is s^2/ Ei xi^2
jus wondering what the proof is for a linear regression model that the expected or estimated value of ^B =B in this circumstance and how to prove that var(^B)=s^2(XtX)^1
ive been working in matrix form, t=transpose as im sure u might have guessed