Prove that the regression slope estimator b is an unbiased estimator of the true slope parameter B.
I know that for b to be an unbiased estimator of B, E[b]=B but I'm not sure how to show it mathematically. I'd also like to see how to prove that a is an unbiased estimator of A.
EDIT:
This is what I have so far. Maybe it'll get give some people an idea of how to complete it.
So then,
So, after some fancy distribution.
We can see that
So, then we have
I see to get stuck at this point though. Any help?
EDIT 2:
Ok, I've gotten further. It's amazing how much clearer things are when typed out instead of written in chicken scratch..
Rewriting the equation as
We can see that
So now we have
From here, I think it's time to try to show that . So
Then, I know there's an assumption in my textbook that . Does that mean I can just do
Which simplifies to
Can anyone confirm if this is correct or not? Thanks