How could I demonstrate

[ewilliams00]

Supposing that we have a regression model that fits the conditions of normal, homoscedasticity and independent residuals, I would like to demonstrate that the variance of the estimators is:



Where is the Coefficient of Determination and

How should I start this?

 

[staassis]

The "Coefficient of Determination" cannot be "over". It is a number. Could you please rephrase your question in detail?

 

[ewilliams00]

The "Coefficient of Determination" cannot be "over". It is a number. Could you please rephrase your question in detail?

Sorry, I edited

 

[staassis]

One approach is deriving the variance of Beta = (Beta_0, Beta_1, ..., Beta_p) in the matrix form, as

sigma^2 * (X' * X)^{-1}, (1)

where X = (1, x) is an N-by-(p+1) matrix. Then you would rewrite formula (1) for the case of simple linear regression (p = 1).

 

[ewilliams00]

Thank you, but sorry it is not so obvious for me

So we have

From where are appearing X' and X?

 

[staassis]

I know it is not obvious to you. That is why you have to figure it out. I intentionally did not expose the complete proof, giving you hints instead. Or were you expecting to have somebody do the whole exercise for you?.. You cannot move smoothly between statistical topics without knowing linear algebra. Use linear algebra to prove the result I stated in the previous post.

 

[ewilliams00]

I didn't expect anybody doing the exercise for me. I just want to learn by getting some leash
It would be really helpful if you could detail the previous steps until you get (1)