Standard Error

[macro90]

Below are two similar problems.

http://www.geocities.com/arkayz_bible/optimization/05112491445.png

For the question above I can do i and know how to do iii but don't see how to get the standard error of eta. The answers are all below. It's just the working out I don't get.

http://www.geocities.com/arkayz_bible/optimization/05112491640.png

For the question above, the same problem arises. It's a similar question. I can do i, ii, and know how to do iv, but don't know how to find the standard error of eta (although I can find the estimate of eta).

I think it has to do with the formula var=\sigma^2(A^{T}A)^{-1}. Looking at the answers below, they take the square root of S^2 times something that contains the numbers in the A^{T}A matrix, which is that matrix shown in (a)i answers.

ANSWERS:

http://www.geocities.com/arkayz_bible/optimization/05112492203.png

http://www.geocities.com/arkayz_bible/optimization/05112492432.png

Source: http://www.ms.unimelb.edu.au/~s620202/

[macro90]

I think I've got it. Variance of eta is just s^2 times the sum of all elements of the A'A (A^{T}A) matrix.