# Regression - Variance of the Prediction Error

• Dec 31st 2012, 10:18 AM
Wevans2303
Regression - Variance of the Prediction Error
Hi,

Given the prediction error (denoted en+1) can be written as:

http://s13.postimage.org/liph5zrbb/image.jpg

Prove it's variance is equal to this (note E(en+1)=0):

http://s8.postimage.org/9e1ciizpx/999.jpg

At the moment I have this:

http://s9.postimage.org/pb0mxmmdr/IMAG0064.jpg

But when I sub in for di I can get the first two terms i.e. 1+1/n but I cannot seem to finish the question off, if anyone can help me in any way I would be most grateful.
• Dec 31st 2012, 03:29 PM
chiro
Re: Regression - Variance of the Prediction Error
Hey Wevans2303.

Why didn't you square the epsilon*a_i term in line 5 of your proof?
• Dec 31st 2012, 04:00 PM
Wevans2303
Re: Regression - Variance of the Prediction Error
Where its sum(didj)E(eiej)?

i=j so sum(didj)E(e^2)

= sigma^2(sum(di^2))

Sorry if I have misinterpreted you.
• Dec 31st 2012, 05:37 PM
chiro
Re: Regression - Variance of the Prediction Error
What I mean is that (epsilon*a_i*e_i)^2 = epsilon^2*(a_i)^2*(e_i)^2: take a look at your working out for more information.
• Jan 1st 2013, 06:27 AM
Wevans2303
Re: Regression - Variance of the Prediction Error
.