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Math Help - Regression - Variance of the Prediction Error

  1. #1
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    Regression - Variance of the Prediction Error

    Hi,

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



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



    At the moment I have this:




    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.
    Last edited by Wevans2303; December 31st 2012 at 10:23 AM.
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  2. #2
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    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?
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  3. #3
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    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.
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  4. #4
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    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.
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  5. #5
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    Re: Regression - Variance of the Prediction Error

    .
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