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Math Help - Conditional expectation in regressions

  1. #1
    Newbie ButterflyM's Avatar
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    Conditional expectation in regressions

    Hello!

    Does anyone know what is the difference in a regression between E[\hat{\beta}] and E[\hat{\beta}|X]? One is called the unconditional one the other conditional. So far I can get it. But conditional on what exactly? Does it mean that E[\hat{\beta}] refers to the expected value of \hat{\beta} in the (total) population, while E[\hat{\beta}|X] to a chosen sample and we treat X as fixed? But if we had no X, how would be obtain E[\hat{\beta}] otherwise? And why would we fix X? I am not exactly sure where their difference lies.. Please help.. I know it's a basic question but it confuses me.

    Thanks!
    Mxo
    Last edited by ButterflyM; March 23rd 2013 at 03:51 PM.
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  2. #2
    MHF Contributor
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    Re: Conditional expectation in regressions

    Hey ButterflyM.

    Is X a sample or is it a design matrix (I'm guessing its a sample set of observations)?
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  3. #3
    Newbie ButterflyM's Avatar
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    Re: Conditional expectation in regressions

    X is a NxK non-singular matrix of random variables. N observations and K independent variables.
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  4. #4
    MHF Contributor
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    Re: Conditional expectation in regressions

    Hint: The thing you have to focus on is whether X is a random variable or not. If it isn't then the expectation won't be affected by the value of X.
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