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For linear regression, is an estimator of the variance of the dependent variable for a fixed x-value $SSE/(n-2)$?

Jeromy Anglim
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James Erl
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1 Answers1

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Yes; you're looking for an estimate of the residual variance. See e.g. the wikipedia article on simple linear regression, though it's rather hidden there. I'd suggest a trip to the library, or buy a copy of Freedman et al, Statistics.

Also note that this is about $\text{var}(y) \cdot (1 - r^2)$.

Karl
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  • The estimator is for $\text{var}(y) \cdot (1-r^2)$? This is the same thing as the residual variance right? –  Sep 25 '11 at 14:28
  • @JamesErl Please register your account -- you will be able to post comments then. Just visit http://stats.stackexchange.com/users/login . –  Sep 25 '11 at 16:18
  • @JamesErl The variance of y for a fixed x is another way of saying residual variance. – Karl Sep 25 '11 at 16:31
  • @Karl Broman: So RMSE is basically the standard deviation of the difference in means of 2 populations? – Damien Sep 25 '11 at 16:40
  • @Damien No, I don't think that's at all related. – Karl Sep 25 '11 at 18:15
  • @Karl Broman: RMSE is the standard deviation of y for a fixed x. If you do a t-test and look at the standard deviation of the difference in means it is the same as the RMSE. Maybe that is just a coincidence? – Damien Sep 25 '11 at 18:23
  • @Damien - but you said "standard deviation of the difference in means". Rather, the residual variance is the within-population variance. The correlation is not so meaningful for the binary x case, and so the formula with $(1-r^2)$ is not so meaningful for the comparison of the means of two populations. – Karl Sep 26 '11 at 00:11
  • @Damien Could you confirm that your the original poster? We could merge your two accounts on the present one (which is actually registered). – chl Sep 26 '11 at 08:34