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Topic: Test constantness of normality of residuals from linear regression
Replies: 8   Last Post: Jan 10, 2013 6:09 PM

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Posts: 517
Registered: 2/23/10
Re: Test constantness of normality of residuals from linear regression
Posted: Jan 10, 2013 6:09 PM
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On Jan 10, 6:00 pm, Michael Press <> wrote:
> In article
> <>,
>  Ray Koopman <> wrote:
> [...]

> > It all depends on what you want. Look up the Gauss-Markov theorem.
> > To justify the usual OLS estimates of the regression coefficients,
> > the errors need only to be unbiased, uncorrelated, and homoscedastic,
> > but to justify all the usual p-values and confidence regions, the
> > errors must be iid normal.

> > However, that's considering only the theoretical justification.
> > In practice, what matters is not whether the assumptions are right
> > or wrong, but how wrong they are -- they're never exactly right.

> > Normality is probably the least important assumption. The most
> > important things to worry about are the general form of the model
> > and whether it includes all the relevant predictor variables. Then
> > you ask how correlated and/or heteroscedastic the errors might be.
> > Finally, you might wonder about shapes of the error distributions.
> > Minor departures from normality are inconsequential. Nothing in the
> > real world is exactly normal, and any test of normality will reject
> > if the sample size is big enough.

> Assuming that the errors are normally distributed is
> equivalent to assuming that the errors have mean zero
> and fixed variance (using the new word I heard today:
> homoscedastic) in that those assumptions least affect
> how close our analysis gets to discerning the
> parameters of interest. Normality is a bad assumption
> only if we are suppressing some knowledge of how the
> errors are distributed beyond the initial assumptions.
> If it somehow turns out that a different set of
> assumptions about the errors is better, for some value
> of better, then that is called scientific discovery,
> not bad assumptions. We should get to the point where
> we cannot wring any more meaning out to the data and
> are left with errors normally distributed around zero.
> It is not that I said anything more than you about the
> mathematics and statistics---only voiced my perspective
> on the process. If you see that I am in error, normal
> for me, I welcome hearing about it.

I learned the word "heteroscedasticity" today. still trying to
pronounce it without tripping.

Thanks for the perspective on the relative importance of normality,
and why.

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