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Re: st: theory reg vs. qreg


From   Nick Cox <njcoxstata@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: theory reg vs. qreg
Date   Tue, 30 Apr 2013 15:31:04 +0100

The deeper idea, I suggest, is that it is the _definition_ of a
regression line (function, more generally) that it is the locus of the
means of the response. On top of that we often build an _assertion_ or
_assumption_ that that function is linear in the parameters.

It's important to separate the assumptions of linear models from the
estimators we happen to use to get at parameters. That the regression
line goes through the means is not a consequence of using OLS.
Nick
njcoxstata@gmail.com


On 30 April 2013 15:09, JVerkuilen (Gmail) <jvverkuilen@gmail.com> wrote:
> On Tue, Apr 30, 2013 at 2:46 AM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>>
>> Roman,
>>
>> The feature you are referring to is the fact that the regression line
>> passes via the sample mean.
>>
>> This is the reason why the projected Y for mean(X) is mean(Y).
>>
>> This outcome emanates from the derivation of the OLS formula, where we
>> minimize the RSS (Residual Sum of Squares).
>
> This is only true if the X matrix has the 1 vector in its column
> space, usually ensured by directly including it. If not, then it may
> be quite different. I suggest the original poster read up on
> statistical theory. The Greene book is a good example. I find that the
> geometry of linear models is discussed in a few other books in more
> detail. One of my favorites is free on the web at the following link:
>
>      http://istics.net/pdfs/anova.pdf
>
> (These are written by John Marden, who was one of my professors.
> Several other books are available on his web page:
> http://istics.net/stat/stat-text-booksfree-not-free/) As to qreg, it's
> minimizing a very different function and of course won't go through
> the mean except by happenstance.
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