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Re: st: theory reg vs. qreg


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: theory reg vs. qreg
Date   Tue, 30 Apr 2013 10:09:01 -0400

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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