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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 13:11:32 -0400

On Tue, Apr 30, 2013 at 10:31 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> 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.

Yes, though of course regression can be even broader and talk about
the notion of other conditional quantities, or, I suppose about
conditional distributions entirely.


> 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.

Right, it's a consequence of the fact that OLS is minimized for the
sample mean and when the vector 1 is in the column space of X it
preserves the mean. Regression through the origin or through some
other constant will not go through the sample mean.

If you switch loss functions, you will get a different answer. By
choosing a different loss function you have, implicitly or explicitly,
asked a different question and are thereby likely to get a different
answer. There's nothing particularly desirable about OLS aside from
the fact that the math for it is "nice".

There's a neat little article on this:

R. DeLaubenfels. 2006. The victory of least squares and orthogonality
in statistics. The American Statistician, 60, 315-321.

-- 
JVVerkuilen, PhD
jvverkuilen@gmail.com

“He uses statistics as a drunken man uses lamp-posts – for support
rather than illumination.”--Andrew Lang

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