[R] qr and Moore-Penrose

Prof Brian Ripley ripley at stats.ox.ac.uk
Wed Jun 30 16:12:25 CEST 1999

> Date: Wed, 30 Jun 1999 15:44:58 +0200 (MET DST)
> From: Torsten Hothorn <hothorn at amadeus.statistik.uni-dortmund.de>
> To: Prof Brian Ripley <ripley at stats.ox.ac.uk>
> cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] qr and Moore-Penrose
> > What is a correct result, by the way?  There are infinitely many solutions
> > for the regression of y on X, and the Moore-Penrose one is just one choice
> > (that assumes that the coefficients are somehow comparable).
> hm, 1.5, -0.5, 0.5, 1.5 should be a unique solution to Xb = y (with
> minimal 2-norm). 

And my point was `what has `minimal 2-norm' got to do with this'?
Regression coefficients are not necessarily in the same units: they are
not in a Euclidean space.  There are lots of other solutions with
claims to be reasonable, including those which use just `rank' of the
columns. qr gives one of the latter.

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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