[Bug-gsl] Covariance estimate in weighted regression

Brian Gough bjg@network-theory.co.uk
Fri Feb 17 16:20:00 GMT 2006

Alex Tartakovsky writes:
 > >From GSL manual (pp. 361-362), standard texts, and just common
 > >sense, one expects that the output produced by a weighted
 > >regression with all the weights set to 1 should be the same as
 > >from unweighted regression.  This is not the case for the
 > >covariance estimates produced by "fit" and "multifit"
 > >least-squares GSL functions.  The reason is that the cov estimates
 > >in the straight versions of the functions include s2 (an estimate
 > >of the error variance):

Giulio Bottazzi writes:
 > Probably it would help to explicitly mention the formula used to
 > compute variance-covariance matrix in ALL the routines, so that the
 > average dumb user (like me), by comparing the different formulas,
 > can immediatly understand were differences can possibly arise. What
 > do you think?

Thanks for the comments, I have added some longer explanations in the
manual about how the covariance matrices are computed and their
definitions for the different cases.  The new chapters are available
at http://www.network-theory.co.uk/download/gsl/newchaps.ps.gz

Brian Gough

Network Theory Ltd,
Publishing Free Software Manuals --- http://www.network-theory.co.uk/

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