[SciPy-user] Fit statistics for sum of squared relative error

zunzun@zunzu... zunzun@zunzu...
Tue Feb 13 02:09:16 CST 2007

I've been doing fits to lowest sum of squared relative
error for a while now.  These are useful when a data
set exhibits increasing heteroscedasticity as the
values of the independent variable increase, i.e.,
data scatter proportional to distance along the x axis.

You can test this at http://zunzun.com by selecting a 
fitting target of "Lowest sum of squared relative errors"
when fitting, and this is also in the Python Equations
package at http://sf.net/ptojects/pythonequations.

Having investigated fit statistics for some time now,
it seems *everything* is geared toward absolute error,
with not the slightest drop that I can find regarding
relative error.  These statistics are needed when
performing SSQREL rather than SSQABS fitting.

Can I safely use existing routines for covariance
matrices and parameter standard errors simply by
substituting dy(relative)/dx and relative error
whenever dy(absolute)/dx and absolute error are
used?  I apologize, but this is over my head and
I would like to report the fit statistics properly.

     James Phillips

P.S. I don't yet have much in the way of fit statistics
on the web site, this is what I'm currently working on.
I found much of what I need in the BSD-style licensed MPFIT.py
at http://cars9.uchicago.edu/software/python/mpfit.html
written by Mark Rivers.

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