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From: Ingo Thies <ingo.thies@gmx.de>
Newsgroups: comp.graphics.apps.gnuplot
Subject: Re: Fitting: How does gnuplot calculate the covariance matrix?
Date: Fri, 15 Apr 2011 13:47:47 +0200
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On 10.04.2011 19:31, Hans-Bernhard Bröker wrote:

>> a = 9.482095E-01 -/+-1.947044E-01, 1.947043E-01
>> b = 4.270960E-01 -/+-8.327496E-02, 8.327495E-02
> 
> Those errors are _way_ too big.  Do yourself a favour and plot your data
> along with the model, using parameters modified by those errors:

I have now found the reason for the large errorbars. I simply had used
the wron degree of freedom for calculating the 68.3% probability ("1
sigma") contours in the (a,b) space. It should be 2 (2 params) for the
contours, and even only 1 for a single contouf (cf Numerical Recipes
chapter 15.6), but I used ndata-2, which is only valid for the
goodness-of-fit estimate. Now the errors are about the same as gnuplot's
given a good fit (i.e. \chi^2 \approx ndata-2).

Gnuplot seems to assume a good fit always, so the a-b errors do not vary
if all sigma(y_i) are scaled by the same factor. Maybe this is a
reasonable assumption since otherwise the whole fit is in question.

I hope I could repair a bit of the confusion I caused with this thread ;-)

-- 
Gruß,
      Ingo