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Re: Fitting: How does gnuplot calculate the covariance matrix?

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On 11.04.2011 03:14, Charles Allen wrote:

> Perhaps there is confusion about "standard error" (error on the mean)
> versus standard deviation.  The factor of 1/sqrt(21) (or however many
> data points there were) seems about right.  Gnuplot is reporting the
> error on the mean, the other program may be reporting the standard
> deviation.

Hmm, I have made some tests. If a,b are strongly correlated (happens
e.g. when the x values are far off the x0 in a formula like
f(x)=a+b*(x-x0), then the error contour of (a,b) is a strongly elongated
"banana" (an ellipse in approximation). In the given case, x0=0. Then,
if you vary a with fixed b=b_best and also vary b with fixed a=a_best,
the resulting errors are about the same as in gnuplot. If, however,
x=xmean (here =2), so that the a-b-correlation vanishes, these errors
increase to the full errors you get from the full extent of the error
ellipse. These are much larger then the errors from gnuplot.

But, tell me, if I have non-correlated a,b, thus an error circle, what
else then the upper and lower rim in both a and b direction of the
1-sigma-circle should I take as the standard deviation of a and b?

-- 
Gruß,
      Ingo

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Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-08 13:05 +0200
  Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-08 17:18 +0200
    Re: Fitting: How does gnuplot calculate the covariance matrix? Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-04-10 19:31 +0200
      Re: Fitting: How does gnuplot calculate the covariance matrix? Charles Allen <ca137tmp@earthlink.net> - 2011-04-10 20:14 -0500
        Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-14 15:41 +0200
      Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-11 21:42 +0200
        Re: Fitting: How does gnuplot calculate the covariance matrix? Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-04-11 23:27 +0200
          Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-12 11:28 +0200
            Re: Fitting: How does gnuplot calculate the covariance matrix? Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-04-16 00:03 +0200
              Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-16 18:06 +0200
      Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-14 15:07 +0200
      Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-15 13:47 +0200
  Re: Fitting: How does gnuplot calculate the covariance matrix? Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-04-10 19:04 +0200
    Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-11 22:13 +0200

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