Re: [Gnuplot-info] =?iso-8859-1?q?Fiting_and_R=B2?=

[Thomas P. <jun...@gm...>]

Hi,
even if this is NOT a math-forum ....
If you have questions about statistics, wolfram's mathworld is always a go=
od start:

http://mathworld.wolfram.com/CorrelationCoefficient.html

If that's too strange, well I would suggest grab some statistics books and=
 study through. 
Correlation matrix and R-square is certainly in the first quarter ...
If you use them you should understand there meaning.

Cheers
Pelusa

On 18 Sep 2006 at 19:54, SB wrote:

> Hello again,
> Sorry, I have to ask the same question again. 
> 
> After half a day on the web I learned a little about statistics, but I
> couldn't find out how to interpret the correlation matrix. Also I am
> still without ideas how to transform it to receive R=B2. 
> 
> Is there an easy explanation available for someone without prior
> statistical knoledge how to do this?
> 
> And one more question:
> My correlation Matrix looks like this:
> 
>                a      b
> a               1.000
> b              -0.684  1.000
> 
> I did several fits to different data, and almost all fits to a line
> (i.e. g(x) =3D a* x + b ; fit g(x) ... via a,b).
> For some reason the bottom left value (in this case -0.684) seems to
> depend only on the number of points that are fitted. 
> 
> Confused,
> 
> Stephan
> 
> end part of one fitting log (g(x) fitted to 6 data points):
> 
> 
> 
> Iteration 5
> WSSR        : 16.6406           delta(WSSR)/WSSR   : -5.61239e-12
> delta(WSSR) : -9.33937e-11      limit for stopping : 1e-05
> lambda    : 0.000319372
> 
> resultant parameter values
> 
> a               =3D 0.451348
> b               =3D 1.72651
> 
> After 5 iterations the fit converged.
> final sum of squares of residuals : 16.6406
> rel. change during last iteration : -5.61239e-12
> 
> degrees of freedom (ndf) : 4
> rms of residuals      (stdfit) =3D sqrt(WSSR/ndf)      : 2.03965
> variance of residuals (reduced chisquare) =3D WSSR/ndf : 4.16016
> 
> Final set of parameters            Asymptotic Standard Error
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D   =
         =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D
> 
> a               =3D 0.451348         +/- 0.02527      (5.599%)
> b               =3D 1.72651          +/- 1.141        (66.09%)
> 
> 
> correlation matrix of the fit parameters:
> 
>                a      b
> a               1.000
> b              -0.684  1.000
> 
> 
> ----------------------------------
> G N U P L O T
>         Version 4.0 patchlevel 0
>         last modified Thu Apr 15 14:44:22 CEST 2004
>         System: Linux 2.6.12-10-386
> 
>         Copyright (C) 1986 - 1993, 1998, 2004
>         Thomas Williams, Colin Kelley and many others
> 
> 
> 
> 
> 
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