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Re: Calculate R-squared value from gnuplot 'fit' output?

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From	wolfgang <cmat.wolfgang@gmail.com>
Newsgroups	comp.graphics.apps.gnuplot
Subject	Re: Calculate R-squared value from gnuplot 'fit' output?
Date	Thu, 29 Dec 2011 00:17:06 -0800 (PST)
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On Dec 28, 3:14 pm, Mike <mesi...@gmail.com> wrote:
> OK, my statistics is perhaps not what it should be. I have a script
> make a linear fit of some x-y pairs:
>
> #
> # Correlations
> #
> set xdata
> set format x
> set term png size 400, 400
> f(x) = m*x + b
> set output "./corr-00.png"
> fit f(x) "2011-10.dat" using 2:3 via m,b
> plot "2011-10.dat" using 2:3 t "C1 vs C2" with dots, f(x) title "Model
> Fit"
>
> And I get the following output, just showing the end here:
>
>  Iteration 0
>  WSSR        : 9404.93           delta(WSSR)/WSSR   : 0
>  delta(WSSR) : 0                 limit for stopping : 1e-05
>  lambda   : 7.53716
>
> After 3 iterations the fit converged.
> final sum of squares of residuals : 1980.57
> rel. change during last iteration : -5.27226e-11
>
> degrees of freedom    (FIT_NDF)                        : 4462
> rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.66624
> variance of residuals (reduced-chisquare) = WSSR/ndf   : 0.443875
>
> Final set of parameters            Asymptotic Standard Error
> =======================            ==========================
>
> m               = 0.889071         +/- 0.002949     (0.3317%)
> b               = 0.881951         +/- 0.03129      (3.548%)
>
> correlation matrix of the fit parameters:
>
>                m      b
> m               1.000
> b              -0.948  1.000
>
> Shouldn't I be able to calculate the R-squared value from this data? I
> read in wikipedia that
>
> R^2 1 - (SS_err / SS_tot)
>
> and that WSSR is SS_err, as far as I can make out. Can anyone help me
> with SS_tot or another way to do it?
>
> Thanks!

Why does that take 3 iterations? That is just a linear LS problem?
Linear LS regression has an analytical solution, i.e. with normal
equations.
Solution should be either intelligent starting values or one iteration
from
dummy starting point?
Wolfgang

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Thread

Calculate R-squared value from gnuplot 'fit' output? Mike <mesimms@gmail.com> - 2011-12-28 12:14 -0800
  Re: Calculate R-squared value from gnuplot 'fit' output? Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-12-28 22:11 +0100
  Re: Calculate R-squared value from gnuplot 'fit' output? wolfgang <cmat.wolfgang@gmail.com> - 2011-12-29 00:17 -0800
    Re: Calculate R-squared value from gnuplot 'fit' output? Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-12-29 12:39 +0100
    Re: Calculate R-squared value from gnuplot 'fit' output? ab <ab.3942@googlemail.com> - 2012-01-02 00:37 -0800

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