correlation matrix always the same!?

  • Sammy Lightfood

    Sammy Lightfood - 2007-03-21

    If I fit the data

    1    2.5
    3    2.1
    6    8
    10    17.01

    f(x) = a*x+b

    I get

    After 1 iterations the fit converged.
    final sum of squares of residuals : 9.65289
    rel. change during last iteration : -1.84023e-016

    degrees of freedom    (FIT_NDF)                        : 2
    rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 2.19692
    variance of residuals (reduced chisquare) = WSSR/ndf   : 4.82645

    Final set of parameters            Asymptotic Standard Error
    =======================            ==========================

    a               = 1.71413          +/- 0.3239       (18.9%)
    b               = -1.16815         +/- 1.957        (167.5%)

    correlation matrix of the fit parameters:

                   a      b
    a               1.000
    b              -0.828  1.000

    The fit seems to work, but if I change the input data, the correlation matrix does not change!? I always get -0.828.
    Or do I misunderstand something and this is correct?

    Thank you for answers,

    • Hans-Bernhard Broeker

      > but if I change the input data, the correlation matrix does not change!?

      If you don't say *how* you changed that input, it's quite impossible to tell what the correlation matrix should be.

    • Sammy Lightfood

      Sammy Lightfood - 2007-04-13

      I changed for example to

      from input data
      1  2.5
      1  2.0

      but it seems any input data leads to the same correlation matrix. Or is this matrix only related to the fit - function? I expected something like correlation coefficients. !?

      (gnuplot version 4.2 patchlevel 0)

      Kind regards,
      Sammy :)

      • Hans-Bernhard Broeker

        You're getting correlation coefficients.  A change as small as that just doesn't have a lot of influence on C_ab.  You have to move it more to see an effect on the correlation.


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