## correlation matrix always the same!? document.SUBSCRIPTION_OPTIONS = { "thing": "thread", "subscribed": false, "url": "subscribe", "icon": { "css": "fa fa-envelope-o" } };

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2007-03-21
2013-02-10
• Sammy Lightfood - 2007-03-21

If I fit the data

1    2.5
3    2.1
6    8
10    17.01

using
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?

Sammylight

• > 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 - 2007-04-13

I changed for example to

from input data
1  2.5
to
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 :)

• 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.