Re: [Gnuplot-info] sum of squares of residuals

[Patrick D. <pd...@gm...>]

===========================================================================
 Patrick DUPRÉ                                 | | email: pd...@gm...
 Laboratoire de Physico-Chimie de l'Atmosphère | |
 Université du Littoral-Côte d'Opale           | |
 Tel.  (33)-(0)3 28 23 76 12                   | | Fax: 03 28 65 82 44
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> Sent: Thursday, August 02, 2018 at 11:25 PM
> From: "Hans-Bernhard Bröker" <HBB...@t-...>
> To: gnuplot <gnu...@li...>
> Subject: Re: [Gnuplot-info] sum of squares of residuals
>
> Am 02.08.2018 um 22:17 schrieb Patrick Dupre:
> 
> > When I do not weight my data, I get the following
> > final sum of squares of residuals : 1.85937
> > 
> > but, when I weight my data, I get:
> > final sum of squares of residuals : 54.6063
> > 
> > The big difference between the 2 values of the Chi2 indicates me that the
> > weighting of the data is not entirely correct.
> 
> That differences can indicate so many different things, all by itself, 
> that it effectively indicates nothing at all.
> 
> > When the data are weighted, if \Sum w(i) = 1, I must get a
> > similar Chi2.
> 
> Even that's not true, because the solution can still be a different one, 
> yielding a wildly different WSSR.
> 
> > How can I get the "weighted final sum of squares of residuals"?
> 
> You're already getting it.
Yes and no.

If \Sum w(i) = 1, I would get the same WSSR if I multiply all the weights (errors) by a constant.
This is not the case with gnuplot.
Actually, by definition the weights should such as \Sum w(i) = 1 (unitless)
This is not the case with gnuplot, strictly speaking the naming "weight"
is inappropriate.
The WSSR provided by gnuplot is unitless (\Sum (y(x) - y_i)^2 / (dy_i)^2) when weighting,
while it has the unit of y^2 when not weighting (uniform weighting) is used, which is not coherent.
Actually both WSSR (WSSR, and normalized WSSR) could be provided.

> 
> 
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