Weighted polyfit?

[Andreas Stahel]

On 26 Mar 2010, at 10:36, Matthias Brennwald wrote:


> > Dear all
> >
> > I am pretty sure  this is something that has been discussed
> > previously, but I was not able to find anything helpful. I'd like to
> > fit a polynomial to my experimental data. The data have errors, and
> > I'd like to use these errors as weights for the data values in the
> > fit. Something like this:
> >
> >    x     = [0:10];                    % x values of experimental data
> >    y     = x.^2;                              % y values of experimental data
> >    y_err = randn(size(x));    % errors of y
> >    [p,s] = polyfit (x,y,2);           % <-- replace this by something that
> > takes into account the errors (y_err), e.g. using the weights 1./
> > y_err for each value in y
> >
> > Any hints or ideas?
> >
> > Matthias
>   

The function LinearRegression.m in the sourceforge package optim allows 
to specify weights and can be used to do polynomial regression.
A Vandermonde matrix (command vander())  might be useful to call 
LinearRegression.

I hope this helps

Andreas

--
Andreas Stahel       E-Mail: address@hidden
Mathematics, BFH-TI  Phone: ++41 +32 32 16 258
Quellgasse 21        Fax:   ++41 +32 321 500
CH-2501 Biel         WWW:   https://prof.ti.bfh.ch/sha1/
Switzerland