Thread Subject: How to estimate the coefficients for an equation with two variables?

I have data values xi, yi, zi.

They follow the function:

z = f(x,y) = A*x*y^2 + B*x^2*y^2

Now I want to estimate the coefficients A and B for the best fit.

Have you any idea to do this with standard matlab? Or do I need a function of a special toolbox for this ?

"Heinz " <heinz.eppler@bizerba.com> wrote in message <he82qi$c18$1@fred.mathworks.com>...
> I have data values xi, yi, zi.
>
> They follow the function:
>
> z = f(x,y) = A*x*y^2 + B*x^2*y^2
>
> Now I want to estimate the coefficients A and B for the best fit.
>
> Have you any idea to do this with standard matlab?

Writing down the relation zi = f(xi,yi), it provides the linear equations in A and B.
Put the equations together in matrix form and solve it (in a least squares sense) using backslash. It takes one lines

AB = [x(:).*y(:).^2 x(:).^2.*y.^2] \ z(:)

Bruno

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <he86d2$hor$1@fred.mathworks.com>...
> "Heinz " <heinz.eppler@bizerba.com> wrote in message <he82qi$c18$1@fred.mathworks.com>...
> > I have data values xi, yi, zi.
> >
> > They follow the function:
> >
> > z = f(x,y) = A*x*y^2 + B*x^2*y^2
> >
> > Now I want to estimate the coefficients A and B for the best fit.
> >
> > Have you any idea to do this with standard matlab?
>
> Writing down the relation zi = f(xi,yi), it provides the linear equations in A and B.
> Put the equations together in matrix form and solve it (in a least squares sense) using backslash. It takes one lines
>
> AB = [x(:).*y(:).^2 x(:).^2.*y.^2] \ z(:)
>
> Bruno
Thanks Bruno.

Your solution works really fine.

Best regards

Heinz