multivariant least square fitting

Can I do the following fitting using any built-in functions? or I have to write my own script?

I have x, y, P as independent variables, and fit a curve B to a function of :

B = b0 +b1*x +b2* y +b3 P + b4 *x^2 + b5*y^2 + b6 * P^2 + b7 x*y + b8*x*P + b9 * y*P;

There are 12 data points to get 10 coefficients, b0-b9.

I'd appreciate any comments. Thanks,

Answer 1

[Matt J]

Looks like it's in the scope of polyfitn ( Download ). I can't vouch for the quality of the result (with any solver), though, seeing as you have such a small number of data points.

[John D'Errico]

While polyfitn will work, I shiver at the thought, and that is my own code.

10 data points for 12 coefficients? The result might be virtually random numbers. More data generally means better estimates of the coefficients. You should look at the estimates of ParameterStd as provided. If those numbers are too large for your comfort, then you should ask if it is possible to get more data.