I have a dataset (x,y) where x is a n-dimensional vector and y is an m-dimensional vector. (m=3, n>2) My goal is to find the best polynomial in x fitting the (x,y) dataset.
The dimension of x is pretty big (right now it is 25), and I don't want to enter manually all the possibilities (ie x1*x3*x5, x1*x4*x6, ...). I can use Matlab, Mathematica and R. How can I do this?
Also, I would be interested in hearing your suggestions about the following problem: how can I choose from the result the most relevant coefficients? (maybe x1*x2 is more relevant than x2*x3)