[R] searching for an analytical function

[Casiano Rodriguez Leon]

Hello all,

This is the problem I am dealing with:

I have an R data frame with the sample of observations of the control
variables "x1", "x2" , ... and the response variable "y".
I also have a set of "base" functions = "x1, "x2", ..., "log(x1)",
"log(x2)", ...

What I need is to have the ANALYTICAL function, i.e. a polynom of the
given base functions, (s.t like x1^3*log(x2) ) that represents my data,
i.e. that minimizes the average errors of the predictions.

I guess that using non-parametric regression I can obtain a non analytical
answer. Do you know of any solutions for that problem or similars?  If so,
where can I find them?

Many, many thanks,

Casiano