Simple multidimensional curve fitting

Question

I have a bunch of data, generally in the form a, b, c, ..., y

where y = f(a, b, c...)

Most of them are three and four variables, and have 10k - 10M records.

Answer 1

Do you know to what power you want to limit your polynomial?

If there is no limit, then you can always get an exact match for N points by matching it to a polynomial that has N coefficients. To do this, you plug N different points into your equation, yielding N equations and N unknowns (the coefficients), which you can then use either simple high school algebra or a matrix to solve for the unknowns.