Fitting polynomials to data

Question

Is there a way, given a set of values (x,f(x)), to find the polynomial of a given degree that best fits the data?

I know polynomial interpolation, whic

Answer 1

Yes, the way this is typically done is by using least squares. There are other ways of specifying how well a polynomial fits, but the theory is simplest for least squares. The general theory is called linear regression.

Your best bet is probably to start with Numerical Recipes.

R is free and will do everything you want and more, but it has a big learning curve.

If you have access to Mathematica, you can use the Fit function to do a least squares fit. I imagine Matlab and its open source counterpart Octave have a similar function.