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

Bare in mind that a polynomial of higher degree ALWAYS fits the data better. Polynomials of higher degree typically leads to highly improbable functions (see Occam's Razor), though (overfitting). You want to find a balance between simplicity (degree of polynomial) and fit (e.g. least square error). Quantitatively, there are tests for this, the Akaike Information Criterion or the Bayesian Information Criterion. These tests give a score which model is to be prefered.