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

If you want to fit the (xi, f(xi)) to an polynomial of degree n then you would set up a linear least squares problem with the data (1, xi, xi, xi^2, ..., xi^n, f(xi) ). This will return a set of coefficients (c0, c1, ..., cn) so that the best fitting polynomial is *y = c0 + c1 * x + c2 * x^2 + ... + cn * x^n.*

You can generalize this two more than one dependent variable by including powers of y and combinations of x and y in the problem.