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Alex Rivera
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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 , which is for finding a polynomial of degree n given n+1 data points, but here there are a large number of values and we want to find a low-degree polynomial (find best linear fit, best quadratic, best cubic, etc.). It might be related to least squares ... More generally, I would like to know the answer when we have a multivariate function -- points like (x,y,f(x,y)) , say -- and want to find the best polynomial ( p(x,y) ) of a given degree in the variables. (Specifically a polynomial, not splines or Fourier series.) Both theory and code/libraries (preferably in Python, but any language is okay) would be useful.
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