Polynomial Best Fit:

Generally an m^th order polynomial also might be utilized for fitting the data (m = i indicate to linear regression). Let an m^th order regression polynomial

              f ( x) = c₀  + c₁ x + c₂  x ²   + . . . + c_m  x^m .

After then, the sum of squares of differences shall be

The coefficients c₀, c₁, c₂, -------------c_m are to be find out through minimizing S. The following system of (m + 1) equations is then get for the unknown coefficients

The solution of these equations yields the wished polynomial for a best fit.

It might be noted down that for most practical difficulty, the value of m is, in general, from 1 to 4.