Polynomial Best Fit:

Generally, an m^th order polynomial also can be used for fitting the data (m = i  refers to linear regression). Consider an m^th order regression polynomial

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

After that, the sum of squares of differences will be

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

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

It can be noted that for most practical problems, the value of m is, usually, from 1 to 4.