Reference: Least Squares entry of the Wikipedia.

Our function is

where {fj(x)} are a basis of linear independent functions: {1,x,x2,x3,...,xm} and {cj } are the coefficients.

The objective is to minimize the sum:

.

To this end, we have to differentiate with respect to ci , and equate to zero:

Obtaining the follow system:

where (a,b)d are defined as:

.