Least-squares fitting of data by polynomials

In the last two columns, we looked at one approach to approximation, interpolating a set of points by piecewise-cubic polynomials forming a cubic spline. We now look at another approach - one that involves fitting a curve to a set of data without restricting that curve to coincide with the data points. Our focus is on least-squares approximation, and, in particular, least-square fitting of polynomials to data.