Statistical - Cubic Regression (Cubic Spline Fit) ?

[Werner]

I have the impression cubic regression (what Thomas described, and very well indeed) and cubic spline regression are mixed up.
Cubic spline regression typically takes 4 or 5 (depending on the number of sample points) splines, and determines the best fit for those splines (with of course endpoints and first and second derivatives equal). That is somewhat more involved than cubic regression, fitting a 3rd degree polynomial to statistical data, which would be the same as using a single spline.
Werner