Statistical - Cubic Regression (Cubic Spline Fit) ?

[jonmoore]

As an aside, ref my use of the word spline.

I work a lot with 3d DCC packages (digital content creation packages such as Maya and Houdini) and CAD packages too (such as Rhino, which incidentally, started out life as a specialist tool for designing boat hulls), and splines are central to their workflows.

The beauty of working with cubic spines in particular is that they lead to wonderfully smooth curves. Bezier curves are another DCC curve type, but these are more typical of 2d creative packages such as Adobe's illustrator. They provide far more control but the nature of how they're defined make them less useful for statistical purposes.

The trick with splines in general is to use as few control points as possible. Using too many control points, especially if some control points are too closely spaced, can lead to unpredictable kinks. These kinks have a greater likelihood with cubic splines as they're not designed for rapid changes of direction.

Working with splines as design tools gives you a great intuition for how they function when applied to statistical data.