C31. Cubic splines and knots
What is a cubic spline, and what is a knot?
Worked answer (click to show)
Definitions/notation. A cubic spline is a piecewise polynomial of degree at most three, joined at specified locations called knots, with the function and its first two derivatives continuous at ordinary interior knots. The knots divide the covariate domain into pieces without introducing jumps in the fitted curve or its first two derivatives.