Segmented Regression Based on B-Splines with Solved Examples

Abstract

The subject of the paper is segmented linear, quadratic, and cubic regression based on B-spline basis functions. In this article we expose the formulas for the computation of B-splines of order one, two, and three that is needed to construct linear, quadratic, and cubic regression. We list some interesting properties of these functions. For a clearer understanding we give the solutions of a couple of elementary exercises regarding these functions.

Keywords

• Normalized B-spline basis functions
• explicit expression
• system of normal equations
• Weibull plot
• Bairstow’s iteration method