Computing orthogonal polynomials

A simple transformation for achieving orthogonal polynomials of any order is described in this article. This transformation, called the residual procedure, is easy to understand, easy to implement in existing programs, and applicable for polynomial regression models whose data are unequally spaced. This same procedure is used in obtaining coefficients for orthogonal contrasts in the analysis of variance. The simplicity of this procedure also makes it easily adaptable to spread-sheet and data base applications.