A New Perturbation Approach to Optimal Polynomial Regression

[摘要] A new approach to polynomial regression is presented using the concepts of orders of magnitudes of perturbations. The data set is normalized with the maximum values of the data first. The polynomial regression of arbitrary order is then applied to the normalized data. Theorems for special properties of the regression coefficients as well as some criteria for determining the optimum degrees of the regression polynomials are posed and proven. The new approach is numerically tested, and the criteria for determining the best degree of the polynomial for regression are discussed.

[学科分类] 计算数学

[关键词] polynomial regression;perturbation analysis;degree of a polynomial