New Criteria for Polynomial Regression

The order of a polynomial for approximating a given data is important in a polynomial regression analysis. By normalizing the data and employing the order of magnitudes from the perturbation theory, new theorems are posed and proven. The theorems outline the basic features of the regression coefficients for the normalized data. Using the theorems and the described algorithm, the optimal degree of a polynomial can be determined. This task is a multiple criteria decision task and numerical examples are given to outline the basics of the algorithm.