Polynomial regression analysis based on constrained data

Abstract

An arbitrary order polynomial regression analysis is presented. Under the assumption of satisfaction of some reference points exactly by the polynomial, the general theory is given for the analysis. The polynomials are expressed in a suitable form so that the lower order coefficients can be calculated easily from the restrictions. The remaining coefficients are calculated from the error minimization. The theory is then applied to linear, quadratic and cubic polynomial regression sample problems having constrained data. Compared to the unrestrained regression analysis, the method reduces the computational cost of calculating coefficients.