Direct solution of polynomial regression of order up to 3

Abstract

This article presents results related to the direct solution of the polynomial regression parameters based on the analytical solving of regression equations. The analytical solution is based on the normalization of the values of independent quantity with equidistance steps. The proposed solution does not need to directly solve a system of polynomial regression equations. The direct expressions to calculate estimators of regression coefficients, their standard deviations, and also standard and expanded deviation of polynomial functions are given. For a given number of measurement points, the parameters of these expressions have the same values independently of the range of input quantity. The proposed solution is illustrated by a numerical example used from a literature source.