Behavior of the Residuals of a Regression Least-Squares Model Which Is Linear in Its Parameters When the Number of Parameters Is Increased. Part 1. State of the Question. Correlation Coefficient between the Residuals

A brief critical review is given of methods and recommendations utilized when analyzing the residuals of a regression least-squares model which is linear in its parameters. The absence of the necessary rigorous solutions and the explicit contradictions present in the recommendations considerably reduce the introduction and utilization efficiency of the information contained in the residuals. A formula is proposed for calculating the correlation coefficient between the residuals together with a compact program created in the Maple V R5 mathematical software applied program package, and examples of calculations are presented.