Evaluation of the Statistical Significance of a Regression and Selection of the Best Regression Using the Coefficient of Determination R2

Statistical methods currently used to analyze experimental data and to select the best-fit regression model are analyzed based on the Fisher F-test. Unfortunately, the judgment of the significance of a regression is often performed by use of the coefficient of determination, available on most calculators. It will be shown that this coefficient of determination can be misused. Two simple equations which take advantage of this coefficient of determination are presented which allow one to analyze the data in an objective manner. The first equation allows one to evaluate the level of confidence of a regression model, and the second equation allows one to evaluate the contribution of a subset of the coefficient to the regression model.