The Trouble with R2

Abstract

Abstract In the theory of cost-estimating-relationship (CER) development using the method of ordinary least-squares (OLS) linear regression, the dependent variable is y (e.g., cost) and the independent variable is x (e.g., weight, power, thrust, etc.). The square of the correlation coefficient between x and y is called the “coefficient of (linear) determination.” Usually denoted by the symbol R2 , the coefficient represents the proportion of variation in y that can be explained by passing variations in x up through the linear relationship. As such, it is often interpreted as providing a measure of the quality of the CER as a predictor of cost. Unfortunately, due to a quirk of mathematical theory, the interpretation of R2 as the “proportion of variation” is valid only in the case of OLS linear regression.