Errors in Computer Packages. Least Squares Regression Through the Origin

In many regression packages, the "regression through the origin" module employs a standard least squares approach to estimate the values of the regression coefficient(s). In so doing, it is assumed that E(E) = 0, where E represents the residual error. In practice, this leads to positively biased estimates of R2, the coefficient of determination, and of the F ratio from the resultant analysis of variance. These biased estimates are a direct consequence of an erroneous definition of the "variance" to be analysed. Within the paper the author indicates how the presence of these errors in definition can be identified and corrected.