In many packages, the regression through the origin module employs a standard least squares approach to estimate the values of the 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.
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Hugh Gordon (1981) studied this question.