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Abstract Individual value of residuals from a least squares regression equation can be analyzed as a set of originally observed quantities. If the analysis of residuals is in the form of another regression analysis, the total analysis of the data can be described as a two-stage regression. Such a two-stage approach is not equivalent to the usual, one-stage analysis, and therefore the resulting estimates and tests are biased. It is the purpose of this paper to obtain expressions for these biases.
Freund et al. (Wed,) studied this question.