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WE SHALL BE principally concerned with simple linear regression where variates are subject to error, although the same problems and methods apply to problems involving three, four, or many variates. By saying that we deal with both variates subject to error we mean that two measured quantities, which we may as well call x and y, are thought of as made up of two independent (or at least orthogonal) parts as follows
John W. Tukey (Thu,) studied this question.