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Abstract

Initially applied in astronomy and geodesy, the linear regression model aimed to find the best estimates for parameters with predefined meanings. E.g., orbital elements, geodetic constants. As its use expanded to other disciplines, often to summarize data without an underlying theoretical model, the need for a general interpretation of regression betas arose. Early attempts by Galton and Karl Pearson met with mixed success. G. U. Yule was the first to develop a general statistical interpretation, the culmination of efforts begun in 1896. Yule interpretation is based on the partial regression theorem, which he proved in 1907.