Fisher and regression

Abstract

In 1922 R. A. Fisher introduced the modern regression model, synthesizing the regression theory of Pearson and Yule and the least squares theory of Gauss. The innovation was based on Fisher's realization that the distribution associated with the regression coefficient was unaffected by the distribution of X. Subsequently Fisher interpreted the fixed X assumption in terms of his notion of ancillarity. This paper considers these developments against the background of the development of statistical theory in the early twentieth century. © Institute of Mathematical Statistics, 2005.