The origins of fixed X regression

Abstract

In 1922 R. A. Fisher introduced the fixed X regression model, synthesising the regression theory of Pearson and Yule with the least squares theory of Gauss. The innovation was based on Fisher's realisation 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 early twentieth century statistical theor