Fisher and Regression

2005/11/01 by John Aldrich · 2 citations
Computer Science · Mathematics · #Statistical and Computational Modeling #Statistical and numerical algorithms

paper · pdf · doi:10.1214/088342305000000331

openalex publication_date 2005/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• X. Contributions to the mathematical theory of evolution.—II. Skew variation in homogeneous material
• Applications of the Theory of Error to the Interpretation of Trends
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• Theory of Statistical Estimation
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• NOTES ON THE HISTORY OF CORRELATION
• On the mathematical foundations of theoretical statistics
• Studies in crop variation. I. An examination of the yield of dressed grain from Broadbalk
• The Goodness of Fit of Regression Formulae, and the Distribution of Regression Coefficients
• THE PROBABLE ERROR OF A MEAN
• On the Foundations of Statistical Inference
• Properties of sufficiency and statistical tests

Cited by

• Fisher Lecture: Dimension Reduction in Regression
• Regression analysis [wikipedia]