Open Access
February 2013 Elliptical Insights: Understanding Statistical Methods through Elliptical Geometry
Michael Friendly, Georges Monette, John Fox
Statist. Sci. 28(1): 1-39 (February 2013). DOI: 10.1214/12-STS402


Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the virtues of the ellipse and her higher-dimensional cousins for both these purposes in a variety of contexts, including linear models, multivariate linear models and mixed-effect models. We emphasize the strong relationships among statistical methods, matrix-algebraic solutions and geometry that can often be easily understood in terms of ellipses.


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Michael Friendly. Georges Monette. John Fox. "Elliptical Insights: Understanding Statistical Methods through Elliptical Geometry." Statist. Sci. 28 (1) 1 - 39, February 2013.


Published: February 2013
First available in Project Euclid: 29 January 2013

zbMATH: 1332.62015
MathSciNet: MR3075337
Digital Object Identifier: 10.1214/12-STS402

Keywords: Added-variable plots , Bayesian estimation , concentration ellipse , data ellipse , discriminant analysis , Francis Galton , hypothesis-error plots , kissing ellipsoids , measurement error , mixed-effect models , multivariate meta-analysis , regression paradoxes , Ridge regression , statistical geometry

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.28 • No. 1 • February 2013
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