Elliptical Insights: Understanding Statistical Methods Through Elliptical Geometry

• Michael Friendly, Georges Monette, John Fox.
• Elliptical Insights: Understanding Statistical Methods Through Elliptical Geometry.
• Statistical Science, vol. 28, no. 1, pp. 1–39, 2013.

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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.

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

@Article{Friendly-etalellipses2012,
  author = {Michael Friendly and Georges Monette and John Fox},
  title = {Elliptical Insights: Understanding Statistical Methods Through Elliptical
                 Geometry},
  journal = {Statistical Science},
  year = {2013},
  volume = {28},
  number = {1},
  pages = {1–39},
  url = {http://datavis.ca/papers/ellipses-STS402.pdf},
  doi = {10.1214/12-STS402},
  supp = {http://datavis.ca/papers/ellipses/},
}