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.
"Elliptical Insights: Understanding Statistical Methods through Elliptical Geometry." Statist. Sci. 28 (1) 1 - 39, February 2013. https://doi.org/10.1214/12-STS402