  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.
