Appendixes | Graphics | Mahalanobis Distances

Mahalanobis Distances
A Mahalanobis Distances plot is commonly used in evaluating classification and cluster analysis techniques. It illustrates the distance of specific observations from the mean center of the other observations. Mahalanobis distance and leverage are often used to detect outliers, especially in the development of linear regression models. A point that has a greater Mahalanobis distance from the rest of the sample population of points is said to have higher leverage since it has a greater influence on the slope or coefficients of the regression equation. Mahalanobis distance is also used to determine multivariate outliers. Regression techniques can be used to determine whether a specific case within a sample population is an outlier via the combination of two or more variable scores. A point can be a multivariate outlier even if it is not a univariate outlier on any variable.
In the Mahalanobis Distances plot shown below, the distance of each row number is plotted. Those outlier points residing above the dotted line correspond to those rows that warrant the most attention due to their significant distance from the mean center of all other observations.