Mahalanobis distance

In statistics, Mahalanobis distance is a distance measure introduced by P. C. Mahalanobis in 1936. It is based on correlations between variables by which different patterns can be identified and analysed. It is a useful way of determining similarity of an unknown sample set to a known one. It differs from Euclidean distance in that it takes into account the correlations of the data set and is scale-invariant, i.e. not dependent on the scale of measurements.
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One can think of the independent variables (in a regression equation) as defining a multidimensional space in which each observation can be plotted. Also, one can plot a point representing the means for all independent variables. This "mean point" in the multidimensional space is also called the centroid. The Mahalanobis distance is the distance of a case from the centroid in the multidimensional space, defined by the correlated independent variables (if the independent variables are uncorrelated, it is the same as the simple Euclidean distance). Thus, this measure provides an indication of whether or not an observation is an outlier with respect to the independent variable values.
See also, standard residual value, deleted residual and Cook’s distance.