Mahalanobis distances are used to

• A. Assess multicollinearity among predictors.
• B. Evaluate the overall goodness-of-fit of a model.
• C. Measure the influence of a case by distance from the means of predictors.
• D. Compute the standard error of regression coefficients.

Answer: (C)

Mahalanobis distance measures how far an observation is from the center of the predictor distribution, accounting for the relationships among predictors. It uses the inverse of the covariance matrix, so the distance reflects both scale and correlation among variables. This makes it especially useful for spotting multivariate outliers or influential cases—points that lie in an unusual combination of predictor values and could disproportionately affect the analysis.

In practice, a case with a large Mahalanobis distance relative to the number of predictors (often compared to a chi-square cutoff) signals a potential outlier in the multivariate space. This is not about assessing collinearity among predictors (that involves VIFs or tolerance), nor about overall model fit (which uses R-squared, F tests, etc.), nor about the standard errors of regression coefficients (which come from the sampling distribution and variance-covariance estimates).