In regression diagnostics, which diagnostic measure is associated with distance from the mean in multivariate space?

In regression diagnostics, which diagnostic measure is associated with distance from the mean in multivariate space?

• A. Cook's distance
• B. Leverage
• C. Mahalanobis distance
• D. Standardized residuals

Answer: (C)

Measuring distance from the center of the data in multivariate space is captured by Mahalanobis distance. It asks how far an observation’s predictor values are from the mean vector, but it adjusts for the spread and the correlations among predictors by using the inverse covariance matrix. This means differences along directions with high variance aren’t treated as equally important as differences along tightly clustered directions, and correlations between variables aren’t double-counted. In regression diagnostics, a large Mahalanobis distance signals a multivariate outlier in the predictor space that could unduly influence the regression results. Leverage looks at how far an observation’s X values are from the center of the X-space and indicates potential influence due to position in X, but it’s not a full multivariate distance from the mean. Cook’s distance combines leverage and residual size to assess overall influence on the fitted model. Standardized residuals measure how far a residual is from zero in standard deviation units, a univariate measure focused on the response variable rather than a multivariate distance.

Measuring distance from the center of the data in multivariate space is captured by Mahalanobis distance. It asks how far an observation’s predictor values are from the mean vector, but it adjusts for the spread and the correlations among predictors by using the inverse covariance matrix. This means differences along directions with high variance aren’t treated as equally important as differences along tightly clustered directions, and correlations between variables aren’t double-counted. In regression diagnostics, a large Mahalanobis distance signals a multivariate outlier in the predictor space that could unduly influence the regression results.

Leverage looks at how far an observation’s X values are from the center of the X-space and indicates potential influence due to position in X, but it’s not a full multivariate distance from the mean. Cook’s distance combines leverage and residual size to assess overall influence on the fitted model. Standardized residuals measure how far a residual is from zero in standard deviation units, a univariate measure focused on the response variable rather than a multivariate distance.