A review of regression diagnostics for behavioral research

Abstract

Influential data points can affect the results of a regression analysis; for example, the usual summary statistics and tests of significance may be misleading. The importance of regression diagnostics in detecting influential points is discussed, and five statistics are recommended for the applied researcher. The suggested diagnostics were used on a small dataset to detect an influential data point, and the effects were analyzed. Colinearity-based diagnostics also are discussed and illustrated on the same dataset. The nonrobustness of the least squares estimates in the presence of influential points is emphasized. Diagnostics for multiple influential points, multivariate regression, multicolinearity, nonlinear regression, and other multivariate procedures also are discussed. Index terms: Andrew-Pregibon measure, colinearity, Cook’s distance, covariance ratio, influential observations, measurement error, partial residual plot, regression diagnostics.