Influential Data Points

Influential data points are observations that exert an unusually large effect on the results of regression analysis. Influential data might be classified as outliers, as leverage points, or as both. An outlier is an anomalous response value, whereas a leverage point has atypical values of one or more of the predictors. It is important to note that not all outliers are influential.

Identification and appropriate treatment of influential observations are crucial in obtaining a valid descriptive or predictive linear model. A single, highly influential data point might dominate the outcome of an analysis with hundreds of observations: It might spell the difference between rejection and failure to reject a null hypothesis or might drastically change estimates of regression coefficients. Assessing influence can reveal data that are ...