Using Leverage and Influence to Introduce Regression Diagnostics

摘要

At a time when introductory texts increasingly mention robustness and the sensitivity of the sample mean to outliers, we feel that students need additional insight into the properties of least-squares regression. In fact, anyone who may use the results of serious regression analysis or use regression to analyze data should have at least a basic understanding of leverage and influence. It would not be surprising to discover that a number of earlier regression analyses, some having serious implications for public policy, had unknowingly reached conclusions that rested on the influence of a single observation, perhaps of dubious validity. Although the research literature contains a number of sophisticated techniques, it is possible to equip even beginning students with a few straightforward regression diagnostics that reveal much about the behavior of any set of regression data. We have offered one sequence of topics for inclusion in courses, starting as soon as the student encounters simple regression. Alternative sequences could draw on several other popular techniques. Keywords: Reprints. (kr)