Characterizations of an Empirical Influence Function for Detecting Influential Cases in Regression

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Abstract
Traditionally, most of the effort in fitting full rank linear regression models has centered on the study of the presence, strength and form of relationships between the measured variables. As is now well known, least squares regression computations can be strongly influenced by a few cases, and a fitted model may more accurately reflect unusual features of those cases than the overall relationships between the variables. It is of interest, therefore, for an analyst to be able to find influential cases and, based on them, make decisions concerning their usefulness in a problem at hand. Based on an empirical influence function, we discuss methodologies for assessing the influence of individual or groups of cases on a regression problem. We conclude with an example using data from the Florida Area Cumulus Experiments (FACE) on cloud seeding.

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