Efficient Computing of Regression Diagnostics

Abstract Multiple regression diagnostic methods have recently been developed to help data analysts identify failures of data to adhere to the assumptions that customarily accompany regression models. However, the mathematical development of regression diagnostics has not generally led to efficient computing formulas. Conflicting terminology and the use of closely related but subtly different statistics has caused confusion. This article attempts to make regression diagnostics more readily available to those who compute regressions with packaged statistics programs. We review regression diagnostic methodology, highlighting ambiguities of terminology and relationships among similar methods. We present new formulas for efficient computing of regression diagnostics. Finally, we offer specific advice on obtaining regression diagnostics from existing statistics programs, with examples drawn from Minitab and SAS.

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