V2501023 Diagnostic Regression Analysis and Shifted Power
TECHNOMETRICS 0, VOL. 25, NO. 1, FEBRUARY 1983 Diagnostic Regression Analysis and Shifted Power Transformations A. C. Atkinson Department of Mathematics imperial College of Science and Technology London, SW7 2B2, England Diagnostic displays for outlying and influential observations are reviewed. In some examples apparent outliers vanish after a power transformation of the data. Interpretation of the score statistic for transformations as regression on a constructed variable makes diagnostic methods available for detection of the influence of individual observations on the transformation, Methods for the power transformation are exemplified and extended to the power transform- ation after a shift in location, for which there are two constructed variables. The emphasis is on plots as diagnostic tools. KEY WORDS: Box and Cox; Cook statistic; Influential observations; Outliers in regression; Power transformations; Regression diagnostics; Shifted power transformation. 1. INTRODUCTION may indicate not inadequate data, but an inadequate It is straightforward, with modern computer soft- model. In some casesoutliers can be reconciled with ware, to fit multiple-regressionequations to data. It is the body of the data by a transformation of the re- often, however, lesseasy to determine whether one, or sponse.But there is the possibility that evidencefor, or a few, observations are having a disproportionate against, a transformation may itself be being unduly effect on the fitted model and hence, more impor- influenced by one, or a few, observations. In Section 3 tantly, on the conclusions drawn from the data. the diagnostic plot for influential observations is ap- Methods for detecting such observations are a main plied to the score test for transformations, which is aim of the collection of techniques known as regres- interpreted in terms of regression on a constructed sion diagnostics, many of which are described in the variable.
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