Diagnostic Regression Analysis and Shifted Power Transformations

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 transformation after a shift in location, for which there are two constructed variables. The emphasis is on plots as diagnostic tools.