An outlier is an observation that is distant from other observations. It may result from measurement error; in which case it should be discarded. Or it may be indicative of a heavy-tailed population distribution, which then violates the assumption of normality.
Box and whisker plots such as the one shown in Exhibit 33.30, reveal outliers in a univariate assessment. For pairs of variables, outliers appear as isolated points on the outskirts of scatterplots. For more than 2 variables, statistical techniques such as Mahalanobis D2 may be used for detecting outliers.
Influential observations are any observations, outliers included, that have a disproportionate effect on the regression results. These need to be carefully examined and should be removed, unless there is a rationale for retaining them.
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