Residuals and Outliers, Revisited

As was discussed in Chapter 3, outliers, or extreme values, pose a significant problem in that, potentially, they will bias the outcome of a regression analysis. When outliers are present, the questions always are Are the outliers truly representative of the data that are extreme and must be considered in the analysis, or do they represent error in measurement, error in recording of data, influence of unexpected variables, and so on The standard procedure is to retain an outlier in an analysis, unless as assignable extraneous cause can be identified that proves the data point to be aberrant. If none can be found, or an explanation is not entirely satisfactory, one can present data analyses that include and omit one or more outliers, along with rationale explaining the implications, with and without. 

In Chapter 3, it was noted that residual analysis is very useful for exploring the effects of outliers and nonnormal distributions of data, for how these relate to adequacy of the regression model, and for identifying and correcting for serially correlated data. At the end of the chapter, formulas for the process of 

Data for Linear Regression to Determine Weights, Example 8.2 

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