The information that is gained through various analyses of the residual scores yielded by the least squares regression model is explored. In fact, the most widely used methods for detecting data that do not fit this model are based on an analysis of residual scores. First, graphical methods of residual analysis are discussed, followed by a review of several quantitative approaches. Only the more widely used approaches are discussed. Example data sets are analyzed through the use of the Statistical Package for the Social Sciences (personal computer version) to illustrate the various strengths and weaknesses of these approaches and to demonstrate the necessity of using a variety of techniques in combination to detect outliers. The underlying premise for using these techniques is that the researcher needs to make sure that conclusions based on the data are not solely dependent on one or two extreme observations. Once an outlier is detected, the researcher must examine the data point's source of aberration. (Contains 3 figures, 5 tables, and 14 references.) (SLD)