Assumptions, Limitations, Practical Considerations - The Importance of Residual Analysis

Even though most assumptions of multiple regression cannot be tested explicitly, gross violations can be detected and should be dealt with appropriately. In particular, outliers (i.e., extreme cases) can seriously bias the results by "pulling" or "pushing" the regression line in a particular direction, thereby leading to biased regression coefficients. Often, excluding just a single extreme case can yield a completely different set of results. Therefore, one of the design goals for Multiple Regression was to make residual analyses as readily available as possible to the user so that violations of assumptions that threaten the validity of results can easily be identified.