The Effects of Major Violations of the Assumptions of the Linear Regression Model

The linear regression model was briefly described in Chapter 20 of the companion book, but it deserves rather more detailed discussion since it plays such a crucial role in the analysis of bivariate samples. Perhaps the greatest merit of the model is that it provides the simplest possible starting point for deriving inferences about a sampled population. All the tests of significance and methods of calculating confidence limits discussed in Chapters 20 and 24 are predicated on the model. Statisticians have not been able to find any other model that offers the same advantages. The problem with other models is that their mathematical properties make it difficult, if not impossible, to carry out tests of significance or to calculate confidence limits. With the linear model inferences of the widest practical importance can be drawn from samples of any size.