Extensions Of The Twovariable Linear Regression Model

Some aspects of linear regression analysis can be easily introduced within the framework of the two-variable linear regression model that we have been discussing so far. First we consider the case of regression through the origin, that is, a situation where the intercept term, p1, is absent from the model. Then we consider the question of the units of measurement, that is, how the Y and X variables are measured and whether a change in the units of measurement affects the regression results. Finally, we consider the question of the functional form of the linear regression model. So far we have considered models that are linear in the parameters as well as in the variables. But recall that the regression theory developed in the previous chapters requires only that the parameters be linear; the variables may or may not enter linearly in the model. By considering models that are linear in the parameters but not necessarily in the variables, we show in this chapter how the two-variable models can deal with some interesting practical problems.

Once the ideas introduced in this chapter are grasped, their extension to multiple regression models is quite straightforward, as we shall show in Chapters 7 and 8.

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