Regression models can also take many functional forms or specifications. For instance, a linear regression will take the form of whereas a nonlinear regression can take the standard form of
where as a nonlinear regression can take the standard form of
However, there are other functional forms depending on the relationship of the variables. Typically, to test for functional form specifications, we revert to using a single independent variable at a time. The following are the most commonly used bivariate functional forms:
These functional forms are tested with one dependent variable and one independent variable. In the case of multivariate regressions, simply run the pairwise models and take the resulting functional forms and combine them into a more complex multivariate structure, with the understanding that when combining different functional forms, some previously statistically significant functions may drop out of the comprehensive model and integrate with other functions in the larger model. Figure 12.46 shows how these functional forms can be tested in BizStats, while Figure 12.47 shows their graphical representations (pay attention to the shape as well as the values on the axes).
Figure 12.46: Bivariate Functional Forms
Figure 12.47: Graphical Representation of the Different Functional Forms
