Chapter 10
Is the Model Any Good?¹

In the last chapter we built regression models that measured the effects of several explanatory variables on a dependent variable. For example, how educational background, prior experience, years with a company, job level, or gender affect salary. We determined how each explanatory variable, whether numerical or categorical, expressed its effect on salary through its coefficient in the regression equation. The process of building such a model is a statistical one; that is, it involves determining a best-fit equation by calculating how much of the total variation is accounted for by the model. This calculation, in turn, is based on certain probabilistic assumptions concerning how the data is distributed. The first section of this chapter concerns how confident we can be that the coefficients of our explanatory variables are trustworthy. This is critically important if we are to make decisions based on our understanding of what a model seems to be telling us. We need criteria to determine which explanatory variables are truly significant in affecting the dependent variable–and which are not–if our model is to be at all useful. This section helps us to separate the wheat from the chaff.

The second section of this chapter furthers the process of building more complex and accurate models from several explanatory variables by considering how interactions between the variables themselves might have an effect on the dependent variable. That is, some of these variables might express their effects on the dependent variable in combination with other explanatory variables. In fact, there are even cases in which an explanatory variable appears to have a significant effect only when it is combined with one or more other explanatory variables. For example, it may be that employees’ gender by itself has no significant effect on salary, but gender together with job level might have a negative impact on salary. That is, the negative effect of gender on salary only has a significant impact when the employee is a female in a higher-level position: the well-known ”glass-ceiling” effect. This section, then, concerns not only the effects of several individual explanatory variables on a dependent variable, but also the effects of pairs of them on the dependent variable. You will learn in this chapter how to create multiple regression models with interaction variables built from both numerical and categorical explanatory variables and assess their significance. You will learn how to analyze and interpret these often complex models.