This is the first of two chapters that examine the linear regression model. In its simplest form, linear regression is a statistical tool we can use to explore the relationship between two interval variables: a dependent variable (the output) and an independent variable (an input). As long as the relationship is linear—that is, a line characterizes the relationship between the output and input—the linear regression model will allow us to perform inference.

Why does this model merit two chapters? Because it's the workhorse of empirical legal studies. This may seem surprising because many variables of interest are nominal; for example, is the defendant guilty or innocent, is a judiciary independent or not, is the judge male or female? But the fact of it is that the basic regression model can be adapted to deal with non-interval dependent variables. We'll see how in Chapter 9. Moreover, and perhaps more important, the model allows us to include more than one independent variable in our analysis, and, depending on our research design, draw causal inferences.

Here we focus, first, on lines and how we can use them to summarize the relationship between variables. Next we describe ordinary least squares, which is a method to find the line that best fits the data. We also define the linear regression model and show how to use it to perform statistical inference. We conclude with a discussion of model performance. As always, we use examples draw from the literature on law and legal institutions to illustrate key concepts.

- end of excerpt -