In the discussion of multiple regression up to this point, we have assumed that the in- dependent variables, x;, have existed over a range and contained many different values. However, in the multiple regression assumptions the only restriction on the indepen- dent variables is that they are fixed values. Thus, we could have an independent variable that took on only two values: x; = 0 and x 1. This structure is commonly defined as a dummy variable, and we will see that it provides a valuable tool for applying multiple regression to situations involving categorical variables. One important example is a lin- ear function that shifts in response to some influence. Consider first a simple regression equation: Y = Bo + BX Now, suppose that we introduce a dummy variable, Xy, that has values 0 and 1 and that the resulting equation is as follows: Y = B + BX + BX, When X2 = 0 in this equation, the constant is Bo, but when X2 = 1, the constant is Be + B2. Thus, we see that the dummy variable shifts the linear relationship between Y and X, by the value of the coefficient B2. In this way we can represent the effect of shifts in our regression equation. Dummy variables are also called indicator variables. We begin our discussion with an example of an important application. x13 Example 12.13 Wage Discrimination Analysis (Dummy Variable Model Estimation) The president of Investors, Ltd., wants to determine if there is any evidence of wage discrimination in the salaries of male and female financial analysts. Figure 12.19 presents an example of annual wages versus years of experience for the analysts. See the data file Gender and Salary. Figure 12.19 Example of Data Pattern Indicating Wage Discrimination Scatterplot of Annual Salary (Y) vs Years Experience (X4) 110000 100000 Gender (X) D-Female 1-Male 0 90000 80000 Annual Salary (1) 70000 - 60000 50000 40000 5.0 7.5 15.0 17.5 10.0 12.5 Years Experience (X)