Dummy Variable Regression for Differences in Slope To determine if there are significant differences in slopes between two discrete conditions, we need to expand our regression model to a more complex form: Y = Bo + BX: + (Bi + B.X2)X1 (12,34) Now, we see that the slope coefficient of X, contains two components, B, and B,X,. When X, equals 0, the slope is the usual Bi. However, when X, equals 1, the slope is equal to the algebraic sum of Bi + Bz. To estimate the model, we actu- ally need to create a new set of transformed variables that are linear. There- fore, the model actually used for estimation is as follows: y = 10 + b2X2 + b1X1 + b4x2x (12.35) The resulting regression model is now linear with three variables. The new variable, x1x2, is often called an interaction variable. Note that when the dummy variable x2 = 0, this variable has a value of o, but when x2 = 1, this variable has the value of xi. The coefficient by is an estimate of the difference in the coefficient of X, when 12 = 1 compared to x2 = 0. Thus, the Student's statistic for B, can be used to test the following hypotheses: Ho: B3 = 0 B 0,B0 k50 HB3 +01B0.B20 If we reject the null hypothesis, we conclude that there is a difference in the slope coefficient for the two subgroups. In many cases we will be interested in both the difference in the constant and the difference in the slope and will test both of the hypotheses presented in this section. Example 12.14 Salary Model for Systems, Inc. (Dummy Variable Model Estimation) The president of Systems, Inc., is interested in knowing if the annual salary increases for the female engineers in the company have maintained the same level as those for the male engineers, There have been some complaints from both male and female engineers that the salaries for female engineers have not increased at the same rate as those for male engineers