1. This exercise is designed to explore further the nature of common causes, and what happens when non-common causes are included in a multiple regression. We will begin our analysis of these data...

1. This exercise is designed to explore further the nature of common causes, and what happens when non-common causes are included in a multiple regression. We will begin our analysis of these data here, and will return to them in Chapter 9 and in Part 2 when we have the tools to explore them more completely. There are two data files for this exercise, both including variables labeled X1 X2 X3 and Y1. In both files, the three X variables are intercorrelated, but variable X2 is not a common cause of variables Y1 and X3. For the data in the first file (common cause 2.sav), variable X2 has no effect on Y1. In the second file (common cause 3.sav), variable X2 has no effect on variable X3. For “common cause 2.sav” regress variable Y1 on variables X1 X2 and X3. Next, regress variable Y1 on just X1 and X3. Compare the regression coefficients for variable X3 in the first versus the second analysis. Did it change substantially? Now do the same analysis for “common cause 3.sav.” Again, does the coefficient for variable X3 change from the first to the second regression? Discuss the meaning of these findings in class.