RULING OUT THIRD VARIABLES WITH MULTIPLE REGRESSION

Suppose that our study indicates that middle school sports participation does predict college GPA, and that temporal precedence is established (sports comes first, then GPA rises). We now have two of the three parts of the causal triangle. But is it possible to rule out potential third variables? What if parental income is involved (high-income parents can afford to let their children participate in sports, and they also provide other enrichment opportunities that lead to later college success)? What if diet is involved? What if motivation is really the important factor?

As long as we can list possible third variables and measure them, we can answer these questions statistically, in a procedure known as multiple regression. Multiple regression allows us to statistically control for the effect of these third variables. If we directly measure whether parental income is correlated with sports participation, and with college GPA, then we can figure out whether sports participation has an independent effect on GPA. Similarly, if we have a measure of the quality of a child's diet, we can see whether that is correlated with sports participation and with college GPA, and statistically control for it. If we have a measure of motivation, we can control for it.

Regression analysis yields a statistic known as beta, which indicates the degree to which a particular predictor variable is independently predictive of an effect (criterion variable). Consider the following beta values for the criterion variable of college GPA:

INDEPENDENT VARIABLE
Middle school sports participation	beta = .24,p < .01
Parents' income	beta = .03,not significant
Child's diet	beta = .08,not significant

In this example, middle school sports participation does predict success, even after we take parents' income and children's diet into account. Parents' income, in fact, has no independent relationship with college success when we control for the other variables, and neither does diet alone.

ACTIVITY

Notice, however, that we still have not definitively established that middle school sports participationcausesa student to be successful in college. We can only rule out the variables that we have thought to measure. What other third variables, not mentioned above, could be predictive of college success? Discuss at least three new variables that you would want to add to this multiple regression.