10.3 What Lies Ahead: Multiple Regression

Don’t worry, this is but a brief farewell. Do me a last favour and imagine we had more ideas about why students end up with different final test scores, or why people end up with different number of years of education. In other words, what else could possibly explain some of the variability in the dependent variables we investigated in the previous sections?

In the case of test scores, perhaps hours of independent study? Doing end-of-chapter exercises? How many classes in total the student is taking that semester? Does the student work for pay? Have they recently experienced problems related to their personal life? Do they have dependents of whom they have to take care at home? Is English their native language? Are they international students? What is their area of study? . . . And so on, and so on; I’m certain you can add more on your own.

In the case of years of schooling, perhaps the family’s socioeconomic status? Wealth? Gender? Race/ethnicity? Citizenship status? Attitudes toward education? The presence of appropriate role models? Being passionate about a specific field of study? Go on, add your ideas to the list.

If there are so many factors that can affect a (dependent) variable, how do we examine their individual effects? Bivariately, one by one? While this is a good first step (to establish something is going on), obviously that cannot be the end of our analysis. We have to be able to account for all of them at the same time, to compare their effects, and to create more complicated models which together to explain more variability in the dependent variable.

Multiple regression allows us to do just that. Instead of one independent variable x, we can consider many independent variables at the same time. Then, the effect of each single variable is provided net of the effects of the other variables (or we say that we control for the other variables), so that we can simultaneously take care of alternative explanations. In this way, a variable’s effect on y may be decreased or increased (from what it used to be in the bivariate case), and its statistical significance may disappear (or even appear, in some cases). In any case, this effect would likely be ‘truer’ than the one obtained bivariately (though this of course depends on the choice of variable controls).

And this is where you will be going, if you choose to continue on the path of statistics enlightenment. If I said there is a lot more to learn it would be a gross understatement — but, given what statistics (proper use of statistics!) enables you to do in social research, it is absolutely and totally worth it.

If you choose not to continue on, then use what statistical knowledge you already have, and use it responsibly (great power, and all that). Either way, here you are, in the last section — you survived! (Possibly even with your sanity mostly intact.) Go celebrate!

With this, I bid you adieu.