Chapter 10 Testing Associations II: Correlation and Regression

This is it: you are finally here, reading the last chapter. (And after nine chapters, what’s just one more?) This is not a heavy chapter as some of the others but regression is sufficiently different form the type of testing about which you learned in Chapter 8 to deserve a heads-up — so if you find yourself despairing at some point, just remind yourself that this is it; once you’ve learned this, you will have a passing knowledge about how, what for, and why statistics is used in sociological research, and you will also be able to do some basic analysis on your own! — and you’ll be done in no time.

Pep talk aside, for this chapter you should review/recall Chapter 7, and specifically Section 7.2.3 (https://pressbooks.bccampus.ca/simplestats/chapter/7-2-3-between-two-continuous-variables/) on examining bivariate associations between two variables, treated as continuous for the purposes of statistical analysis. We did that visually through a scatterplot (with a line of best fit) and numerically through the coefficient of correlation called Pearson’s r.

In this chapter, you will learn what r actually is, and that it has its own t-test and a p-value to test its significance. In addition, I will present a relatively brief and basic introduction into the topic of regression, a powerful and versatile technique with truly impressive number of applications which readily allows for doing multivariate analysis.

After all, recall that when we do bivariate analysis, we ignore the complexity of the real world where variables are/may be tangled in a veritable web of almost endless interrelationships. With bivariate analysis we ignore all that to focus on how just two variables are statistically associated. But because of that, we cannot say anything about causality as we cannot account for additional variables that could serve as alternative explanations to what we observe. And while multivariate regression cannot completely do that either (in the social sciences establishing causality is a pretty tall order), with careful assumptions and the right specifications, it can help bring us more than a few steps further in that direction.

Of course, even if I haven’t already told you, you would have been able to tell by now that multivariate regression analysis falls beyond the scope of what we do here. What follows is a necessary stepping stone, however; once you have the right idea about how regression works with two continuous variables, everything else regression follows the same basic principle and thus can be built on top of the foundation you will have by the end of this chapter (and book!).

So, ready? Let’s go then! The end is just several sections away!