Regression analysis is a powerful—if limited—tool that uses statistical techniques to identify otherwise elusive correlations. Correlation is nothing more than a statistical term that indicates whether two variables move together. It tends to be cold outside when it snows; those two factors are positively correlated. Sunshine and rain, meanwhile, are negatively correlated. Easy enough—as long as there are only a couple of variables. But with a couple hundred variables, things get harder. Regression analysis is the tool that enables an economist to sort out these huge piles of data. It does so by artificially holding constant every variable except the two he wishes to focus on, and then showing how those two co-vary.

In the case of a complicated data set that concerns, for instance, the test scores of 20,000 schoolchildren, it might help to think of regression analysis as performing the following task: converting each of those schoolchildren into a sort of circuit board with an identical number of switches. Each switch represents a single category of the child's data: his first-grade math score, his third-grade math score, his first-grade reading score, his third-grade reading score, his mother's education level, his father's income, the number of books in his home, the relative affluence of his neighborhood, and so on. Now a researcher is able to tease some insights from this very complicated set of data. He can line up all the children who share many characteristics—all the circuit boards that have their switches flipped the same direction—and then pinpoint the single characteristic they don't share. This is how he isolates the true impact of that single switch on the sprawling circuit board. This is how the effect of that switch— and, eventually, of every switch—becomes manifest. (From pages 161-162 of Freakonomics.)