The Inaugural Coase Lecture

An Introduction to Regression Analysis
Alan O. Sykes* Regression analysis is a statistical tool for the investigation of relationships between variables. Usually, the investigator seeks to ascertain the causal effect of one variable upon another—the effect of a price increase upon demand, for example, or the effect of changes in the money supply upon the inflation rate. To explore such issues, the investigator assembles data on the underlying variables of interest and employs regression to estimate the quantitative effect of the causal variables upon the variable that they influence. The investigator also typically assesses the “statistical significance” of the estimated relationships, that is, the degree of confidence that the true relationship is close to the estimated relationship. Regression techniques have long been central to the field of economic statistics (“econometrics”). Increasingly, they have become important to lawyers and legal policy makers as well. Regression has been offered as evidence of liability under Title VII of the Civil Rights Act of , as evidence of racial bias in death penalty litigation, as evidence of damages in contract actions, as evidence of violations under the Voting Rights Act, and as evidence of damages in antitrust litigation, among other things. In this lecture, I will provide an overview of the most basic techniques of regression analysis—how they work, what they assume,
Professor of Law, University of Chicago, The Law School. I thank Donna Cote for helpful research assistance.  See, e.g, Bazemore v. Friday,  U.S. ,  ().  See, e.g., McClesky v. Kemp,  U.S.  ().  See, e.g., Cotton Brothers Baking Co. v. Industrial Risk Insurers,  F.d  (th Cir. ).  See, e.g., Thornburgh v. Gingles,  U.S.  ().  See, e.g., Sprayrite Service Corp. v. Monsanto Co., 