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# Introduction to Regression Analysis

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.

### What is Regression?

For purposes of illustration, suppose that we wish to identify and quantify the factors that determine earnings in the labor market. A moment’s reflection suggests a myriad of factors that are associated with variations in earnings across individuals—occupation, age, experience, educational attainment, motivation, and innate ability come to mind, perhaps along with factors such as race and gender that can be of particular concern to lawyers. For the time being, let us restrict attention to a single factor—call it education. Regression analysis with a single explanatory variable is termed “simple regression"