2. The Simple Regression Model

Regression analysis consists in studying the dependence of a variable (the explained variable) on one or more other variables (the explanatory variables). This chapter deals with the simple regression model, which is a linear model comprising a single equation linking an explained variable to only one explanatory variable. Since the parameters of the simple regression model are unknown, they must be estimated to quantify the relationship between the two variables. The chapter presents the ordinary least squares (OLS) method, i.e., the most frequently used method to estimate the parameters of the simple regression model. It also establishes the properties of the OLS estimators and describes the tests on the regression coefficients. Several empirical applications are provided to illustrate in a simple way the various concepts.