3. The Multiple 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 presents the multiple regression model, which is a linear model comprising a single equation linking an explained variable to several explanatory variables. Since the parameters of this model are unknown, they must be estimated to quantify the relationship between the dependent and the explanatory variables. The chapter presents the most frequently used estimation method, i.e., the ordinary least squares (OLS) method. It also establishes the properties of the OLS estimators, describes the various tests on the regression coefficients, and presents key indicators such as the (adjusted) coefficient of determination. All the concepts are illustrated thanks to several empirical applications.