After reviewing elements of linear algebra, including the use of vector and matrix notation, students use it to analyze least squares estimation in the multivariate linear model. This is followed by a discussion of several of the assumptions on which least squares estimation is based, and what corrective actions should be taken if they are violated. The last part of the course moves into an analysis of random utility models of selection, and simultaneous equations models of supply and demand, to show how the techniques of regression analysis can be extended to quantify and test economic theories.