Linear Regression Basics

This lecture covers the basics of linear regression, starting with the Ordinary Least Squares (OLS) approach to minimize squared approximation errors. The instructor explains the OLS vector, residual and predicted values, hat matrix, and residual maker matrix. The lecture also delves into the Fresh-Vaux-Laval theorem, decomposition of multiple regression, and goodness of fit using the coefficient of determination. Additionally, the Gauss-Markov assumptions are introduced, highlighting the properties of OLS under these ideal conditions.