26 Mechanical properties 1-3 in scalar notation

In this video, we explore the mechanical properties of Ordinary Least Squares (OLS) in econometrics. Lydia explains the first three key properties: the sum of OLS residuals is zero, OLS residuals are uncorrelated with explanatory variable sample values, and the OLS regression line cuts through the means. Each property is mathematically defined and proven using the first order conditions derived from the OLS minimization problem. A worked example with a small dataset is included to demonstrate and verify these properties in practice. Discover the fundamental principles behind OLS and how these properties arise directly from its mathematical structure. Subscribe to @AxiomTutoringCourses for more econometrics insights!