27 Mechanical properties 4 and 5 in scalar notation

This video delves into the final two mechanical properties of econometrics: the sample dependent variable mean equaling the mean of the fitted OLS values (Y bar equals Y hat bar), and the OLS fitted values being uncorrelated with OLS residuals (sum of Y I hat times epsilon I hat equals zero). Learn the mathematical expressions and detailed proofs for both properties, building upon summation operator rules and previously established concepts. This lesson concludes the scalar interpretation of OLS mechanical properties, preparing you for the matrix notation and geometric concepts in future videos. Subscribe to @AxiomTutoringCourses for more econometrics insights.