15 The math behind OLS the slope

This video dives into the mathematical derivation of the OLS coefficient beta one hat, continuing from our previous discussion on beta null hat. We meticulously break down the derivative process, starting from the minimization of squared residuals and applying key calculus and summation properties. Discover the algebraic manipulations that transform the initial derivative expression into the familiar formulas for beta one hat, including the covariance over variance form and the summation notation. We also explore a crucial identity involving the sum of (xi - x_bar)(yi - y_bar) and prove why a specific term simplifies to zero, a technique valuable for other econometrics proofs. Subscribe to @AxiomTutoringCourses for more econometrics tutorials.