101 Coefficient interpretation Level level model mathematical derivation

In this video, we delve into the mathematical proof behind the interpretation of the slope coefficient (beta one) in a level-level simple linear regression model. We explain why the change in the dependent variable (Y) for a one-unit increase in the independent variable (X) is constant. Starting with the population model, we apply the crucial conditional expectation assumption to derive the conditional mean of Y given X. By taking the derivative of this conditional mean with respect to X, we rigorously demonstrate that the marginal effect is consistently equal to beta one. This proves that the marginal effect is constant across all values of X, as it does not depend on X itself. Subscribe to @AxiomTutoringCourses for more econometric insights.