In Deriving the OLS Estimator, You Minimize the Sum of Squared

Essay

In deriving the OLS estimator, you minimize the sum of squared residuals with respect to the two parameters $\hat { \beta }$ ₀ and $\hat { \beta }$ ₁. The resulting two equations imply two restrictions that OLS places on the data, namely that $\sum _ { i = 1 } ^ { n } \hat { u } _ { i } = 0$ and $\sum _ { i = 1 } ^ { n } \hat { u } _ { i } X _ { i } = 0$ Show that you get the same formula for the regression slope and the intercept if you impose these two conditions on the sample regression function.