(Requires Appendix Material) in Deriving the OLS Estimator, You Minimize $\hat { \beta } _ { 0 } \text { and } \hat { \beta } _ { 1 }$

(Requires Appendix material) In deriving the OLS estimator, you minimize the sum of squared residuals with respect to the two parameters $\hat { \beta } _ { 0 } \text { and } \hat { \beta } _ { 1 }$
. 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.