(Requires Calculus)For the case of the multiple regression problem with two explanatory variables, show that minimizing the sum of squared residuals results in three conditions: $$\sum _ { i = 1 } ^ { n } { \hat u_ { i } } = 0 ; \sum _ { i = 1 } ^ { n } \hat { u _ { i } } X _ { 1 i } = 0 ; \sum _ { i = 1 } ^ { n } \hat { u _ { i } } X _ { 2 i } = 0$$

Question

(Requires Calculus)For the case of the multiple regression problem with two explanatory variables, show that minimizing the sum of squared residuals results in three conditions: $$\sum _ { i = 1 } ^ { n }  { \hat u_ { i } } = 0 ; \sum _ { i = 1 } ^ { n } \hat { u _ { i } } X _ { 1 i } = 0 ; \sum _ { i = 1 } ^ { n } \hat { u _ { i } } X _ { 2 i } = 0$$

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The Answer of (Requires Calculus)For the case of the multiple regression problem with two explanatory variables, show that minimizing the sum of squared residuals results in three conditions: $$\sum _ { i = 1 } ^ { n }  { \hat u_ { i } } = 0 ; \sum _ { i = 1 } ^ { n } \hat { u _ { i } } X _ { 1 i } = 0 ; \sum _ { i = 1 } ^ { n } \hat { u _ { i } } X _ { 2 i } = 0$$

(Requires Calculus)For the Case of the Multiple Regression Problem with Two