In the multiple regression model Y_i = ?₀ + ?₁X₁_i+ ?₂ X₂_i + ... + ?_kX_ki + u_i, i = 1,..., n, the OLS estimators are obtained by minimizing the sum of A)squared mistakes in $\sum _ { i = 1 } ^ { n } \left( Y _ { i } - b _ { 0 } - b _ { 1 } X _ { 1 i } - \ldots - b _ { k } X _ { k i } \right) ^ { 2 }$ B)squared mistakes in $\sum _ { i = 1 } ^ { n } \left( Y _ { i } - b _ { 0 } - b _ { 1 } X _ { 1 i } - \ldots - b _ { k } X _ { k i } - u _ { i } \right) ^ { 2 }$ C)absolute mistakes in $\sum _ { i = 1 } ^ { n } \left| \left( Y _ { i } - b _ { 0 } - b _ { 1 } X _ { 1 i } - \ldots - b _ { k } X _ { k i } \right) \right|$ D)squared mistakes in $\sum _ { i = 1 } ^ { n } \left( Y _ { i } - b _ { 0 } - b _ { 1 } X _ { i } \right) ^ { 2 }$

Question

Quizplus · Accepted Answer

The OLS estimators are obtained by minimizing the sum of squared residuals, which is the difference between the observed values and the values predicted by the model without including the error term $u_i$.

In the Multiple Regression Model Yi = ?0 + ?1X1i ∑i=1n(Yi−b0−b1X1i−…−bkXki)2\sum _ { i = 1 } ^ { n } \left( Y _ { i } - b _ { 0 } - b _ { 1 } X _ { 1 i } - \ldots - b _ { k } X _ { k i } \right) ^ { 2 }∑i=1n​(Yi​−b0​−b1​X1i​−…−bk​Xki​)2

In the Multiple Regression Model Y_i = ?₀ + ?₁X₁_i $\sum _ { i = 1 } ^ { n } \left( Y _ { i } - b _ { 0 } - b _ { 1 } X _ { 1 i } - \ldots - b _ { k } X _ { k i } \right) ^ { 2 }$