Minimization of $\sum _ { i = 1 } ^ { n } \left( Y _ { i } - b _ { 0 } - b _ { 1 } X _ { 1 i } - \cdots - b _ { k } X _ { k i } \right) ^ { 2 }$ results in
A) $X ^ { \prime } \boldsymbol { Y } = \boldsymbol { X } \hat { \boldsymbol { \beta } }$
B) $\boldsymbol { X } \hat { \boldsymbol { \beta } } = \mathbf { 0 } _ { k + 1 }$
C) $\boldsymbol { X } ^ { \prime } ( \boldsymbol { Y } - \boldsymbol { X } \hat { \boldsymbol { \beta } } ) = \mathbf { 0 } _ { k + 1 }$
D) $\boldsymbol { R } \boldsymbol { \beta } = \boldsymbol { r } \text {. }$

Question

Minimization of  $\sum _ { i = 1 } ^ { n } \left( Y _ { i } - b _ { 0 } - b _ { 1 } X _ { 1 i } - \cdots - b _ { k } X _ { k i } \right) ^ { 2 }$  results in
A) $X ^ { \prime } \boldsymbol { Y } = \boldsymbol { X } \hat { \boldsymbol { \beta } }$
B) $\boldsymbol { X } \hat { \boldsymbol { \beta } } = \mathbf { 0 } _ { k + 1 }$
C) $\boldsymbol { X } ^ { \prime } ( \boldsymbol { Y } - \boldsymbol { X } \hat { \boldsymbol { \beta } } ) = \mathbf { 0 } _ { k + 1 }$
D) $\boldsymbol { R } \boldsymbol { \beta } = \boldsymbol { r } \text {. }$

Quizplus · Accepted Answer

The Answer is C

Minimization Of ∑i=1n(Yi−b0−b1X1i−⋯−bkXki)2\sum _ { i = 1 } ^ { n } \left( Y _ { i } - b _ { 0 } - b _ { 1 } X _ { 1 i } - \cdots - b _ { k } X _ { k i } \right) ^ { 2 }∑i=1n​(Yi​−b0​−b1​X1i​−⋯−bk​Xki​)2

Minimization Of $\sum _ { i = 1 } ^ { n } \left( Y _ { i } - b _ { 0 } - b _ { 1 } X _ { 1 i } - \cdots - b _ { k } X _ { k i } \right) ^ { 2 }$