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If the Three Least Squares Assumptions Hold, Then the Large β^\hat { \beta }

Question 62

Multiple Choice

If the three least squares assumptions hold, then the large sample normal distribution of β^\hat { \beta } 1 is


A) N(0,1nvar[Xiμx) ui][var(Xi) ]2) N \left( 0 , \frac { 1 } { n } \frac { \left. \operatorname { var } \left[ X _ { i } - \mu _ { x } \right) u _ { i } \right] } { \left[ \operatorname { var } \left( X _ { i } \right) \right] ^ { 2 } } \right)
B) N(β1,1nvar(ui) ]2[var(Xi) ]2) N \left( \beta _ { 1 } , \frac { 1 } { n } \frac { \left. \operatorname { var } \left( u _ { i } \right) \right] ^ { 2 } } { \left[ \operatorname { var } \left( X _ { i } \right) \right] ^ { 2 } } \right)
C) N(β1,σu2i=1n(XlXˉ) 2N \left( \beta _ { 1 } , \frac { \sigma _ { u } ^ { 2 } } { \sum _ { i = 1 } ^ { n } \left( X _ { l } - \bar { X } \right) ^ { 2 } } \right.
D) N(β1,1nvar(ul) ][var(Xl) ]2) N \left( \beta _ { 1 } , \frac { 1 } { n } \frac { \left. \operatorname { var } \left( u _ { l } \right) \right] } { \left[ \operatorname { var } \left( X _ { l } \right) \right] ^ { 2 } } \right)

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