In the Case of a Simple Regression, Where the Independent

question 44

Short Answer

In the case of a simple regression, where the independent variable is measured with i.i.d. error, a. $\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } } \beta _ { 1 }$

b. $\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } }$ .

c. $\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \frac { \sigma _ { w } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } } \beta _ { 1 }$ .

d. $\hat { \beta } _ { 1 } \stackrel { p } { \rightarrow } \beta _ { 1 } + \frac { \sigma _ { X } ^ { 2 } } { \sigma _ { X } ^ { 2 } + \sigma _ { w } ^ { 2 } }$ .

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