The 95% confidence interval for $\beta _ { 1 }$ is the interval
A) $\left( \beta _ { 1 } - 1.96 S E \left( \beta _ { 1 } \right) , \beta _ { 1 } + 1.96 S E \left( \beta _ { 1 } \right) \right)$
B) $\left( \widehat { \beta } _ { 1 } - 1.645 \operatorname { SE } \left( \widehat { \beta } _ { 1 } \right) , \widehat { \beta } _ { 1 } + 1.645 \operatorname { SE } \left( \widehat { \beta } _ { 1 } \right) \right)$
C) $\left( \widehat { \beta } _ { 1 } - 1.96 \operatorname { SE } \left( \widehat { \beta } _ { 1 } \right) , \widehat { \beta } _ { 1 } + 1.96 \operatorname { SE } \left( \widehat { \beta } _ { 1 } \right) \right)$
D) $\left( \widehat { \beta } _ { 1 } - 1.96 , \widehat { \beta } _ { 1 } + 1.96 \right)$

Question

The  95%  confidence interval for  $\beta _ { 1 }$ is the interval
A) $\left( \beta _ { 1 } - 1.96 S E \left( \beta _ { 1 } \right) , \beta _ { 1 } + 1.96 S E \left( \beta _ { 1 } \right) \right)$
B) $\left( \widehat { \beta } _ { 1 } - 1.645 \operatorname { SE } \left( \widehat { \beta } _ { 1 } \right) , \widehat { \beta } _ { 1 } + 1.645 \operatorname { SE } \left( \widehat { \beta } _ { 1 } \right) \right)$
C) $\left( \widehat { \beta } _ { 1 } - 1.96 \operatorname { SE } \left( \widehat { \beta } _ { 1 } \right) , \widehat { \beta } _ { 1 } + 1.96 \operatorname { SE } \left( \widehat { \beta } _ { 1 } \right) \right)$
D) $\left( \widehat { \beta } _ { 1 } - 1.96 , \widehat { \beta } _ { 1 } + 1.96 \right)$

Quizplus · Accepted Answer

The 95% confidence interval for $\beta _ { 1 }$ is given by:$$\left( \widehat { \beta } _ { 1 } - 1.96 \operatorname { SE } \left( \widehat { \beta } _ { 1 } \right) , \widehat { \beta } _ { 1 } + 1.96 \operatorname { SE } \left( \widehat { \beta } _ { 1 } \right) \right)$$where $\widehat { \beta } _ { 1 }$ is the sample estimate of $\beta _ { 1 }$ and $\operatorname { SE } \left( \widehat { \beta } _ { 1 } \right)$ is the standard error of the estimate.

The 95% Confidence Interval For β1\beta _ { 1 }β1​

The 95% Confidence Interval For $\beta _ { 1 }$