In the simple linear regression model Y = $\beta _ { 0 } + \beta _ { 1 } x + \varepsilon$ the quantity E is a random variable, assumed to be normally distributed with E( $ \varepsilon$ ) = 0, and V( $ \varepsilon$ ) = $\sigma ^ { 2 }$ . The estimated standard error of $\hat { \beta } _ { 1 }$ (the least squares estimated of $\beta _ { 1 }$ ), denoted by , is __________ divided by __________, where $s = \sqrt { S S E ( n - 2 ) } \text { and } S _ { xx } = \sum \left( x _ { i } - \bar {x} \right) ^ { 2 }$ .

Question

In the simple linear regression model Y = $\beta _ { 0 } + \beta _ { 1 } x + \varepsilon$ the quantity E is a random variable, assumed to be normally distributed with E( $ \varepsilon$   ) = 0, and V( $ \varepsilon$   ) = $\sigma ^ { 2 }$ . The estimated standard error of $\hat { \beta } _ { 1 }$ (the least squares estimated of $\beta _ { 1 }$ ), denoted by  , is __________ divided by __________, where $s = \sqrt { S S E ( n - 2 ) } \text { and } S _ { xx } = \sum \left( x _ { i } - \bar {x} \right) ^ { 2 }$ .

Quizplus · Accepted Answer

The Answer is s,

\sqrt { S _ {xx} }

In the Simple Linear Regression Model Y = β0+β1x+ε\beta _ { 0 } + \beta _ { 1 } x + \varepsilonβ0​+β1​x+ε

In the Simple Linear Regression Model Y = $\beta _ { 0 } + \beta _ { 1 } x + \varepsilon$