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

question 8

Essay

In the simple linear regression model Y = β0+β1x+ε\beta _ { 0 } + \beta _ { 1 } x + \varepsilon the quantity E is a random variable, assumed to be normally distributed with E( ε \varepsilon ) = 0, and V( ε \varepsilon ) = σ2\sigma ^ { 2 } . The estimated standard error of β^1\hat { \beta } _ { 1 } (the least squares estimated of β1\beta _ { 1 } ), denoted by  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 }  . , is __________ divided by __________, where s=SSE(n2) and Sxx=(xixˉ)2s = \sqrt { S S E ( n - 2 ) } \text { and } S _ { xx } = \sum \left( x _ { i } - \bar {x} \right) ^ { 2 } .

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