In the simple linear regression model $Y = \beta _ { 0 } + \beta _ { 1 } x + E ,$ the quantity E is a random variable, assumed to be normally distributed with E( $ \varepsilon$
) = 0 and V( $ \varepsilon$
) = $\sigma ^ { 2}$ . The estimator $\hat { \beta } _ { 1 }$ has a __________ distribution, because it is a linear function of independent __________ random variables.

Question

In the simple linear regression model $Y = \beta _ { 0 } + \beta _ { 1 } x + E ,$ the quantity E is a random variable, assumed to be normally distributed with E( $ \varepsilon$  
 ) = 0 and V( $ \varepsilon$  
 ) = $\sigma ^ { 2}$ . The estimator $\hat { \beta } _ { 1 }$ has a __________ distribution, because it is a linear function of independent __________ random variables.

Quizplus · Accepted Answer

The Answer is normal, normal

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

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