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

Short Answer

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.