If $\sum \left( x _ { i} - \bar { x } \right) \left( y _ { i } - \bar { y } \right) = 128 \text { and } \sum \left( x _ { i } - \bar { x } \right) ^ { 2 } = 80$ then the least squares estimate of the slope coefficient $\beta _ { 1 }$ of the true regression line $y = \beta _ { 0 } + \beta _ { 1 } x$ is
A) 11.314
B) 8.944
C) 1.600
D) 0.625
E) cannot be determined from the given information

Question

Quizplus · Accepted Answer

The least squares estimate of the slope coefficient $\beta_1$ in a simple linear regression is given by $\beta_1 = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$. Substituting the given values, we get $\beta_1 = \frac{128}{80} = 1.6$.

If Then the Least Squares Estimate of the Slope Coefficient β1\beta _ { 1 }β1​

If Then the Least Squares Estimate of the Slope Coefficient $\beta _ { 1 }$