Using the assumptions of linearity, constant variance, and independence, along with the fact that A and B can each be expressed as a linear function of the Y i s, derive the sampling variances of A...

Using the assumptions of linearity, constant variance, and independence, along with the fact that A and B can each be expressed as a linear function of the Y_is, derive the sampling variances of A and B in simple regression. [Hint: V(B) =

The formula for the sampling variance of B in simple regression,

shows that, to estimate β precisely, it helps to have spread out xs. Explain why this result is intuitively sensible, illustrating your explanation with a graph. What happens to V(B) when there is no variation in X?