Assume the response schedule Yi,x = a + bx + i. The i are IID N (0, σ2). The variables Xi are IID N (0, τ 2). In fact, the pairs (i, Xi)

are IID in i, and jointly normal. However, the correlation between

(i, Xi) is ρ, which may not be 0. The parameters

a, b, σ2, τ 2, ρ are unknown. You observe Xi and Yi = Yi,Xi for i = 1,..., 500.

(a) If you run a regression of Yi on Xi, will you get unbiased estimates for a and b?

(b) Is the relationship between X and Y causal?

Explain briefly.