Question 2 16 pts Suppose D; is the treatment dummy and {Yoi.Y₁) are the potential outcomes. Denote the observed outcome as Y₁ =Yoi + Di *(Y1i-Yoi). Define the causal effect as the average treatment effect E(Y₁i-Yoi). Suppose we collect an i.i.d. observational data set {Y₁, D₁, i = 1,...,n}. (1) If we find evidence that Y; and D; are independent, does it imply D; has no causal effect on Y; ? Briefly explain. (2) If we find evidence that Y; and D; are correlated, does it imply D; has a causal effect on Y; ? Briefly explain. Now suppose we collect another data set {Yj, Dj, j = 1,...,m} from a randomized controlled experiment. (3) If we find evidence that Y; and D; are independent, does it imply D; has no causal effect on Y; ? Briefly explain. (4) If we find evidence that Y; and D; are correlated, does it imply D; has a causal effect on Y; ? Briefly explain.