Problem 3 An analyst believes that X, W, and 5' determine Y according to the following relationship Y:3+4X+2W+6. The analyst species that data are generated according to Y,- = n + 51X+ 521% + \"i: and assumes MLR.1MLR.4 hold. In addition, the joint distribution of Y,, X,, and W,- satises: Var(Y) : 13 Var(W) : 1 Var(X) : 1 Cov(Y, W) = 4 Cov(X, W) = .5 i. Suppose an analyst has a sample of independent and identically distributed observations of the form (YhXi, W,). The analyst regresses 1",; on X, and W,. (1",; is the regressand, and X,- and W, are the regressors.) Let the corresponding slope coeicient estimators be denoted (:11 for the slope of X, and 32 for the slope of W. Using the information above, what do you think 31 should be close to if the sample size is very large? ii. Does your answer to part (i) use an economic model (E) or statistical model (S)? Please answer either: neither; E; S; or E and S. iii. Maintain the assumptions of the previous part, but assume that the analyst regresses Y,- on X, (but not Wi). Let the slope coeicient estimator on X be denoted 6i. Using the information above, what do you think 5'1 should be close to if the sample size is very large? iv. What is Cov(X, Y)? Please briey show how you obtained your