3. (4 marks) You have data on variables Y, X, Z. W. Suppose in the data,...

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3. (4 marks) You have data on variables Y, X, Z. W. Suppose in the data, cov(X, Z) = 0 and cov(X, W) = 0. You run: - an OLS regression of Y on 1, X to get ₁ as coefficient of X and the residual variable ê - an OLS regression of Y on 1, X, Z, W to get as coefficient of X and the residual variable Is ₁=1? Is ê=n? If not, under what conditions are they equal? Give reasons. 3. (4 marks) You have data on variables Y, X, Z. W. Suppose in the data, cov(X, Z) = 0 and cov(X, W) = 0. You run: - an OLS regression of Y on 1, X to get ₁ as coefficient of X and the residual variable ê - an OLS regression of Y on 1, X, Z, W to get as coefficient of X and the residual variable Is ₁=1? Is ê=n? If not, under what conditions are they equal? Give reasons.

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