Consider the regression model Y = XB + U. Partition X as [X1
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Consider the regression model Y = XB + U. Partition X as [X1 X2] and B as [B? 1 B? 2]?, where X1 has k1 columns and X2 h
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Consider the regression model Y = XB + U. Partition X as [X1 X2] and B as [B? 1 B? 2]?, where X1 has k1 columns and X2 has k2 columns. Suppose that X? 2Y = 0k2 * 1. Let R = [Ik1 0k1 * k2 ]. a. Show that Bn ?(X?X)Bn = (RBn)?[R(X?X)-1 R] -1 (RBn). b. Consider the regression described in Equation (12.17). Let W = [1 W1 W2 c Wr], where 1 is an n * 1 vector of ones, W1 is the n * 1 vector with i th element W1i , and so forth. Let Un TSLS denote the vector of two-stage least squares residuals. i. Show that W?Un TSLS = 0. ii. Show that the method for computing the J-statistic described in Key Concept 12.6 (using a homoskedasticity-only F-statistic) and the formula in Equation (18.63) produce the same value for the J-statistic
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