(Solution) - The regression model to be analyzed is y X1 1 X2 2 -(2025 Original AI-Free Solution)

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The regression model to be analyzed is y = X1?1 + X2?2 + ?, where X1 and X2 have K1 and K2 columns, respectively. The restriction is ?2 = 0. a. Using (6-14), prove that the restricted estimator is simply [b1*, 0], where b1* is the least squares coefficient vector in the regression of y on X1. b. Prove that if the restriction is ?2 = ?02 for a nonzero ?02, then the restricted estimator of ?1 is b1* = (X'1X1) ?1 X'1 (y ? X2?02).