2. Partitioned regression and geometric interpretation. Suppose you regress Y on X and obtain the fitted values Y. Also, suppose X is partitioned as X=[X1,X2], where X1 and X2 are both n1 vectors. Now, you regress Y on X1 and Y. Let ^ be the OLS estimator of the coefficient on Y. What is the value of ^ ? Provide both analytic and geometric arguments to support your answer. 2. Partitioned regression and geometric interpretation. Suppose you regress Y on X and obtain the fitted values Y. Also, suppose X is partitioned as X=[X1,X2], where X1 and X2 are both n1 vectors. Now, you regress Y on X1 and Y. Let ^ be the OLS estimator of the coefficient on Y. What is the value of ^ ? Provide both analytic and geometric arguments to support your