The data matrix is (Y ,X )with X [X 1,X 2] , and consider the transformed regressor matrix Z [X 1,X 2 X

The data matrix is (Y ,X )with X Æ [X 1,X 2] , and consider the transformed regressor matrix Z Æ [X 1,X 2 ¡X 1] . Suppose you do a least squares regression of Y on X , and a least squares regression of Y on Z. Let b¾

2 and e¾

2 denote the residual variance estimates from the two regressions. Give a formula relating b¾

2 and e¾

2? (Explain your reasoning.)