6. Residual and estimation of 2 the population variance o 1. Residual e=Y-Y=Y-Xb=[-X(XXXY PY(P=I-X(XX) X 1) P is idempotent(幂等的) 2)E(e)=0 3)var(e=e(ee)=oP 4) >2=rY-bX'Y=tr(ee)6. Residual and Estimation of the population variance 1. Residual 1) P is idempotent (幂等的) 2) 3) 4) 2  ˆ ˆ [ ] ( ) = − = − = −   = = −   -1 -1 e Y Y Y Xb I X(X X) X Y PY P I X(X X) X E( ) e 0 = 2 var( ) E( ) e ee P = =   2 1 ˆ tr( ) n i i e =  = − = Y Y bX Y ee   