itellin 打不出来公式，要把下式理解了，还要给残差向量带一顶绿帽子，把帽子搞清楚了，就可以折腾了。 Cov(w^) = E[w^ - E(w^)][w^ - E(w^)]' = E[(Z'Z)^(-1)Z'ee'Z(Z'Z)^(-1)] = (Z'Z)^(-1)Z'E(ee')Z(Z'Z)^(-1) = E(ee')(Z'Z)^(-1)Z'Z(Z'Z)^(-1) = E(ee')(Z'Z)^(-1)
zjgslxh $$Cov(\hat{w})=E[\hat{w}-E(\hat{w})][\hat{w}-E(\hat{w})]^{'}=E[\hat{w}-w][\hat{w}-w]^{'}$$ \(\hat{w}=( Z^{T}Z )^{-1}Z^{T}y=(Z^{T}Z)^{-1}Z^{T}(Zw+E)=w+(Z^{T}Z)^{-1}Z^{T}E\)，即\(\hat{w}-w=(Z^{T}Z)^{-1}Z^{T}E\) 带入上式子可得结果。
