以下是引用kamekame在2008-10-3 19:21:00的发言：

附录B的三个定理，只证出那个α……我是笨蛋泪奔|||||||||

其他的试着用定义写了一下，没化出来TT跪求指点！！！！！！！！！

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我不会打出希腊字符，就用abcd代替了，你应该可以看懂：

1. y=a+bx+u

cov(x, y)=cov(x, a+bx+u)=b*cov(x,x), because of cov(x, a)=0, cov(x, u)=0, which is exogenous assumption.

Thus b=cov(x, y)/cov(x,x)=cov(x, y)/var(x). which is the last part of theorem b.3.

2.

Var_x [E(y|x)]=E_x [E(y|x)²] - {E_x [E(y|x)]}²=E_x [E(y|x)²] - {E(y)}^2,  Which is the general variance formula.

E_x[Var(y|x)]=E_x[E(y²|x)-E(y|x)²]=E(y²)-E(y|x)²]

The first equation plus the second one implies conclusion (B.69)

3. (b.70) is a rearrangement of (b.69).

Now all the three conclusions are proved.

Good Luck to you.