普通最小二乘法 Ordinary least squares procedure) 求b和b使残差平方和最小 ∑c=∑(x-1)=∑y-(+bx Let x,=X-X and y=YY Then b=∑x/∑ Xi (OLSE) -Y-bX
普通最小二乘法(Ordinary least squares procedure): 求 使残差平方和最小: Let Then (OLSE) 0 1 b b 和 2 2 2 0 1 ˆ ˆ ˆ ( ) [ ( )] i i i i i e Y Y Y b b X = − = − + and i i i i x X X y Y Y = − = − 2 1 0 1 ˆ ˆ ˆ i i i b x y x b Y b X = = −
The properties of the OlsE 1.无偏性 unbiased) E(b)=b,, E(bo=bo O ∑X 2.Ⅴar vari 2 ∑ cov(6o, 6= 2
The properties of the OLSE: 1. 无偏性(unbiased): 2. 1 1 0 0 ˆ ˆ E b b E b b ( ) , ( ) = = 2 2 2 1 0 2 2 ˆ ˆ var( ) , var( ) i i i X b b x n x = = 2 0 1 2 ˆ ˆ cov( , ) i X b b x = −