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# 罗 汉 - PowerPoint PPT Presentation

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( 湖南大学 数学与计量经济学院)

Q(a, b)=

min

Q(a, b)=

min

y = a +bx

Q(b1,b2 ,…,bm)=

f (x)=b1r1(x)+ b2r2(x) +… + bmrm(x)

min

(1)建立回归模型(经验方程)

(2)对回归模型可信度进行检验

(3)判断自变量 x 对 y 的影响是否显著

(4)诊断回归模型是否适合这组数据

(5)利用模型进行预报和控制

y =a + bx + e

(2) Var( ei) = 2；

(1) E( ei ) = 0；

(3) Cov( ei,ej ) = 0，i  j；

(4) Cov( ei,Xi ) = 0；

(5) e ~ N (0,2).

OLS估计:min Q(a, b)=

(1) 回归系数的显著性检验 ( t 检验 )

H0: b = 0.

(2) 回归方程的显著性检验 ( F 检验 )

H0: b = 0.

(3) 拟合优度检验

y =b0+ b1x1 + b2x2 + … + bkxk+e

Y = Xb + e

(1) E(e) = 0；

(2) E(eeT ) = 2I；

OLS估计: min Q(b)=|| Y –Xb ||2

(3) E(XTe) = 0；

(4) rank(X) = k+1；

(5) e ~ N (0,2I ).