3.3 最小二乘(OLS)估计量的特性2.残差的方差s?=2= 'a/ [T-(k+1)]是 的无偏估计量,E(s)=E(2)=β的估计的方差协方差矩阵是Var (β) = s? (X'X)l =α2 (X'X)*(第4版第57页)
3.3 最小二乘(OLS)估计量的特性 (第4版第57页)
3.4可决系数(R2)1.多重确定系数(多重可决系数)Y=Xβ+u=Y+u, TSS=RSS+ESSY'Y-T2RSSTSS = RSS + ESS, R?=TSSY'Y-Ty2有0≤R2≤1。R2→>1,拟合优度越好。2.调整的多重确定系数ESS /(T -k -1)TSS - RSSR2=1--TSSTSS /(T - 1)T-1(第4版第64页)T-k-
3.4 可决系数(R2) (第4版第64页)
Dependent Variable:YMethod:LeastSquaresDate:01/31/07 Time:20:48例题3.1Sample:110Included observations:10ProbVariableCoefficientStd.Errort-Statisticc113.834328.165574.0416120.0049Y:某商品需求量X1-8.3553422.290749-3.6474280.0082X1:该商品价格X20.1800720.39720.1997270.901589X2:消费者平均收入0.883136R-squared78.00000MeandependentvarAdiusted R-squared0.84974619.57890S.D.dependentvarS.Eofregression7.5892907.134678Akaike info criterionSum squared resid403.18137.225454Schwarz criterionLog likelihood-32.6733926.44931F-statistic1.7671430.000546Durbin-Watson statProb(F-statistic)S.D.2 ×(10 -1) - ESS19.57892×9-403.1813TSSESSRSSR?==0.8831TSSTSSS.D.2 ×(10 - 1)19.57892×9(第4版第66页)
例题3.1 Y:某商品需求量 X1:该商品价格 X2:消费者平均收入 (第4版第66页)