Dependent Variable: Y1 Method: Least Squares Date:03/04/03Time:02:30 Sample: 1 10 Included observations: 10 Variable Coefficient Std Error t-Statistic Prob 2.7333330.6747994.0505900.0037 2.0484850.10875418.836000.0000 R-squared 0.977949 Mean dependent var 14.00000 Adjusted R-squared 0.975193 S.D. dependent var 6.271629 S.E. of regression 0.987804 akaike info criterion 2.990192 Sum squared resid 7.806061 Schwarz criterion 3.050709 Log likelihood 1295096 F-statistic 354.7950 Durbin-Watson stat 3.449139 Prob (F-statistic) 0.000000
Dependent Variable: Y1 Method: Least Squares Date: 03/04/03 Time: 02:30 Sample: 1 10 Included observations: 10 Variable Coefficient Std. Error t-Statistic Prob. C 2.733333 0.674799 4.050590 0.0037 X 2.048485 0.108754 18.83600 0.0000 R-squared 0.977949 Mean dependent var 14.00000 Adjusted R-squared 0.975193 S.D. dependent var 6.271629 S.E. of regression 0.987804 Akaike info criterion 2.990192 Sum squared resid 7.806061 Schwarz criterion 3.050709 Log likelihood -12.95096 F-statistic 354.7950 Durbin-Watson stat 3.449139 Prob(F-statistic) 0.000000
Dependent Variable: Y2 Method Least Squares Date:03/04/03Time:02:36 Sample: 1 10 Included observations 10 Variable Coefficient Std Error t-statistic Prob 2.4666671.3495981.8277050.1050 2.0969700.2175079.6409130.0000 R-squared 0.920751 Mean dependent var 14.00000 Adjusted R-squared 0.910844 S.D. dependent var 6.616478 S.E. of regression 1.975609 Akaike info criterion 4376487 Sum squared resid 31.22424 Schwarz criterion 4.437004 Log likelihood -19.88243 F-statistic 92.94720 Durbin-Watson stat 3.4491 39 Prob(F-statistic) 0.000011
Dependent Variable: Y2 Method: Least Squares Date: 03/04/03 Time: 02:36 Sample: 1 10 Included observations: 10 Variable Coefficient Std. Error t-Statistic Prob. C 2.466667 1.349598 1.827705 0.1050 X 2.096970 0.217507 9.640913 0.0000 R-squared 0.920751 Mean dependent var 14.00000 Adjusted R-squared 0.910844 S.D. dependent var 6.616478 S.E. of regression 1.975609 Akaike info criterion 4.376487 Sum squared resid 31.22424 Schwarz criterion 4.437004 Log likelihood -19.88243 F-statistic 92.94720 Durbin-Watson stat 3.449139 Prob(F-statistic) 0.000011
2、总体平方和、残差平方和和回归平方和 定义 TSS=∑(y2-y)2 ESS=Σ(v-y) RSS=Σ(y2-y) TSS为总体平方和( Total Sum of Squares),反 映样本观测值总体离差的大小;ESS为回归平方和 ( Explained Sum of Squares),反映由模型中 解释变量所解释的那部分离差的大小;RSS为残差 平方和( Residual Sum of Squares),反映样本 观测值与估计值偏离的大小,也是模型中解释变 量未解释的那部分离差的大小
2、总体平方和、残差平方和和回归平方和 • 定义 • TSS为总体平方和（Total Sum of Squares），反 映样本观测值总体离差的大小；ESS为回归平方和 （Explained Sum of Squares），反映由模型中 解释变量所解释的那部分离差的大小；RSS为残差 平方和（Residual Sum of Squares），反映样本 观测值与估计值偏离的大小，也是模型中解释变 量未解释的那部分离差的大小。 TSS y y ESS y y RSS y y i i i i = − = − = − ( ) ( ) ( ) 2 2 2
既然ESS反映样本观测值与估计值偏离的大小,可 否直接用它作为拟合优度检验的统计量? 不行 统计量必须是相对量 TSS、ESS、RSS之间的关系 TSS=RSS+ESS
• 既然ESS反映样本观测值与估计值偏离的大小，可 否直接用它作为拟合优度检验的统计量？ 不行 统计量必须是相对量 • TSS、ESS、RSS之间的关系 TSS=RSS+ESS
3、一个有趣的现象 (y2-y)=(y-j)+(-y) (y-y)2≠(y1-y)2+(y1-y) ∑(y-y)2=X(7-)2+X(-y 矛盾吗?可能吗?
3、一个有趣的现象 • 矛盾吗？可能吗？ ( ) ( ˆ ) ( ˆ ) i i i i i y − y = y − y + y − y 2 2 2 ( y y) ( y y ˆ ) ( y ˆ y) i − = i − i + i − 2 2 2 ( ) ( ˆ ) ( ˆ ) i i i i i y − y y − y + y − y