Sum squared resid Log likelihood Durbin-Watson stat R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat
5.69E+08 Schwarz criterion -209.4988 F-statistic 1.327333 Prob(F-statistic) Unweighted Statistics 20.24223 1103.241 0.000000 101966.4 81193.29 4.71E+09 0.964300 Mean dependent var 0.962421 S.D. dependent var 15739.48 Sum squared resid 0.107792 用权数w2的结果: Dependent Variable: Y Method: Least Squares Date: 05/27/10 Time: 19:12 Sample: 1988 2008 Included observations: 21 Weighting series: W2 Variable C X R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat
Coefficient 6391.108 29.93823 Std. Error 554.5822 0.619152 t-Statistic 11.52418 48.35358 Prob. 0.0000 0.0000 30182.36 20115.05 17.36831 17.46778 2338.069 0.000000 101966.4 81193.29 8.90E+09 Weighted Statistics 0.995616 Mean dependent var 0.995385 S.D. dependent var 1366.514 Akaike info criterion 35479839 Schwarz criterion -180.3672 F-statistic 2.119407 Prob(F-statistic) Unweighted Statistics 0.932483 Mean dependent var 0.928929 S.D. dependent var 21645.41 Sum squared resid 0.078262 用权数w3的结果: Dependent Variable: Y Method: Least Squares Date: 05/27/10 Time: 19:14 Sample: 1988 2008 Included observations: 21 Weighting series: W3 Variable C X R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat
Coefficient 13340.99 34.54781 Std. Error 2762.403 1.076811 t-Statistic 4.829488 32.08344 Prob. 0.0001 0.0000 76321.45 38571.85 21.07040 21.16988 1029.347 0.000000 Weighted Statistics 0.951671 Mean dependent var 0.949127 S.D. dependent var 8699.896 Akaike info criterion 1.44E+09 Schwarz criterion -219.2392 F-statistic 1.118407 Prob(F-statistic) Unweighted Statistics 101966.4 81193.29 2.98E+09 0.977429 Mean dependent var 0.976242 S.D. dependent var 12514.95 Sum squared resid 0.130199 从以上三种估计结果中知道,运用用权数w2的结果最好,运用用权数w2的
结果如下:
Y = 6391.107567 + 29.93823178*X
(11.52418) (48.35358)
R2=0.995616,DW=2.119407,F=2338.069 括号中数据为t统计量值。
可以看出运用加权最小二乘法消除了异方差性后,参数t检验均显著,可决系数大幅度提高,F检验也显著,并说明人均消费水平每增长1元,国内生产总值将增长29.93823178亿元。