47853
0.99347904520.9937402677
90804 79564 41508
18469 44782 93492
18469 1 28471 80459
44782 28471 1 50381
93492 80459 0.8109403346
50381 1
0.85618358020.9862411656
0.87701448860.85563773470.8561835802
0.98360271980.98493529650.98624116560.8109403346
发现模型存在多重共线性。接下来运用逐步回归法对模型进行修正:
①将各个解释变量分别加入模型,进行一元回归: 作Y与X1的回归，结果如下:
Dependent Variable: Y Method: Least Squares Date: 11/22/11 Time: 23:02 Sample: 1990 2009 Included observations: 20
Variable C X1
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -755.6610 1.144994
Std. Error 145.2330 0.005760
t-Statistic -5.203094 198.7931
Prob. 0.0001 0.0000 20556.75 19987.03 15.09765 15.19722 39518.70 0.000000
0.999545 Mean dependent var 0.999519 S.D. dependent var 438.1521 Akaike info criterion 3455590. Schwarz criterion -148.9765 F-statistic 0.475046 Prob(F-statistic)
作Y与X2的回归，结果如下:
Dependent Variable: Y Method: Least Squares Date: 11/22/11 Time: 23:06 Sample: 1990 2009 Included observations: 20
Variable C X2
Coefficient -5222.077 0.207689
Std. Error 861.2067 0.005548
t-Statistic -6.063674 37.43267
Prob. 0.0000 0.0000
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
0.987317 Mean dependent var 0.986612 S.D. dependent var 2312.610 Akaike info criterion 96267005 Schwarz criterion -182.2478 F-statistic 0.188013 Prob(F-statistic)
20556.75 19987.03 18.42478 18.52435 1401.205 0.000000
作Y与X3的回归，结果如下:
Dependent Variable: Y Method: Least Squares Date: 11/22/11 Time: 23:08 Sample: 1990 2009 Included observations: 20
Variable C X3
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 2607.879 10.03073
Std. Error 773.9988 0.294311
t-Statistic 3.369358 34.08209
Prob. 0.0034 0.0000 20556.75 19987.03 18.60971 18.70929 1161.589 0.000000
0.984740 Mean dependent var 0.983893 S.D. dependent var 2536.645 Akaike info criterion 1.16E+08 Schwarz criterion -184.0971 F-statistic 1.194389 Prob(F-statistic)
作Y与X4的回归，结果如下:
Dependent Variable: Y Method: Least Squares Date: 11/22/11 Time: 23:08 Sample: 1990 2009 Included observations: 20
Variable C X4
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -272959.3 4.097403
Std. Error 37203.65 0.518467
t-Statistic -7.336894 7.902918
Prob. 0.0000 0.0000 20556.75 19987.03 21.29492 21.39449 62.45611 0.000000
0.776276 Mean dependent var 0.763846 S.D. dependent var 9712.824 Akaike info criterion 1.70E+09 Schwarz criterion -210.9492 F-statistic 0.157356 Prob(F-statistic)
②依据可决系数最大的原则选取X1作为进入回归模型的第一个解释变量,再依次将其余变量分别代入回归得:
作Y与X1、X2的回归，结果如下
Dependent Variable: Y Method: Least Squares Date: 11/22/11 Time: 23:09 Sample: 1990 2009 Included observations: 20
Variable C X1 X2
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -188.4285 1.281594 -0.025055
Std. Error 239.0743 0.049472 0.009029
t-Statistic -0.788159 25.90568 -2.774908
Prob. 0.4415 0.0000 0.0130 20556.75 19987.03 14.82405 14.97341 27118.20 0.000000
0.999687 Mean dependent var 0.999650 S.D. dependent var 374.0345 Akaike info criterion 2378330. Schwarz criterion -145.2405 F-statistic 0.683510 Prob(F-statistic)
作Y与X1、X3的回归，结果如下
Dependent Variable: Y Method: Least Squares Date: 11/22/11 Time: 23:10 Sample: 1990 2009 Included observations: 20
Variable C X1 X3
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -351.1054 0.992813 1.356936
Std. Error 83.15053 0.018707 0.165109
t-Statistic -4.222527 53.07196 8.218410
Prob. 0.0006 0.0000 0.0000 20556.75 19987.03 13.59361 13.74297 92839.33 0.000000
0.999908 Mean dependent var 0.999898 S.D. dependent var 202.1735 Akaike info criterion 694859.9 Schwarz criterion -132.9361 F-statistic 1.177765 Prob(F-statistic)
作Y与X1、X4的回归，结果如下
Dependent Variable: Y Method: Least Squares Date: 11/22/11 Time: 23:10 Sample: 1990 2009 Included observations: 20
Variable C X1 X4
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 11853.46 1.185886 -0.186645
Std. Error 1824.522 0.006645 0.026984
t-Statistic 6.496748 178.4608 -6.917003
Prob. 0.0000 0.0000 0.0000 20556.75 19987.03 13.85886 14.00822 71206.90 0.000000
0.999881 Mean dependent var 0.999867 S.D. dependent var 230.8464 Akaike info criterion 905931.0 Schwarz criterion -135.5886 F-statistic 1.459938 Prob(F-statistic)
③在满足经济意义和可决系数的条件下选取X3作为进入模型的第二个解释变量,再次进行回归则:
作Y与X1、X3、X2的回归，结果如下
Dependent Variable: Y Method: Least Squares Date: 11/22/11 Time: 23:13 Sample: 1990 2009 Included observations: 20
Variable C X1 X3 X2
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood
Coefficient -76.04458 1.085924 1.210853 -0.014073
Std. Error 100.1724 0.029801 0.133444 0.003944
t-Statistic -0.759137 36.43881 9.073877 -3.567901
Prob. 0.4588 0.0000 0.0000 0.0026 20556.75 19987.03 13.10826 13.30741 104602.9
0.999949 Mean dependent var 0.999939 S.D. dependent var 155.5183 Akaike info criterion 386975.0 Schwarz criterion -127.0826 F-statistic
Durbin-Watson stat
1.196933 Prob(F-statistic)
0.000000
作Y与X1、X3、X4的回归，结果如下 Dependent Variable: Y Method: Least Squares Date: 11/22/11 Time: 23:13 Sample: 1990 2009 Included observations: 20
Variable C X1 X3 X4
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 6781.764 1.068642 0.891069 -0.107639
Std. Error 1024.745 0.014514 0.107949 0.015451
t-Statistic 6.618003 73.62764 8.254551 -6.966675
Prob. 0.0000 0.0000 0.0000 0.0000 20556.75 19987.03 12.29900 12.49814 234970.9 0.000000
0.999977 Mean dependent var 0.999973 S.D. dependent var 103.7654 Akaike info criterion 172276.1 Schwarz criterion -118.9900 F-statistic 1.451447 Prob(F-statistic)
④可见加入其余任何一个变量都会导致系数符号与经济意义不符,故最终修正后的回归模型为:
Dependent Variable: Y Method: Least Squares Date: 11/30/11 Time: 12:18 Sample: 1990 2009 Included observations: 20
Variable C X1 X3
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood
Coefficient -351.1054 0.992813 1.356936
Std. Error 83.15053 0.018707 0.165109
t-Statistic -4.222527 53.07196 8.218410
Prob. 0.0006 0.0000 0.0000 20556.75 19987.03 13.59361 13.74297 92839.33
0.999908 Mean dependent var 0.999898 S.D. dependent var 202.1735 Akaike info criterion 694859.9 Schwarz criterion -132.9361 F-statistic