Durbin-Watson stat
1.177765 Prob(F-statistic)
0.000000
Y??351.1054?0.992813X1?1.356936X3
(-4.222527) ( 53.07196) ( 8.218410)
R2?0.999908 R?0.9998 F?92839.33 D.W?1.17776 59 82⑵异方差检验与修正
① 图示法
ee与X1的散点图如下：
200000160000120000EE800004000000100002000030000400005000060000X1 说明ee与X1存在单调递增型异方差性。
ee与X3的散点图如下：
200000160000120000EE80000400000020004000X360008000 说明ee与X3存在单调递增型异方差性。 ②G-Q检验
对20组数据剔除掉中间四组剩下的进行分组后， 第一组（1990-1997）数据的回归结果：
Dependent Variable: Y Method: Least Squares Date: 11/30/11 Time: 12:54 Sample: 1990 1997 Included observations: 8
Variable X1 X3 C
R-squared Adjusted R-squared
Coefficient 0.984123 0.851518 -28.34275
Std. Error 0.016255 0.156688 45.36993
t-Statistic 60.54320 5.434472 -0.624703
Prob. 0.0000 0.0029 0.5596 5179.791 2099.840
0.999686 Mean dependent var 0.999560 S.D. dependent var
S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
44.05899 Akaike info criterion 9705.972 Schwarz criterion -39.75573 F-statistic 1.663630 Prob(F-statistic)
10.68893 10.71872 7947.575 0.000000
残差平方和RSS1=9705.972 第二组（2002-2009）数据的回归结果：
Dependent Variable: Y Method: Least Squares Date: 11/30/11 Time: 12:55 Sample: 2002 2009 Included observations: 8
Variable X1 X3 C
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 1.066404 0.847228 -1184.159
Std. Error 0.027747 0.215114 261.8258
t-Statistic 38.43321 3.938503 -4.522698
Prob. 0.0000 0.0110 0.0063 39824.41 18639.16 13.52594 13.55573 36705.08 0.000000
0.999932 Mean dependent var 0.999905 S.D. dependent var 182.0047 Akaike info criterion 165628.5 Schwarz criterion -51.10375 F-statistic 1.326122 Prob(F-statistic)
残差平方和RSS2= 165628.5
所以F= RSS2/RSS1= 165628.5/9705.972=17.0646 在给定?=5%下查得临界值 F0.05(4,4)?6.39，F?F0.05(4,4)
因此否定两组子样方差相同的假设，从而该总体随机项存在递增异方差性。 ③White 方法检验
White Heteroskedasticity Test: F-statistic Obs*R-squared
6.142010 Probability 12.41812 Probability
0.003919 0.014498
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares Date: 11/30/11 Time: 13:21 Sample: 1990 2009 Included observations: 20
Variable C X1 X1^2 X3 X3^2
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 24856.50 -20.57327 0.000212 237.1813 -0.024073
Std. Error 19211.30 7.549127 8.04E-05 78.61323 0.006568
t-Statistic 1.293848 -2.725252 2.639982 3.017067 -3.665230
Prob. 0.2153 0.0156 0.0186 0.0087 0.0023 34743.00 49156.00 23.92212 24.17105 6.142010 0.003919
0.620906 Mean dependent var 0.519815 S.D. dependent var 34062.86 Akaike info criterion 1.74E+10 Schwarz criterion -234.2212 F-statistic 1.560937 Prob(F-statistic)
n?R2?20?0.620906?12.41812
?=5%下，临界值?20.05(4)?9.488拒绝同方差性
④
修正
Coefficient -314.2074 0.979758 1.457291
Std. Error 43.68550 0.008622 0.065922
t-Statistic -7.192486 113.6336 22.10629
Prob. 0.0000 0.0000 0.0000 27246.27 74471.17 11.58127
Dependent Variable: Y Method: Least Squares Date: 11/30/11 Time: 14:29 Sample: 1990 2009 Included observations: 20 Weighting series: 1/E1
Variable C X1 X3
R-squared Adjusted R-squared S.E. of regression
Weighted Statistics
0.999999 Mean dependent var 0.999999 S.D. dependent var 73.91795 Akaike info criterion
Sum squared resid 92885.67 Schwarz criterion 11.73063 Log likelihood -112.8127 F-statistic 3138195. Durbin-Watson stat
0.956075 Prob(F-statistic) 0.000000
Unweighted Statistics
R-squared 0.999902 Mean dependent var 20556.75 Adjusted R-squared 0.999891 S.D. dependent var 19987.03 S.E. of regression 209.0283 Sum squared resid 742778.2
Durbin-Watson stat
1.365483
Y??314.2074?0.979758X1?1.457291X3
(-7.192486) ( 113.6336) ( 22.10629)
R2?0.999999 R2?0.9999 9 9F?313819 5 D.W?1.36548 3⑶序列相关性检验
①从残差项e2与e2(-1)及e与时间t的关系图（如下）看，随机项呈现正序列相关性。
6004002001)-2(0E-200-400-600-600-400-2000200400600E2