?2?n?ce/?k?2i??2?? = 5.912306
求F统计量为 F=
?2?n?ce?k??1i/??2?n?c?n?c?给定??0.05，查F分布表，得临界值为F?k，?k?? = 3.79 （?）?22?c.比较临界值与F统计量值，有F=5.912306 ﹥F(?)=3.79 ，说明该模型的随机误差项存在异方差。
修正异方差
在运用加权最小二乘法估计过程中，分别选用了权数?1t=1/Xt，?2t=1/Xt，?3t=1/Xt。 1、在“Workfile”页面：点击“Generate”，输入“w1=1/x”—OK ；同样的输入“w2=1/x^2” “w3=1/sqr(x)”；
2、在“Equation”页面：点击“Estimate Equation”,输入“y c x”,点击“weighted”,输入“w1”,出现如图6：
Dependent Variable: Y Method: Least Squares Date: 11/01/10 Time: 12:31 Sample: 1985 2007 Included observations: 23 Weighting series: W1
Variable C X2
R-squared
Coefficient
75342.48 0.861496
Std. Error
1955.930 0.087308
t-Statistic
38.52002 9.867306
Prob.
0.0000 0.0000
102600.2 77372.86 21.20823 21.30697 97.36373 0.000000
139364.6 51705.05
2 Weighted Statistics
0.986045 Mean dependent var 0.985380 S.D. dependent var 9355.386 Akaike info criterion 1.84E+09 Schwarz criterion -241.8947 F-statistic 0.269103 Prob(F-statistic)
Unweighted Statistics
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
R-squared
0.925702 Mean dependent var 0.922164 S.D. dependent var
Adjusted R-squared
S.E. of regression Durbin-Watson stat
Dependent Variable: Y Method: Least Squares
14425.26 Sum squared resid 0.141803
4.37E+09
Coefficient
61583.22 1.867721
Std. Error
2022.139 0.173762
t-Statistic
30.45449 10.74873
Prob.
0.0000 0.0000
89007.62 134618.1 20.27121 20.36995 115.5353 0.000000
Date: 11/01/10 Time: 12:33 Sample: 1985 2007 Included observations: 23 Weighting series: W2
Variable C X2
R-squared
Weighted Statistics
0.998194 Mean dependent var 0.998108 S.D. dependent var 5855.843 Akaike info criterion 7.20E+08 Schwarz criterion -231.1189 F-statistic 0.389451 Prob(F-statistic)
Unweighted Statistics
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
R-squared
139364.6 51705.05 2.63E+11
-3.468653 Mean dependent var -3.681446 S.D. dependent var 111872.4 Sum squared resid 0.023839
Adjusted R-squared S.E. of regression Durbin-Watson stat
Dependent Variable: Y Method: Least Squares
Coefficient
Std. Error
t-Statistic
Prob. Date: 11/01/10 Time: 12:34 Sample: 1985 2007 Included observations: 23 Weighting series: W3
Variable
C X2
R-squared
79134.39 0.741651
2101.452 0.041457
37.65700 17.88981
0.0000 0.0000
117941.4 26545.81 21.10572 21.20446 320.0453 0.000000
Weighted Statistics
0.892994 Mean dependent var 0.887898 S.D. dependent var 8887.964 Akaike info criterion 1.66E+09 Schwarz criterion -240.7158 F-statistic 0.251182 Prob(F-statistic)
Unweighted Statistics
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
R-squared
139364.6 51705.05 1.87E+09
0.968188 Mean dependent var 0.966673 S.D. dependent var 9439.115 Sum squared resid 0.303249
Adjusted R-squared S.E. of regression Durbin-Watson stat
?= 75342.48 + 0.861496 X 用权数?1t的估计结果为： Yii（38.52002） （9.867306）
R2= 0.986045 DW= 0.269103 F=97.36373
括号中的数据为t统计量值。
由上可以看出，运用加权最小二乘法消除了异方差后，参数?2的t检验显著，可决系数提高了不少，F检验也显著，并说明销售收入每增长1元，销售利润平均增长0.861496元。
这说明在其他因素不变的情况下，当国民收入每上升1%时，能源消费就平均增加0.23585%。
Dependent Variable: Y Method: Least Squares Date: 11/01/10 Time: 12:31 Sample: 1985 2007 Included observations: 23 Weighting series: W1
Variable C
Coefficient
75342.48
Std. Error
1955.930
t-Statistic
38.52002
Prob.
0.0000
X2
R-squared
0.861496 0.087308 9.867306
0.0000
102600.2 77372.86 21.20823 21.30697 97.36373 0.000000
Weighted Statistics
0.986045 Mean dependent var 0.985380 S.D. dependent var 9355.386 Akaike info criterion 1.84E+09 Schwarz criterion -241.8947 F-statistic 0.269103 Prob(F-statistic)
Unweighted Statistics
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
R-squared
139364.6 51705.05 4.37E+09
0.925702 Mean dependent var 0.922164 S.D. dependent var 14425.26 Sum squared resid 0.141803
Adjusted R-squared S.E. of regression Durbin-Watson stat
Dependent Variable: Y Method: Least Squares Date: 11/01/10 Time: 12:52 Sample: 1985 2007 Included observations: 23
Variable C X2
R-squared
Coefficient
79687.88 0.734835
Std. Error
3069.322 0.029027
t-Statistic
25.96270 25.31517
Prob.
0.0000 0.0000
139364.6 51705.05 21.22343 21.32217 640.8577 0.000000
0.968271 Mean dependent var 0.966760 S.D. dependent var 9426.750 Akaike info criterion 1.87E+09 Schwarz criterion -242.0695 F-statistic 0.304578 Prob(F-statistic)
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
N=23 , k=1 , dL=1.257 dU=1.437 DW=0.269103 正相关
30000025000020000020000100000-10000-2000086889092949698Actual0002040615000010000050000Residual
Dependent Variable: ET1 Method: Least Squares Date: 11/01/10 Time: 12:57 Sample (adjusted): 1986 2007
Included observations: 22 after adjustments
Variable C X2 ET1(-1)
R-squared
Coefficient
1162.307 -0.007452 0.824785
Fitted
Std. Error
1751.698 0.016204 0.118841
t-Statistic
0.663532 -0.459863 6.940220
Prob.
0.5150 0.6508 0.0000
437.7797 9178.547 20.04760 20.19638 24.18392 0.000006
0.717966 Mean dependent var 0.688279 S.D. dependent var 5124.568 Akaike info criterion 4.99E+08 Schwarz criterion -217.5236 F-statistic 0.782175 Prob(F-statistic)
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
0.824785
ls et1 c x2 et1(-1) 回归方程et1=0.824785et1(-1)
Y－0.824785Yt-1=(1－0.824785)p1＋（Xt－0.824785Xt-1）p2+vt
ls lny-0.824785*lny(-1) c lnx2-0.824785*lnx2(-1)
Dependent Variable: Y-0.824785*Y(-1) Method: Least Squares Date: 11/01/10 Time: 13:03 Sample (adjusted): 1986 2007
Included observations: 22 after adjustments
Variable C
X2-0.824785*X2(-1) R-squared
Coefficient
14784.99 0.722670
Std. Error
1699.579 0.055449
t-Statistic
8.699208 13.03305
Prob.
0.0000 0.0000
31999.94 15083.71 19.96536 20.06455 169.8604 0.000000
0.894659 Mean dependent var 0.889392 S.D. dependent var 5016.499 Akaike info criterion 5.03E+08 Schwarz criterion -217.6190 F-statistic 0.782158 Prob(F-statistic)
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
N=22 , k=1 , dL=1.239 dU=1.429 DW=0.782158 正相关
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