计量经济学庞皓第二版第五章答案
5.2 (1) 对原模型OLS回归分析结果:
Dependent Variable: Y Method: Least Squares Date: 04/01/09 Time: 15:44 Sample: 1 60
Included observations: 60
Variable C X
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 9.347522 0.637069
Std. Error 3.638437 0.019903
t-Statistic 2.569104 32.00881
Prob. 0.0128 0.0000 119.6667 38.68984 7.272246 7.342058 1024.564 0.000000
0.946423 Mean dependent var 0.945500 S.D. dependent var 9.032255 Akaike info criterion 4731.735 Schwarz criterion -216.1674 F-statistic 1.790431 Prob(F-statistic)
(2)
White检验结果:
White Heteroskedasticity Test: F-statistic Obs*R-squared
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares Date: 04/01/09 Time: 15:45 Sample: 1 60
Included observations: 60
Variable C X X^2
R-squared
Adjusted R-squared S.E. of regression
Coefficient -10.03614 0.165977 0.001800
Std. Error 131.1424 1.619856 0.004587
t-Statistic -0.076529 0.102464 0.392469
Prob. 0.9393 0.9187 0.6962 78.86225 111.1375 12.14285
6.301373 Probability 10.86401 Probability
0.003370 0.004374
0.181067 Mean dependent var 0.152332 S.D. dependent var 102.3231 Akaike info criterion
Sum squared resid Log likelihood Durbin-Watson stat
596790.5 Schwarz criterion -361.2856 F-statistic 1.442328 Prob(F-statistic)
12.24757 6.301373 0.003370
nR2=10.86401, 查表得20.05(2)=5.99147,nR2>5.99147,所以拒绝原假设,表明模型中随机误差项存在异方差。 Goldfeld-Quandt检验:
Dependent Variable: Y Method: Least Squares Date: 04/01/09 Time: 16:16 Sample: 1 22
Included observations: 22
Variable C X
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 12.53695 0.605911
Std. Error 7.069578 0.063910
t-Statistic 1.773365 9.480730
Prob. 0.0914 0.0000 78.63636 12.56050 6.330594 6.429780 89.88424 0.000000
0.817990 Mean dependent var 0.808890 S.D. dependent var 5.490969 Akaike info criterion 603.0148 Schwarz criterion -67.63654 F-statistic 1.136382 Prob(F-statistic)
Dependent Variable: Y Method: Least Squares Date: 04/01/09 Time: 16:17 Sample: 39 60
Included observations: 22
Variable C X
R-squared
Adjusted R-squared S.E. of regression Sum squared resid
Coefficient -39.54393 0.841215
Std. Error 27.08272 0.113266
t-Statistic -1.460116 7.426927
Prob. 0.1598 0.0000 160.8182 21.13367 7.751033 7.850219
0.733898 Mean dependent var 0.720593 S.D. dependent var 11.17103 Akaike info criterion 2495.840 Schwarz criterion
Log likelihood Durbin-Watson stat
-83.26137 F-statistic 0.610587 Prob(F-statistic)
55.15924 0.000000
eF=e
2221
=2495.840/603.0148=4.139, 查得F0.05(20,20)=2.12,
4.139>2.12,则拒绝原假设,表明模型中随机误差项存在异方差。
(3) 加权最小二乘法修正异方差 W1=1/X
Dependent Variable: Y Method: Least Squares Date: 04/01/09 Time: 15:53 Sample: 1 60
Included observations: 60 Weighting series: W1
Variable C X
Weighted Statistics R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Unweighted Statistics R-squared
Adjusted R-squared S.E. of regression Durbin-Watson stat
Coefficient 10.37051 0.630950
Std. Error 2.629716 0.018532
t-Statistic 3.943587 34.04667
Prob. 0.0002 0.0000 106.2101 8.685376 6.973470 7.043281 15.55188 0.000219
119.6667 38.68984 4739.526
0.211441 Mean dependent var 0.197845 S.D. dependent var 7.778892 Akaike info criterion 3509.647 Schwarz criterion -207.2041 F-statistic 1.969805 Prob(F-statistic)
0.946335 Mean dependent var 0.945410 S.D. dependent var 9.039689 Sum squared resid 1.796748
White Heteroskedasticity Test: F-statistic Obs*R-squared
Test Equation:
Dependent Variable: STD_RESID^2 Method: Least Squares Date: 04/01/09 Time: 15:54 Sample: 1 60
Included observations: 60
Variable C X X^2
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 238.8363 -2.139584 0.005690
Std. Error 73.63191 0.909493 0.002575
t-Statistic 3.243652 -2.352502 2.209642
Prob. 0.0020 0.0221 0.0312 58.49412 59.49678 10.98844 11.09316 3.138491 0.050925
3.138491 Probability 5.951910 Probability
0.050925 0.050999
0.099198 Mean dependent var 0.067591 S.D. dependent var 57.45087 Akaike info criterion 188134.3 Schwarz criterion -326.6533 F-statistic 1.606243 Prob(F-statistic)
虽然White检验结果nR2=5.95191
Dependent Variable: Y Method: Least Squares Date: 04/01/09 Time: 15:55 Sample: 1 60
Included observations: 60 Weighting series: W2
Variable C X
Coefficient 10.12327 0.633029
Std. Error 2.755775 0.024590
t-Statistic 3.673475 25.74374
Prob. 0.0005 0.0000
Weighted Statistics R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Unweighted Statistics R-squared
Adjusted R-squared S.E. of regression Durbin-Watson stat
94.01206 41.02965 7.057130 7.126941 1451.660 0.000000
0.961581 Mean dependent var 0.960918 S.D. dependent var 8.111184 Akaike info criterion 3815.896 Schwarz criterion -209.7139 F-statistic 2.091305 Prob(F-statistic)
119.6667 38.68984 4735.444
0.946381 Mean dependent var 0.945457 S.D. dependent var 9.035795 Sum squared resid 1.795043
White Heteroskedasticity Test: F-statistic Obs*R-squared
Test Equation:
Dependent Variable: STD_RESID^2 Method: Least Squares Date: 04/01/09 Time: 15:56 Sample: 1 60
Included observations: 60
Variable C X X^2
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 735.7452 -7.380790 0.018132
Std. Error 89.80882 1.109309 0.003141
t-Statistic 8.192349 -6.653505 5.772821
Prob. 0.0000 0.0000 0.0000 63.59827 106.2429 11.38565 11.49037 39.31455 0.000000
39.31455 Probability 34.78417 Probability
0.000000 0.000000
0.579736 Mean dependent var 0.564990 S.D. dependent var 70.07281 Akaike info criterion 279881.3 Schwarz criterion -338.5696 F-statistic 1.520939 Prob(F-statistic)
虽然R2=0.9616,拟合优度很高,但Whit e检验结果nR2=34.78417>20.05(2)=5.99147,显示异方差仍存在,不是理想的结
果。 W3=1/X
Dependent Variable: Y Method: Least Squares Date: 04/01/09 Time: 15:57 Sample: 1 60
Included observations: 60 Weighting series: W3
Variable C X
Weighted Statistics R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Unweighted Statistics R-squared
Adjusted R-squared S.E. of regression Durbin-Watson stat
Coefficient 10.10908 0.632671
Std. Error 2.980789 0.018379
t-Statistic 3.391409 34.42341
Prob. 0.0013 0.0000 112.9123 18.33568 7.086817 7.156628 234.6742 0.000000
119.6667 38.68984 4735.718
0.801827 Mean dependent var 0.798411 S.D. dependent var 8.232480 Akaike info criterion 3930.877 Schwarz criterion -210.6045 F-statistic 1.874009 Prob(F-statistic)
0.946378 Mean dependent var 0.945454 S.D. dependent var 9.036056 Sum squared resid 1.795491
White Heteroskedasticity Test: F-statistic Obs*R-squared
Test Equation:
Dependent Variable: STD_RESID^2 Method: Least Squares Date: 04/01/09 Time: 15:57 Sample: 1 60
Included observations: 60
Variable
Coefficient
Std. Error
t-Statistic
Prob.
2.192831 Probability 4.286664 Probability
0.120928 0.117263
C X X^2
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
86.12439 -0.647230 0.002737
93.86113 1.159362 0.003283
0.917572 -0.558264 0.833779
0.3627 0.5789 0.4079 65.51461 74.70055 11.47392 11.57864 2.192831 0.120928
0.071444 Mean dependent var 0.038864 S.D. dependent var 73.23460 Akaike info criterion 305708.5 Schwarz criterion -341.2176 F-statistic 1.510631 Prob(F-statistic)
R2=0.8018,拟合优度很高,且各t检验也通过,
Whit e检验结果nR2=4.2867
ˆ10.109080.6327XY
t(3.3914)(34.4234)R0.8018
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5.4
(1) 对原模型OLS回归分析结果:
Dependent Variable: Y Method: Least Squares Date: 05/25/11 Time: 15:04 Sample: 1901 1931 Variable C R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -648.1236 Std. Error 118.1625 t-Statistic -5.485018 Prob. 0.0000 820.9407 13.92404 14.01655 300.7324 0.000000
0.912050 Mean dependent var 1250.323 0.909017 S.D. dependent var 247.6234 Akaike info criterion 1778203. Schwarz criterion -213.8226
F-statistic 0.911579 Prob(F-statistic)
(2) 检验
White检验结果:
White Heteroskedasticity Test: F-statistic 7.840687 Probability 0.001977 Whit e检验结果nR2=11.1288>20.05(2)=5.99147,显示存在异方差。
ARCH检验结果: P=1
F-statistic Obs*R-squared
6.172299 Probability 5.418686 Probability
0.019226 0.019922
ARCH检验结果(n-p)R2=5.4187>20.05(1)=3.841,显示存在异方差。 P=2
F-statistic 2.781654 Probability 0.080405 ARCH检验结果(n-p)R2=5.1115
ARCH Test: F-statistic Obs*R-squared
1.594897 Probability 4.654257 Probability
0.216709 0.198937
ARCH检验结果(n-p)R2=4.6543
(3) 加权最小二乘法修正异方差 W1=1/X
Dependent Variable: Y Method: Least Squares Date: 05/25/11 Time: 15:12 Sample: 1901 1931 Included observations: 31 Weighting series: W1
C X
R-squared
-722.5037 0.088139
72.36495 0.004372 -9.984166 20.15822 0.0000 0.0000 0.774641 Mean dependent var 894.6561
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat R-squared
Adjusted R-squared S.E. of regression 0.766870 S.D. dependent var 192.8008 Akaike info criterion 1077992. Schwarz criterion -206.0648 F-statistic 0.994618 Prob(F-statistic)
399.3095 13.42353 13.51605 99.68358 0.000000
0.910496 Mean dependent var 1250.323 0.907409 S.D. dependent var 249.8017 Sum squared resid 820.9407 1809626.
White Heteroskedasticity Test: F-statistic 1.002103 Probability 0.379894 虽然White检验结果nR2=2.0707
Dependent Variable: Y Method: Least Squares Date: 05/25/11 Time: 15:14 Sample: 1901 1931 Included observations: 31 Variable C Weighted Statistics R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat R-squared
Coefficient -652.4734
Std. Error 79.37501
t-Statistic -8.220136
Prob. 0.0000
0.010693 Mean dependent var 593.3507 -0.023421 S.D. dependent var 195.8941 Akaike info criterion 1112860. Schwarz criterion -206.5582 F-statistic 0.953349 Prob(F-statistic)
193.6396 13.45537 13.54788 0.313448 0.579871
0.908426 Mean dependent var 1250.323
Adjusted R-squared S.E. of regression Durbin-Watson stat
0.905269 S.D. dependent var 252.6729 Sum squared resid 0.882689
820.9407 1851464.
F-statistic Obs*R-squared
5.314130 Probability 8.529405 Probability
0.011055 0.014056
R2=0.0107,拟合优度很低,Whit
e检验结果
nR2=8.5294>20.05(2)=5.99147,显示异方差仍存在,不是理想的结果。
W3=1/X
Dependent Variable: Y Method: Least Squares Date: 05/25/11 Time: 15:15 Sample: 1901 1931 Included observations: 31 C R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Unweighted Statistics R-squared
Adjusted R-squared S.E. of regression Durbin-Watson stat
-706.6985 87.89896 -8.039896 0.0000 0.873482 Mean dependent var 1071.763 0.869119 S.D. dependent var 214.2931 Akaike info criterion 1331725. Schwarz criterion -209.3411 F-statistic
592.3382 13.63491 13.72742 200.2157
0.911182 Mean dependent var 1250.323 0.908119 S.D. dependent var 248.8427 Sum squared resid 0.892586
820.9407 1795757.
F-statistic
2.876158 Probability
0.073108
R2=0.8735,拟合优度很高,且各t检验也通过,
Whit e检验结果nR2=5.2832
ˆ706.69850.0873XY
t(8.0399)(20.1399)R0.8735
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