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对此模型进行White检验： Heteroskedasticity Test: White

F-statistic 3.523832 Prob. F(5,28) 0.0135

Obs*R-squared 13.13158 Prob. Chi-Square(5) 0.0222 Scaled explained SS 12.14373 Prob. Chi-Square(5) 0.0329

Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 12/24/15 Time: 22:34 Sample: 1 34 Included observations: 34

Variable Coefficient Std. Error t-Statistic Prob. C 0.422872 0.273746 1.544759 0.1336 LNX 0.080712 0.031833 2.535502 0.0171 LNX^2 -0.003917 0.003037 -1.289564 0.2078 LNX*LNP -0.004955 0.005136 -0.964765 0.3429 LNP -0.254992 0.129858 -1.963631 0.0596 LNP^2 0.026470 0.012675 2.088390 0.0460 R-squared 0.386223 Mean dependent var 0.004813

Adjusted R-squared 0.276620 S.D. dependent var 0.007286 S.E. of regression 0.006197 Akaike info criterion -7.170690 Sum squared resid 0.001075 Schwarz criterion -6.901332 Log likelihood 127.9017 Hannan-Quinn criter. -7.078831 F-statistic 3.523832 Durbin-Watson stat 2.264261 Prob(F-statistic) 0.013502

从上图中可以看出，nR2=13.13158，比较计算的统计量的临界值，因为nR2=13.13158>

0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在

异方差，所以此模型没有消除异方差。

②当w1=1/x时，用软件分析如下： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 22:49 Sample: 1 34 Included observations: 34 Weighting series: W1

Variable Coefficient Std. Error t-Statistic X 0.723218 0.022965 31.49212 P 0.719506 0.141085 5.099795 C -44.72084 13.11268 -3.410502 Weighted Statistics R-squared 0.992755 Mean dependent var

Adjusted R-squared 0.992287 S.D. dependent var S.E. of regression 28.40494 Akaike info criterion Sum squared resid 25012.05 Schwarz criterion Log likelihood -160.4567 Hannan-Quinn criter. F-statistic 2123.843 Durbin-Watson stat Prob(F-statistic) 0.000000

Unweighted Statistics R-squared 0.977704 Mean dependent var

Adjusted R-squared 0.976266 S.D. dependent var S.E. of regression 183.1446 Sum squared resid Durbin-Watson stat 1.740795

所得模型为：

Y=0.723218X+0.719506p-44.72084

Prob. 0.0000 0.0000 0.0018 457.8505 41.70384 9.615100 9.749779 9.661030 1.298389

1295.802 1188.791 1039800.

对此模型进行White检验得： Heteroskedasticity Test: White

F-statistic 2.088840 Prob. F(5,28) 0.0966

Obs*R-squared 9.236835 Prob. Chi-Square(5) 0.1000 Scaled explained SS 25.50696 Prob. Chi-Square(5) 0.0001

Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/24/15 Time: 22:50 Sample: 1 34 Included observations: 34 Collinear test regressors dropped from specification

Variable Coefficient Std. Error t-Statistic Prob. C 3861.793 1068.806 3.613183 0.0012 WGT^2 3260.199 4309.988 0.756429 0.4557 X*WGT^2 13.72241 8.453473 1.623287 0.1157 X*P*WGT^2 -0.151725 0.061588 -2.463567 0.0202 P^2*WGT^2 0.431162 0.278315 1.549186 0.1326 P*WGT^2 -76.13221 73.40636 -1.037134 0.3085

R-squared 0.271672 Mean dependent var 735.6486

Adjusted R-squared 0.141613 S.D. dependent var 1924.655 S.E. of regression 1783.177 Akaike info criterion 17.96897 Sum squared resid 89032169 Schwarz criterion 18.23832 Log likelihood -299.4724 Hannan-Quinn criter. 18.06082 F-statistic 2.088840 Durbin-Watson stat 2.336495 Prob(F-statistic) 0.096616

因为nR2=9.236835<0.05（5）=11.0705，所以接受原假设。该模型不存在异方差，所以此模型消除了异方差。

③当w2=1/x2，用软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 23:00 Sample: 1 34 Included observations: 34 Weighting series: W2

Variable Coefficient Std. Error t-Statistic X 0.639012 0.039216 16.29477 P 1.200751 0.206023 5.828234 C -81.85973 15.77499 -5.189209 Weighted Statistics R-squared 0.991614 Mean dependent var

Adjusted R-squared 0.991073 S.D. dependent var S.E. of regression 11.37136 Akaike info criterion Sum squared resid 4008.543 Schwarz criterion Log likelihood -129.3309 Hannan-Quinn criter. F-statistic 1832.775 Durbin-Watson stat Prob(F-statistic) 0.000000

Unweighted Statistics R-squared 0.956816 Mean dependent var

Adjusted R-squared 0.954030 S.D. dependent var S.E. of regression 254.8849 Sum squared resid Durbin-Watson stat 1.002870

所得模型为：

Y=0.639012X+1.200751p-81.85973

Prob. 0.0000 0.0000 0.0000 230.2433 247.1718 7.784170 7.918849 7.830100 1.167961

1295.802 1188.791 2013955.

对该模型进行White检验得： Heteroskedasticity Test: White

F-statistic 43.19853 Prob. F(6,27) 0.0000

Obs*R-squared 30.79235 Prob. Chi-Square(6) 0.0000 Scaled explained SS 47.42430 Prob. Chi-Square(6) 0.0000

Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/26/15 Time: 07:20 Sample: 1 34 Included observations: 34

Variable Coefficient Std. Error t-Statistic Prob. C 27.51002 20.12556 1.366919 0.1829 WGT^2 -1245.193 837.2352 -1.487268 0.1485 X^2*WGT^2 0.007732 0.005450 1.418649 0.1674 X*WGT^2 7.948582 4.884597 1.627275 0.1153 X*P*WGT^2 -0.111755 0.064061 -1.744525 0.0924 P^2*WGT^2 0.184342 0.164562 1.120199 0.2725 P*WGT^2 -3.127017 23.56724 -0.132685 0.8954

R-squared 0.905657 Mean dependent var 117.8983

Adjusted R-squared 0.884692 S.D. dependent var 230.3570 S.E. of regression 78.22224 Akaike info criterion 11.73823 Sum squared resid 165205.4 Schwarz criterion 12.05248 Log likelihood -192.5498 Hannan-Quinn criter. 11.84539 F-statistic 43.19853 Durbin-Watson stat 1.794799 Prob(F-statistic) 0.000000

因为nR2=30.79235>0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。