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

F-statistic 0.299395 Prob. F(2,28) 0.7436

Obs*R-squared 0.649065 Prob. Chi-Square(2) 0.7229 Scaled explained SS 1.798067 Prob. Chi-Square(2) 0.4070

Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/24/15 Time: 16:34 Sample: 1 31 Included observations: 31 Collinear test regressors dropped from specification

Variable Coefficient Std. Error t-Statistic Prob. C 61927.89 1045682. 0.059222 0.9532 WGT^2 -593927.9 1173622. -0.506064 0.6168 X*WGT^2 282.4407 747.9780 0.377606 0.7086

R-squared 0.020938 Mean dependent var 269442.8

Adjusted R-squared -0.048995 S.D. dependent var 689166.5 S.E. of regression 705847.6 Akaike info criterion 29.86395 Sum squared resid 1.40E+13 Schwarz criterion 30.00273 Log likelihood -459.8913 Hannan-Quinn criter. 29.90919 F-statistic 0.299395 Durbin-Watson stat 1.922336 Prob(F-statistic) 0.743610

从上可知，nR2=0.649065，比较计算的统计量的临界值，因为nR2=0.649065<（2）=5.9915，所以接受原假设，该模型消除了异方差。

估计结果为：

Y=1.425859X-334.8131

t=（11.97157）（-0.972298）

R2=0.875855 F=143.3184 DW=1.369081

0.05

②用权数w2=1/x2,用回归分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 16:40 Sample: 1 31 Included observations: 31 Weighting series: W2

Variable Coefficient Std. Error t-Statistic Prob. X 1.557040 0.145392 10.70922 0.0000 C -693.1946 376.4760 -1.841272 0.0758 Weighted Statistics R-squared 0.798173 Mean dependent var 3635.028

Adjusted R-squared 0.791214 S.D. dependent var 1029.830 S.E. of regression 466.8513 Akaike info criterion 15.19224 Sum squared resid 6320554. Schwarz criterion 15.28475 Log likelihood -233.4797 Hannan-Quinn criter. 15.22240 F-statistic 114.6875 Durbin-Watson stat 1.562975 Prob(F-statistic) 0.000000

Unweighted Statistics R-squared 0.834850 Mean dependent var 4443.526

Adjusted R-squared 0.829156 S.D. dependent var 1972.072 S.E. of regression 815.1229 Sum squared resid 19268334 Durbin-Watson stat 1.678365

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

F-statistic 0.299790 Prob. F(3,27) 0.8252

Obs*R-squared 0.999322 Prob. Chi-Square(3) 0.8014 Scaled explained SS 1.789507 Prob. Chi-Square(3) 0.6172

Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/24/15 Time: 16:45 Sample: 1 31 Included observations: 31

Variable Coefficient Std. Error t-Statistic Prob. C -111661.8 549855.7 -0.203075 0.8406 WGT^2 426220.2 2240181. 0.190262 0.8505 X^2*WGT^2 0.194888 0.516395 0.377402 0.7088 X*WGT^2 -583.2151 2082.820 -0.280012 0.7816

R-squared 0.032236 Mean dependent var 203888.8

Adjusted R-squared -0.075293 S.D. dependent var 419282.0 S.E. of regression 434780.1 Akaike info criterion 28.92298 Sum squared resid 5.10E+12 Schwarz criterion 29.10801 Log likelihood -444.3062 Hannan-Quinn criter. 28.98330 F-statistic 0.299790 Durbin-Watson stat 1.835854 Prob(F-statistic) 0.825233

2

从上可知，nR=0.999322，比较计算的统计量的临界值，因为nR2=0.999322<（2）=5.9915，所以接受原假设，该模型消除了异方差。 估计结果为：

Y=1.557040X-693.1946

t=（10.70922）（-1.841272）

R2=0.798173 F=114.6875 DW=1.562975

0.05

③用权数w3=1/sqr（x）,用回归分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 16:49 Sample: 1 31 Included observations: 31 Weighting series: W3

Variable Coefficient Std. Error t-Statistic Prob. X 1.330130 0.098345 13.52507 0.0000 C -47.40242 313.1154 -0.151390 0.8807 Weighted Statistics R-squared 0.863161 Mean dependent var 4164.118

Adjusted R-squared 0.858442 S.D. dependent var 991.2079 S.E. of regression 586.9555 Akaike info criterion 15.65012 Sum squared resid 9990985. Schwarz criterion 15.74263 Log likelihood -240.5768 Hannan-Quinn criter. 15.68027 F-statistic 182.9276 Durbin-Watson stat 1.237664 Prob(F-statistic) 0.000000

Unweighted Statistics R-squared 0.890999 Mean dependent var 4443.526

Adjusted R-squared 0.887240 S.D. dependent var 1972.072 S.E. of regression 662.2171 Sum squared resid 12717412 Durbin-Watson stat 1.314859

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

F-statistic 0.423886 Prob. F(2,28) Obs*R-squared 0.911022 Prob. Chi-Square(2) Scaled explained SS 2.768332 Prob. Chi-Square(2)

Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/24/15 Time: 16:57 Sample: 1 31 Included observations: 31 Collinear test regressors dropped from specification

Variable Coefficient Std. Error t-Statistic C 1212308. 2141958. 0.565981 WGT^2 -715673.0 1301839. -0.549740 X^2*WGT^2 -0.015194 0.082276 -0.184677

R-squared 0.029388 Mean dependent var

Adjusted R-squared -0.039942 S.D. dependent var S.E. of regression 880429.8 Akaike info criterion Sum squared resid 2.17E+13 Schwarz criterion Log likelihood -466.7426 Hannan-Quinn criter. F-statistic 0.423886 Durbin-Watson stat Prob(F-statistic) 0.658628

从上可知，nR2=0.911022，比较计算的

0.6586 0.6341 0.2505 Prob. 0.5759 0.5869 0.8548 322289.8 863356.7 30.30597 30.44475 30.35121 1.887426

0.05统计量的临界值，因为nR2=0.911022<（2）=5.9915，所以接受原假设，该模型消除了异方差。 估计结果为：

Y=1.330130X-47.40242

t=（13.52507）（-0.151390）

R2=0.863161 F=182.9276 DW=1.237664

经过检验发现，用权数w1的效果最好，所以综上可知，即修改后的结果为： Y=1.425859X-334.8131

t=（11.97157）（-0.972298）

R2=0.875855 F=143.3184 DW=1.369081