计量经济学 - 庞皓 - 第三版课后答案(5)

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R-squared 0.875855 Mean dependent var 4443.526

Adjusted R-squared 0.871574 S.D. dependent var 1972.072 S.E. of regression 706.7236 Sum squared resid 14484289 Durbin-Watson stat 1.532908

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: 12/10/14 Time: 21:13 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，nR=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: 12/09/14 Time: 21:08 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: 12/10/14 Time: 21:29 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

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 ③用权数w3=1/sqr（x）,用回归分析得： Dependent Variable: Y Method: Least Squares Date: 12/09/14 Time: 21:35 Sample: 1 31 Included observations: 31 Weighting series: W3

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

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

Unweighted Statistics R-squared 0.890999 Mean dependent var

0.05

Prob. 0.0000 0.8807 4164.118 991.2079 15.65012 15.74263 15.68027 1.237664

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) 0.6586

Obs*R-squared 0.911022 Prob. Chi-Square(2) 0.6341 Scaled explained SS 2.768332 Prob. Chi-Square(2) 0.2505

Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/09/14 Time: 20:36 Sample: 1 31 Included observations: 31 Collinear test regressors dropped from specification

Variable Coefficient Std. Error t-Statistic Prob. C 1212308. 2141958. 0.565981 0.5759 WGT^2 -715673.0 1301839. -0.549740 0.5869 X^2*WGT^2 -0.015194 0.082276 -0.184677 0.8548

R-squared 0.029388 Mean dependent var 322289.8

Adjusted R-squared -0.039942 S.D. dependent var 863356.7 S.E. of regression 880429.8 Akaike info criterion 30.30597 Sum squared resid 2.17E+13 Schwarz criterion 30.44475 Log likelihood -466.7426 Hannan-Quinn criter. 30.35121 F-statistic 0.423886 Durbin-Watson stat 1.887426 Prob(F-statistic) 0.658628

从上可知，nR2=0.911022，比较计算的统计量的临界值，因为nR2=0.911022<0.05（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 5.6 (1)

a)用Eviews模型分析得： Dependent Variable: Y Method: Least Squares Date: 12/10/14 Time: 20:16 Sample: 1978 2011 Included observations: 34

Variable Coefficient Std. Error t-Statistic X 0.746241 0.019120 39.03027 C 92.55422 42.80529 2.162215 R-squared 0.979426 Mean dependent var

Adjusted R-squared 0.978783 S.D. dependent var S.E. of regression 173.1597 Akaike info criterion Sum squared resid 959497.2 Schwarz criterion Log likelihood -222.4566 Hannan-Quinn criter. F-statistic 1523.362 Durbin-Watson stat Prob(F-statistic) 0.000000

得回归模型为：

Y=0.746241 X+92.55422

b)检验是否存在异方差：

①用Goldfeld-Quanadt检验如下：

1）当定义区间为1-13时，由软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/11/14 Time: 11:47 Sample: 1 13 Included observations: 13

Variable Coefficient Std. Error t-Statistic X 0.967839 0.026879 36.00771 C -18.86861 8.963780 -2.104984 R-squared 0.991587 Mean dependent var

Adjusted R-squared 0.990823 S.D. dependent var S.E. of regression 12.17039 Akaike info criterion Sum squared resid 1629.301 Schwarz criterion Log likelihood -49.84742 Hannan-Quinn criter.

Prob. 0.0000 0.0382 1295.802 1188.791 13.20333 13.29311 13.23395 1.534491

Prob. 0.0000 0.0591 280.1377 127.0409 7.976527 8.063442 7.958662

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