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1、第五章习题解答5.1 随机干扰项的异方差性可以看成与某个解释变量之间的函数关系，即请问：（1）这样做的理由是什么？（2）在异方差的检验中，是否也体现出这种利用函数关系的思想呢？答：（1）当异方差不为常数的时候，即为变量，自然可以看作为某个解释变量的函数。 （2）是的，在异方差检验中，也是利用了残差的绝对值或残差的平方来替代随机变量的方差，从而假设残差存在某种函数关系，由此可以判断异方差性。5.2 请问：产生异方差的原因是什么？答：请参阅教材。5.3 请问：如果模型存在异方差性，其后果是什么？OLS估计量是否还是BLUE?答：请参阅教材。5.4 表5.7给出了一个30户家庭的消费（Y）与收入（X
2、）数据。根据表中数据构建家庭消费与收入之间关系的简单线性回归模型：。请（1）用Goldfeld-Quandt检验和White检验对简单线性回归模型进行异方差性检验。（2）选用适当方法修正异方差，并给出修正后的模型。表5.7 假想消费（Y）与收入（X）数据（美元）YXYXYX5580741051522206510011016014421070851131501752458011012516518026079120108145135190841151151801402059813014022517826595140120200191270901251452401372307590130185189
3、250 数据来源：古扎拉蒂,计量经济学基础上册，第五版，中国人民大学出版社，2011，p.383.解：（1）Goldfeld-Quandt检验：先按照X从小到大进行排序，然后去掉中间的4个观测值，将样本分为两部分，容量为。回归结果如下：Dependent Variable: YMethod: Least SquaresDate: 08/05/13 Time: 05:04Sample: 1 13Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C3.4094298.7049240.3916670.7028
4、 X0.6967740.0743669.3695310.0000 R-squared0.888651 Mean dependent var83.5385 Adjusted R-squared0.878528 S.D. dependent var16.8009 S.E. of regression5.855582 Akaike info criterion6.5133 Sum squared resid377.1663 Schwarz criterion6.6002 Log likelihood-40.33649 Hannan-Quinn criter.6.4954 F-statistic87.
5、7881 Durbin-Watson stat2.1235 Prob(F-statistic)0.000001Dependent Variable: YMethod: Least SquaresDate: 08/05/13 Time: 05:13Sample: 18 30Included observations: 13VariableCoefficientStd. Errort-StatisticProb. C-28.0271730.64214-0.9146610.3800 X0.7941370.1315826.0353070.0001 R-squared0.768054 Mean depe
6、ndent var155.8462 Adjusted R-squared0.746969 S.D. dependent var23.4977 S.E. of regression11.81986 Akaike info criterion7.9181 Sum squared resid1536.8 Schwarz criterion8.0050 Log likelihood-49.4675 Hannan-Quinn criter.7.9002 F-statistic36.42493 Durbin-Watson stat1.4766 Prob(F-statistic)0.000085给定，查F分
7、布表得临界值为，从而拒绝原假设，模型存在异方差。注意：当给定，因此，不能拒绝同方差假定。White检验：对原模型做OLS回归，并在回归模型窗口内，选择View Residual tests heteroscedasticity tests White include White cross terms(打)。Heteroskedasticity Test: WhiteF-statistic2.917301 Prob. F(2,27)0.0713Obs*R-squared5.330902 Prob. Chi-Square(2)0.0696Scaled explained SS4.592566 P
8、rob. Chi-Square(2)0.1006Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 08/05/13 Time: 06:37Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-StatisticProb. C-12.29621191.7731-0.0641190.9493X0.1973852.368760.0833290.9342X20.00170.0067070.2535030.8018R-squared0.17
9、7697 Mean dependent var78.70511Adjusted R-squared0.116785 S.D. dependent var112.5823S.E. of regression105.8043 Akaike info criterion12.2557Sum squared resid302252.7 Schwarz criterion12.39582Log likelihood-180.8355 Hannan-Quinn criter.12.30052F-statistic2.917301 Durbin-Watson stat1.856573Prob(F-stati
10、stic)0.071274，在条件下，说明White检验不能检验模型异方差性。（2）取权数，得到修正模型为：Dependent Variable: YMethod: Least SquaresDate: 08/06/13 Time: 07:06Sample: 1 30Included observations: 30Weighting series: 1/XVariableCoefficientStd. Errort-StatisticProb. C10.279033.7827282.7173580.0112X0.631870.02665723.703410.0000 Weighted Sta
11、tisticsR-squared0.95253 Mean dependent var106.2583Adjusted R-squared0.950835 S.D. dependent var8.739846S.E. of regression7.912234 Akaike info criterion7.039038Sum squared resid1752.896 Schwarz criterion7.132451Log likelihood-103.5856 Hannan-Quinn criter.7.068922F-statistic561.8517 Durbin-Watson stat
12、1.906046Prob(F-statistic)0.00000 Unweighted StatisticsR-squared0.946556 Mean dependent var119.7333Adjusted R-squared0.944647 S.D. dependent var39.06134S.E. of regression9.190044 Sum squared resid2364.793Durbin-Watson stat1.585596 5.5 请对习题2.10建立的国际旅游收入对入境旅游人数的简单线性模型进行异方差性检验。解：由表2.15的数据得OLS回归模型：先用White检验法对模型进行异方差性检验。Heteroskedasticity Test: WhiteF-statistic5.514648 Prob. F(2,37)0.008Obs*R-squared9.185473 Prob. Chi-Square(2)0.0101Scaled explained SS74.53093 Prob. Chi-Square(2)0Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 08/05/13 Time: 07:09Sample: 1 40V
