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1、第五章习题答案演示一、数据如下：（表5.1）YX264877710592109099541311050812210979107119124061274750313499431142695881552289816730950176637791857581919635122221163170222880157824127165425604140026500182926760220028300201727430210529560160028150225032100242032500257035250172033500190036000210036200280028200二、数据输入EVIEWS软件，
2、注意输入过程中要定义e2“quick”菜单下“estimate equation”结果如下：（表5.2）Dependent Variable: YMethod: Least SquaresDate: 04/13/08 Time: 16:01Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. C-700.4110116.6679-6.0034580.0000X0.0878310.00482718.195750.0000R-squared0.919464 Mean dependent
3、var1266.452Adjusted R-squared0.916686 S.D. dependent var846.7570S.E. of regression244.4088 Akaike info criterion13.89790Sum squared resid1732334. Schwarz criterion13.99042Log likelihood-213.4175 F-statistic331.0852Durbin-Watson stat1.089829 Prob(F-statistic)0.000000最小二乘估计结果如下:Estimation Command:=LS
4、Y C XEstimation Equation:=Y = C(1) + C(2)*XSubstituted Coefficients:=Y = -700.4109607 + 0.08783115594*X三、检验模型的异方差：（一）图形法1、EViews软件操作。由路径：Quick/Qstimate Equation，进入Equation Specification窗口，键入“y c x”，确认并“ok”，得样本回归估计结果，见表5.2。（1） 生成残差平方序列。在得到表5.2估计结果后，回到以下界面：点击“procs”下的“generate series”菜单，输入公式“e2=(resid
5、)2”回到以下界面（e2已经生成，即残差序列生成）：（2） 在该界面下：单击“views”菜单下的“multple graphs”下的“scatter”, 操作如下： （3） 显示结果如下（图5.1）：（4）从图5.3分析可知：大致看出残差平方随的变动呈增大的趋势，因此，模型很可能存在异方差。但是否确实存在异方差还应通过更进一步的检验。（二）Goldfeld-Quanadt检验1、EViews软件操作。（1）对变量取值排序（按递增或递减）。在Procs菜单里选Sort Series命令，出现排序对话框，如果以递增型排序，选Ascenging，如果以递减型排序，则应选Descending，键入X
6、，点ok。本例选递增型排序，这时变量Y与X将以X按递增型排序。（2）构造子样本区间，建立回归模型。在本例中，样本容量n=31，删除中间1/4的观测值，即大约9个观测值，余下部分平分得两个样本区间：111和2131，它们的样本个数均是11个，即。由路径：Quick/Qstimate Equation，进入Equation Specification窗口，键入“y c x”，确认并“ok”，得样本回归估计结果，(注意：sample:1 11)（表5.3）Dependent Variable: YMethod: Least SquaresDate: 04/13/08 Time: 22:26Sampl
7、e: 1 11Included observations: 11VariableCoefficientStd. Errort-StatisticProb. C-744.6351195.4108-3.8106140.0041X0.0882580.0157055.6196190.0003R-squared0.778216 Mean dependent var331.3636Adjusted R-squared0.753574 S.D. dependent var260.8157S.E. of regression129.4724 Akaike info criterion12.72778Sum s
8、quared resid150867.9 Schwarz criterion12.80012Log likelihood-68.00278 F-statistic31.58011Durbin-Watson stat1.142088 Prob(F-statistic)0.000326Estimation Command:=LS Y C XEstimation Equation:=Y = C(1) + C(2)*XSubstituted Coefficients:=Y = -744.6350676 + 0.08825777732*X由路径：Quick/Qstimate Equation，进入Equ
9、ation Specification窗口，键入“y c x”，确认并“ok”，得样本回归估计结果，(注意：sample:21 31)注意：期间是21 31输出结果如下(表5.4)：Dependent Variable: YMethod: Least SquaresDate: 04/14/08 Time: 10:27Sample: 21 31Included observations: 11VariableCoefficientStd. Errort-StatisticProb. C666.3811911.25850.7312760.4832X0.0457790.0278981.6409710
10、.1352R-squared0.230295 Mean dependent var2152.909Adjusted R-squared0.144772 S.D. dependent var354.4462S.E. of regression327.7867 Akaike info criterion14.58557Sum squared resid966997.0 Schwarz criterion14.65791Log likelihood-78.22063 F-statistic2.692786Durbin-Watson stat2.743586 Prob(F-statistic)0.13
11、5222Estimation Command:=LS Y C XEstimation Equation:=Y = C(1) + C(2)*XSubstituted Coefficients:=Y = 666.3810693 + 0.04577902024*X（3）求F统计量值。基于表5.3和表5.4中残差平方和的数据，即Sum squared resid的值。由表5.3计算得到的残差平方和为，由表5.4计算得到的残差平方和为，根据Goldfeld-Quanadt检验，F统计量为 (5.1)（4）判断。在下，式（5.1）中分子、分母的自由度均为11，查F分布表得临界值为，因为，所以拒绝原假设，表
12、明模型确实存在异方差。（三）White检验由表5.2估计结果，按路径view/residual tests/white heteroskedasticity（no cross terms or cross terms），进入White检验。根据White检验中辅助函数的构造，最后一项为变量的交叉乘积项，因为本例为一元函数，故无交叉乘积项，因此应选no cross terms，则辅助函数为 （5.2）经估计出现White检验结果，见表5.5。从表5.5可以看出，由White检验知，在下，查分布表,得临界值（在（5.2）式中只有两项含有解释变量，故自由度为2），比较计算的统计量与临界值，因为，所以
13、拒绝原假设，不拒绝备择假设，表明模型存在异方差。表5.5White Heteroskedasticity Test:F-statistic5.819690 Probability0.007699Obs*R-squared9.102584 Probability0.010554Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 04/14/08 Time: 11:02Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-Statist
14、icProb. C19975.9882774.930.2413290.8111X-2.1986328.094419-0.2716230.7879X20.0001460.0001760.8300460.4135R-squared0.293632 Mean dependent var55881.73Adjusted R-squared0.243177 S.D. dependent var77875.67S.E. of regression67748.39 Akaike info criterion25.17675Sum squared resid1.29E+11 Schwarz criterion
15、25.31553Log likelihood-387.2397 F-statistic5.819690Durbin-Watson stat2.580140 Prob(F-statistic)0.007699四、异方差性的修正 （一）加权最小二乘法（WLS）在运用WLS法估计过程中，我们分别选用了权数。权数的生成过程如下，由图5.4，的主菜单中点击“quick”下的“Estimation Equation”键，输入公式：Y C X,同时，点击“option”键，在菜单中“weight”后面的空白处输入“1/X”,点击该键，输入权重权重:可赋予不同形式，目标是消除异方差下面仅给出用权数W1t的结果
16、。Dependent Variable: YMethod: Least SquaresDate: 04/25/08 Time: 22:28Sample: 1 31Included observations: 31Weighting series: 1/XVariableCoefficientStd. Errort-StatisticProb. C-742.468471.91567-10.324150.0000X0.0897510.00434720.646960.0000Weighted StatisticsR-squared0.786117 Mean dependent var903.0766
17、Adjusted R-squared0.778742 S.D. dependent var406.6195S.E. of regression191.2661 Akaike info criterion13.40755Sum squared resid1060899. Schwarz criterion13.50006Log likelihood-205.8170 F-statistic426.2970Durbin-Watson stat1.081175 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.919023 Mean d
18、ependent var1266.452Adjusted R-squared0.916231 S.D. dependent var846.7570S.E. of regression245.0763 Sum squared resid1741810.Durbin-Watson stat1.074712基于上述结果的E残差WHITE检验White Heteroskedasticity Test:F-statistic0.986241 Probability0.385562Obs*R-squared2.040103 Probability0.360576Test Equation:Dependen
19、t Variable: STD_RESID2Method: Least SquaresDate: 06/03/11 Time: 08:47Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb. C110552.854963.862.0113730.0540X-7.3424685.374822-1.3660860.1828X20.0001510.0001171.2934010.2064R-squared0.065810 Mean dependent var34222.55Adjusted R-squared-0.000918 S.D. dependent var44965.37S.E. of regression44986.00 Akaike info criterion24.35786Sum squared resid5.67E+10 Schwarz criterion24.49663Log likelihood-374.5468 F-statistic0.986241Durbin-Watson stat1.733930 Prob(F-statistic)0.385562TR2=31*0.065810=2.04011X2(g),结果表明，加权最小二乘法后为同方差。