(完整版)EViews计量经济学实验报告-异方差的诊断及修正模板

1、姓名 学号实验题目异方差的诊断与修正一、实验目的与要求：要求目的：1、用图示法初步判断是否存在异方差，再用 White检验异方差；2、用加权最小二乘法修正异方差。二、实验内容根据1998年我国重要制造业的销售利润与销售收入数据，运用EV软件，做回归分析，用图示法，White检验模型是否存在异方差， 如果存在异方差，运用加权最小二乘法修正异方差。三、实验过程：（实践过程、实践所有参数与指标、理论依据说明等）（一） 模型设定为了研究我国重要制造业的销售利润与销售收入是否有关，假定销售利润与销售收入之间满足线性约束，则理论模型设定为：Yi= 1+ 2Xi+ i其中，Y表示销售利润，Xi表示销售收入。

2、由1998年我国重要制造业的销售收入与销售利润的数据，如图1:1988年我国重要制造业销售收入与销售利润的数据（单位：亿元）行业名称销售利润Y销售收入X食品加工业187.253180.44食品制造业111.421119.88饮料制造业205.421489.89烟草加工业183.871328.59纺织业316.793862.9服装制造业157.71779.1皮革羽绒制品81.731081.77木材加工业35.67443.74家具制造业31.06226.78造纸及纸制品134.41124.94印刷业90.12499.83文教体育用品54.4504.44石油加工业194.452363.8化学原料制品

3、502.614195.22医药制造业238.711264.1化学纤维制造81.57779.46橡胶制品业77.84692.08塑料制品业144.341345非金属矿制业339.262866.14黑色金属冶炼367.473868.28有色金属冶炼144.291535.16金属制品业201.421948.12普通机械制造354.692351.68专用设备制造238.161714.73交通运输设备511.944011.53电子机械制造409.833286.15电子通信设备508.154499.19仪器仪表设备72.46663.68(二)参数估计Dependent Variable: YMethod:

4、 Least SquaresDate: 10/19/05 Time: 15:27Sample: 1 28Included observations: 28VariableCoefficientStd. Errort-StatisticProb.C12.0356419.517790.6166500.5428X0.1043930.00844112.366700.0000R-squared0.854696Mean dependent var213.4650Adjusted R-squared0.849107S.D. dependent var146.4895S.E. of regression56.

5、90368Akaike info criterion10.98935Sum squared resid84188.74Schwarz criterion11.08450Log likelihood-151.8508F-statistic152.9353Durbin-Watson stat1.212795Prob(F-statistic)0.000000估计结果为：Y? = 12.03564 + 0.104393 Xi(19.51779 ) (0.008441) t= (0.616650 )(12.36670 )R 2=0.854696R2 =0.849107 S.E.=56.89947 DW=

6、1.212859 F=152.9353这说明在其他因素不变的情况下，销售收入每增长 1元，销售利润平均增长0.104393元。2R =0.854696 ,拟合程度较好。在给定 =0.0 时，t=12.36670 > t0.025(26) =2.056，拒绝原假设，说明销售收入对销售利润有显著性影响。F=152.9353 > F0.05（1,26） = 4.23 ,表明方程整体显著。（三）检验模型的异方差 X （一）图形法600500400Y 300200010002000300040005000X100 06、判断由图3可以看出，被解释变量 Y随着解释变量 X的增大而逐渐分散，离散

7、程度越来越大；同样，由图4可以看出，残差平方 e2对解释变量X的散点图主要分布在图形中的下三角部分，大致看出残差平方 02随Xi的变动呈增大趋势。 因此，模型很可能存在异方差。 但是否确实存在异方差还应该通过更近一步的检验。X （二）White 检验White检验结果2t = 0 + 1 Xt+ 2 XtWhite Heteroskedasticity Test:F-statisticObs*R-squared3.6072186.270612ProbabilityProbability0.0420360.043486Test Equation:Dependent Variable: RESID

8、A2Method: Least SquaresDate: 10/19/05Time: 15:29Sample: 1 28Included observations: 28VariableCoefficientStd. Errort-StatisticProb.C-3279.7792857.117-1.1479330.2619X5.6706343.1093631.8237280.0802XA2-0.0008710.000653-1.3340000.1942R-squared0.223950Mean dependent var3006.741Adjusted R-squared0.161866S.

9、D. dependent var5144.470S.E. of regression4709.744Akaike info criterion19.85361Sum squared resid5.55E+08Schwarz criterion19.99635Log likelihood-274.9506F-statistic3.607218Durbin-Watson stat1.479908Prob(F-statistic)0.0420362、因为本例为一元函数，没有交叉乘积项，则辅助函数为从上表可以看出,2n R =6.270612 ,有 White 检验知，在,2 .=0,05下，查分布表

10、,得临界值 20.05 (2)2=5.99147。比较计算的2统计量与临界值,2因为 nR = 6.270612 >20.05(2) =5.991473t =曾 J X t。,所以拒绝原假设，不拒绝备择假设，这表明模型存在异方差。（四）异方差的修正在运用加权最小二乘法估计过程中，分别选用了权数1t=1/Xt, 2t=1/Xt2,用权数1t的结果Dependent Variable: YMethod: Least SquaresDate: 10/22/10Time: 00:13Sample: 1 28Included observations: 28Weighting series: W1

11、VariableCoefficientStd. Errort-StatisticProb.C5.9883516.4033920.9351840.3583X0.1086060.00815513.317340.0000Weighted StatisticsR-squared0.032543Mean dependent var123.4060Adjusted R-squared-0.004667S.D. dependent var31.99659S.E. of regression32.07117Akaike info criterion9.842541Sum squared resid26742.

12、56Schwarz criterion9.937699Log likelihood-135.7956F-statistic177.3515Durbin-Watson stat1.465148Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.853095Mean dependent var213.4650Adjusted R-squared0.847445S.D. dependent var146.4895S.E. of regression57.21632Sum squared resid85116.40Durbin-Watson

13、 stat1.261469用权数 2t的结果Dependent Variable: YMethod: Least SquaresDate: 10/22/10 Time: 00:16Sample: 1 28Included observations: 28Weighting series: W2VariableCoefficientStd. Errort-StatisticProb.C6.4967033.4865261.8633740.0737X0.1068920.0109919.7252600.0000Weighted StatisticsR-squared0.922715Mean depen

14、dent var67.92129Adjusted R-squared0.919743S.D. dependent var75.51929S.E. of regression21.39439Akaike info criterion9.032884Sum squared resid11900.72Schwarz criterion9.128041Log likelihood-124.4604F-statistic94.58068Durbin-Watson stat1.905670Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.85

15、4182Mean dependent var213.4650Adjusted R-squared0.848573S.D. dependent var146.4895S.E. of regression57.00434Sum squared resid84486.88Durbin-Watson stat1.242212用权数 3t的结果Dependent Variable: YMethod: Least SquaresDate: 10/22/10 Time: 00:17Sample: 1 28Included observations: 28Weighting series: W3Variabl

16、eCoefficientStd. Errort-StatisticProb.C8.64034111.187330.7723330.4469X0.1061530.00774613.704730.0000Weighted StatisticsR-squared0.611552Mean dependent var165.8420Adjusted R-squared0.596612S.D. dependent var67.13044S.E. of regression42.63646Akaike info criterion10.41205Sum squared resid47264.56Schwar

17、z criterion10.50720Log likelihood-143.7686F-statistic187.8197Durbin-Watson stat1.275429Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.854453Mean dependent var213.4650Adjusted R-squared0.848855S.D. dependent var146.4895S.E. of regression56.95121Sum squared resid84329.44Durbin-Watson stat1.2

18、33545经估计检验，发现用权数3t的结果，其可决系数反而减小；只有用权数2t的效果最好，可决系数增大。用权数 2t的结果Dependent Variable: YMethod: Least SquaresDate: 10/22/10 Time: 00:16Sample: 1 28Included observations: 28Weighting series: W2VariableCoefficientStd. Errort-StatisticProb.C6.4967033.4865261.8633740.0737X0.1068920.0109919.7252600.0000Weighte

19、d StatisticsR-squared0.922715Mean dependent var67.92129Adjusted R-squared0.919743S.D. dependent var75.51929S.E. of regression21.39439Akaike info criterion9.032884Sum squared resid11900.72Schwarz criterion9.128041Log likelihood-124.4604F-statistic94.58068Durbin-Watson stat1.905670Prob(F-statistic)0.0

20、00000Unweighted StatisticsR-squared0.854182Mean dependent var213.4650Adjusted R-squared0.848573S.D. dependent var146.4895S.E. of regression57.00434Sum squared resid84486.88Durbin-Watson stat1.242212用权数 2t的估计结果为：Y?= 6.496703 + 0.106892 Xi( 1.863374 )(9.725260 )2 _ _R =0.922715 DW=1.905670 F= 94.58068

21、括号中的数据为t统计量值。由上可以看出，运用加权最小二乘法消除了异方差后，参数 2的1检验显著，可决系数提高了不少，F检验也显著，并说明销售收入每增长1元，销售利润平均增长0.106892元。四、实践结果报告：被解释变量Y随着解释变量X的增大而逐渐分散,1、用图示法初步判断是否存在异方差：2离散程度越来越大；同样的，残差平万ei对解释变量X的散点图主要分布在图形中的下三2角部分，大致看出残差平万ei随Xi的变动呈增大趋势。因此，模型很可能存在异方差。但是否确实存在异方差还应该通过更近一步的检验。再用White检验异方差：因为nR2 = 6.270612 >20.05 (2) =5.991

22、47 ,所以拒绝原假设，不拒绝备择假设，这表明模型存在异方差。2、用加权最小二乘法修正异方差：发现用权数2t的效果最好，则估计结果为：Y?= 6.496703+ 0.106892 Xi( 1.863374 )(9.725260 )2一R =0.922715DW=1.905670 F= 94.58068括号中的数据为t统计量值。由上可以看出，R2 =0.922715,拟合程度较好。在给定 =0.0时，t= 9.725260 >t0.025 (26)=2.056，拒绝原假设，说明销售收入对销售利润有显著性影响。F=94.58068 > F0.05 (1,26) = 4.23 ,表明方程整体显著。运用加权最小二乘法后，参数2的t检验显著，可决系数提高了不少，F检验也显著，并说明销售收入每增长 1元，销售利润平均增长0.106892元。3、再用 White检验修正后的模型是否还存在异方差：White检验结果White Heteroskedasticity Test:F-statistic3.144597Probability0.060509Obs*R-s