异方差性的检验和补救.doc

_异方差性的检验和补救一、 研究目的和要求表1列出了1998年我国主要制造工业销售收入与销售利润的统计资料，请利用统计软件Eviews建立我国制造业利润函数模型，检验其是否存在异方差，并加以补救。表 1 我国制造工业1998年销售利润与销售收入情况行业名称销售利润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服装制品业157.71779.1皮革羽绒制品81.71081.77木材加工业35.67443.74家具制造业31.06226.78造纸及纸品业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化学原料纸品502.614195.22医药制造业238.711264.1化学纤维制品81.57779.46橡胶制品业77.84692.08塑料制品业144.341345非金属矿制品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电子通讯设备508.154499.19仪器仪表设备72.46663.68二、 参数估计EVIEWS 软件估计参数结果如下Dependent Variable: YMethod: Least SquaresDate: 06/01/16 Time: 20:16Sample: 1 28Included observations: 28VariableCoefficientStd. Errort-StatisticProb.C12.0334919.518090.6165300.5429X0.1043940.00844212.366580.0000R-squared0.854694Mean dependent var213.4639Adjusted R-squared0.849105S.D. dependent var146.4905S.E. of regression56.90455Akaike info criterion10.98938Sum squared resid84191.34Schwarz criterion11.08453Log likelihood-151.8513Hannan-Quinn criter.11.01847F-statistic152.9322Durbin-Watson stat1.212781Prob(F-statistic)0.000000用规范的形式将参数估计和检验结果写下三、 检验模型的异方差（一） 图形法1. 相关关系图X Y 相关关系图2. 残差图形生成残差平方序列，做与解释变量 X 的散点图如下。与 X 散点图3. 判断由图可以看出，残差平方 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 随 X 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. 排序使用 Sort X 命令对解释变量 X 进行排序。2. 构造子样本区间，建立回归模型样本容量 n=28，去掉中间 c=8 个样本值，得到两个样本区间 110、1928的两组样本值。110区间回归估计Dependent Variable: YMethod: Least SquaresDate: 06/01/16 Time: 20:35Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb.C15.7646614.820221.0637270.3185X0.0858940.0191824.4779370.0021R-squared0.714814Mean dependent var77.06400Adjusted R-squared0.679166S.D. dependent var31.70225S.E. of regression17.95685Akaike info criterion8.790677Sum squared resid2579.587Schwarz criterion8.851194Log likelihood-41.95338Hannan-Quinn criter.8.724289F-statistic20.05192Durbin-Watson stat2.280129Prob(F-statistic)0.0020611928区间回归估计Dependent Variable: YMethod: Least SquaresDate: 06/01/16 Time: 20:36Sample: 19 28Included observations: 10VariableCoefficientStd. Errort-StatisticProb.C-11.99687138.6642-0.0865170.9332X0.1105520.0393672.8082090.0229R-squared0.496413Mean dependent var369.2440Adjusted R-squared0.433465S.D. dependent var118.6175S.E. of regression89.28163Akaike info criterion11.99833Sum squared resid63769.67Schwarz criterion12.05884Log likelihood-57.99163Hannan-Quinn criter.11.93194F-statistic7.886037Durbin-Watson stat2.489267Prob(F-statistic)0.0229063. F统计量值对样本 110回归分析对样本 1928 回归分析4. 判断取显著性水平 ，子样本个数为 10，变量个数为 2，因此子样本的残差平方和的自由度为 8，查 F 分布表得 所以拒绝原假设，表明模型确实存在异方差性。（三） White检验对前文参数检验的结果进行 White 检验，结果如下图Heteroskedasticity Test: WhiteF-statistic3.607090Prob. F(2,25)0.0420Obs*R-squared6.270439Prob. Chi-Square(2)0.0435Scaled explained SS7.630696Prob. Chi-Square(2)0.0220Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/01/16 Time: 20:38Sample: 1 28Included observations: 28VariableCoefficientStd. Errort-StatisticProb.C-3279.6692857.119-1.1478940.2619X2-0.0008710.000653-1.3340330.1942X5.6706873.1093661.8237440.0802R-squared0.223944Mean dependent var3006.833Adjusted R-squared0.161860S.D. dependent var5144.454S.E. of regression4709.748Akaike info criterion19.85361Sum squared resid5.55E+08Schwarz criterion19.99635Log likelihood-274.9506Hannan-Quinn criter.19.89725F-statistic3.607090Durbin-Watson stat2.576402Prob(F-statistic)0.042040故 ，取，则，所以拒绝原假设，表明模型确实存在异方差性。四、 异方差的修正（加权最小二乘法）1. 权数将权数分别设置为2. 最小二乘估计在 Eviews 命令窗口输入得到如下结果Dependent Variable: YMethod: Least SquaresDate: 06/01/16 Time: 21:39Sample: 1 28Included observations: 28Weighting series: W1Weight type: Inverse standard deviation (EViews default scaling)VariableCoefficientStd. Errort-StatisticProb.C5.9883516.4036910.9351410.3583X0.1086050.00815613.316590.0000Weighted StatisticsR-squared0.872130Mean dependent var123.4049Adjusted R-squared0.867212S.D. dependent var31.99804S.E. of regression32.07267Akaike info criterion9.842635Sum squared resid26745.07Schwarz criterion9.937792Log likelihood-135.7969Hannan-Quinn criter.9.871726F-statistic177.3317Durbin-Watson stat2.386165Prob(F-statistic)0.000000Weighted mean dep.67.92073Unweighted StatisticsR-squared0.853094Mean dependent var213.4639Adjusted R-squared0.847443S.D. dependent var146.4905S.E. of regression57.21696Sum squared resid85118.31Durbin-Watson stat2.472027权数为W1 时的最小二乘估计结果Dependent Variable: YMethod: Least SquaresDate: 06/01/16 Time: 21:46Sample: 1 28Included observations: 28Weighting series: W2Weight type: Inverse standard deviation (EViews default scaling)VariableCoefficientStd. Errort-StatisticProb.C6.4971483.4866251.8634490.0737X0.1068900.0109919.7248240.0000Weighted StatisticsR-squared0.784362Mean dependent var67.92073Adjusted R-squared0.776068S.D. dependent var75.51949S.E. of regression21.39500Akaike info criterion9.032941Sum squared resid11901.39Schwarz criterion9.128098Log likelihood-124.4612Hannan-Quinn criter.9.062031F-statistic94.57221Durbin-Watson stat2.826376Prob(F-statistic)0.000000Weighted mean dep.36.45271Unweighted StatisticsR-squared0.854180Mean dependent var213.4639Adjusted R-squared0.848571S.D. dependent var146.4905S.E. of regression57.00507Sum squared resid84489.02Durbin-Watson stat2.489641权数为W2 时的最小二乘估计结果Dependent Variable: YMethod: Least SquaresDate: 06/01/16 Time: 21:48Sample: 1 28Included observations: 28Weighting series: W3Weight type: Inverse standard deviation (EViews default scaling)VariableCoefficientStd. Errort-StatisticProb.C8.63927111.187680.7722130.4470X0.1061530.00774613.704300.0000Weighted StatisticsR-squared0.878396Mean dependent var165.8409Adjusted R-squared0.873718S.D. dependent var67.13183S.E. of regression42.63779Akaike info criterion10.41211Sum squared resid47267.52Schwarz criterion10.50727Log likelihood-143.7695Hannan-Quinn criter.10.44120F-statistic187.8079Durbin-Watson stat2.423771Prob(F-statistic)0.000000Weighted mean dep.123.4049Unweighted StatisticsR-squared0.854451Mean dependent var213.4639Adjusted R-squared0.848853S.D. dependent var146.4905S.E. of regression56.95205Sum squared resid84331.95Durbin-Watson stat2.493962权数为W3 时的最小二乘估计结果3. 判断由上述三个结果可以看出，W1 的 t 检验均显著，F 检验也显著，即对异方差的修正效果最好。选择以 W1 为权数建立的回归模型为4. 对所估计的模型再次进行 White 检验，观察异方差调整情况Heteroskedasticity Test: WhiteF-statistic0.555565Prob. F(2,25)0.5807Obs*R-squared1.191508Prob. Chi-Square(2)0.5511Scaled explained SS1.227886Prob. Chi-Square(2)0.5412Test Equation: