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1、时间 地点 实验题目 异方差诊断与修正 一、实验目与要求:要求目: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:其中,表示销售利润,表示销售收入。由1998年我国重要制造业销售收入与销
2、售利润数据,如图1:1988年我国重要制造业销售收入与销售利润数据 (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502.614195.22医药制造业238
3、.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1、双击“Eviews”,进入主页。输入数据:点击主菜单中 /EV Work异方差数据2.xls
4、 ;2、在EV主页界面窗口,输入“ls y c x”,按“Enter”。出现OLS回归结果,如图2: 估计样本回归函数Dependent Variable: YMethod: 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 depende
5、nt var213.4650Adjusted R-squared0.849107S.D. dependent var146.4895S.E. of regression56.90368Akaike 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: = 12.03564 + 0.104393(19.5177
6、9) (0.008441)t=(0.616650) (12.36670)=0.854696 =0.849107 S.E.=56.89947 DW=1.212859 F=152.9353这说明在其他因素不变情况下,销售收入每增长1元,销售利润平均增长0.104393元。=0.854696 , 拟合程度较好。在给定=0.0时,t=12.36670 =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 = 4.23 ,表明方程整体显著。(三) 检验模型异方差(一)图形法1、在“Workfile”页面:选中x,y序列,点击鼠标右键,点击Openas GroupYes2、
7、在“Group”页面:点击ViewGraphScatterSimple Scatter, 得到X,Y散点图(图3所示):3、在“Workfile”页面:点击Generate,输入“e2=resid2”OK4、选中x,e2序列,点击鼠标右键,Openas GroupYes5、在“Group”页面:点击ViewGraphScatterSimple Scatter, 得到X,e2散点图(图4所示):6、判断由图3可以看出,被解释变量Y随着解释变量X增大而逐渐分散,离散程度越来越大;同样,由图4可以看出,残差平方对解释变量X散点图主要分布在图形中下三角部分,大致看出残差平方随变动呈增大趋势。因此,模型
8、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检验。 (二)White检验1、 在“Equation”页面:点击ViewResidual TestsWhite检验(no cross),(本例为一元函数,没有交叉乘积项)得到检验结果,如图5:White检验结果White Heteroskedasticity Test:F-statistic3.607218Probability0.042036Obs*R-squared6.270612Probability0.043486Test Equation:Dependent Variable: RESID2Method: Least Squa
9、resDate: 10/19/05 Time: 15:29Sample: 1 28Included observations: 28VariableCoefficientStd. Errort-StatisticProb.C-3279.7792857.117-1.1479330.2619X5.6706343.1093631.8237280.0802X2-0.0008710.000653-1.3340000.1942R-squared0.223950Mean dependent var3006.741Adjusted R-squared0.161866S.D. dependent var5144
10、.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,n=6.270612 ,有White检验知,在=0,05下,查分布表,得临界值(2)=5.99147。比较计算统计量与临
11、界值,因为n= 6.270612 (2)=5.99147 ,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) 异方差修正在运用加权最小二乘法估计过程中,分别选用了权数=1/,=1/,=1/。1、在“Workfile”页面:点击“Generate”,输入“w1=1/x”OK ;同样输入“w2=1/x2”“w3=1/sqr(x)”;2、在“Equation”页面:点击“Estimate Equation”,输入“y c x”,点击“weighted”,输入“w1”,出现如图6:用权数结果Dependent Variable: YMethod: Least SquaresDate: 10
12、/22/10 Time: 00:13Sample: 1 28Included observations: 28Weighting series: W1VariableCoefficientStd. 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
13、. of regression32.07117Akaike info criterion9.842541Sum squared resid26742.56Schwarz 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
14、var146.4895S.E. of regression57.21632Sum squared resid85116.40Durbin-Watson stat1.2614693、在“Equation”页面:点击“Estimate Equation”,输入“y c x”,点击“weighted”,输入“w2”,出现如图7:用权数结果Dependent Variable: YMethod: Least SquaresDate: 10/22/10 Time: 00:16Sample: 1 28Included observations: 28Weighting series: W2Variable
15、CoefficientStd. Errort-StatisticProb.C6.4967033.4865261.8633740.0737X0.1068920.0109919.7252600.0000Weighted StatisticsR-squared0.922715Mean dependent var67.92129Adjusted R-squared0.919743S.D. dependent var75.51929S.E. of regression21.39439Akaike info criterion9.032884Sum squared resid11900.72Schwarz
16、 criterion9.128041Log likelihood-124.4604F-statistic94.58068Durbin-Watson stat1.905670Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.854182Mean dependent var213.4650Adjusted R-squared0.848573S.D. dependent var146.4895S.E. of regression57.00434Sum squared resid84486.88Durbin-Watson stat1.24
17、22124、在“Equation”页面:点击“Estimate Equation”,输入“y c x”,点击“weighted”,输入“w3”,出现如图8:用权数结果Dependent Variable: YMethod: Least SquaresDate: 10/22/10 Time: 00:17Sample: 1 28Included observations: 28Weighting series: W3VariableCoefficientStd. Errort-StatisticProb.C8.64034111.187330.7723330.4469X0.1061530.00774
18、613.704730.0000Weighted StatisticsR-squared0.611552Mean dependent var165.8420Adjusted R-squared0.596612S.D. dependent var67.13044S.E. of regression42.63646Akaike info criterion10.41205Sum squared resid47264.56Schwarz criterion10.50720Log likelihood-143.7686F-statistic187.8197Durbin-Watson stat1.2754
19、29Prob(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 stat1.233545经估计检验,发现用权数,结果,其可决系数反而减小;只有用权数效果最好,可决系数增大。 用权数结果Dependent Variable: YMethod: Lea
20、st 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 dependent var67.92129Adjusted R-squared0.919743S.D. depende
21、nt 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-squared0.854182Mean dependent var213.4650Adjusted R-squared0.8485
22、73S.D. dependent var146.4895S.E. of regression57.00434Sum squared resid84486.88Durbin-Watson stat1.242212用权数估计结果为: = 6.496703 + 0.106892(1.863374) (9.725260)=0.922715 DW=1.905670 F=94.58068括号中数据为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。四、实践结果报告: 1、用图示法初步判
23、断是否存在异方差:被解释变量Y随着解释变量X增大而逐渐分散,离散程度越来越大;同样,残差平方对解释变量X散点图主要分布在图形中下三角部分,大致看出残差平方随变动呈增大趋势。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检验。再用White检验异方差:因为n= 6.270612 (2)=5.99147 ,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:发现用权数效果最好,则估计结果为: = 6.496703 + 0.106892(1.863374) (9.725260)=0.922715 DW=1.905670 F=94.58068括号中
24、数据为t统计量值。由上可以看出,=0.922715,拟合程度较好。在给定=0.0时,t=9.725260 =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 = 4.23 , 表明方程整体显著。运用加权最小二乘法后,参数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检验修正后模型是否还存在异方差:White检验结果White Heteroskedasticity Test:F-statistic3.144597Probability0.060509Obs*R-squared5.62
25、8058Probability0.059963Test Equation:Dependent Variable: STD_RESID2Method: Least SquaresDate: 10/22/10 Time: 00:17Sample: 1 28Included observations: 28VariableCoefficientStd. Errort-StatisticProb.C1927.346675.22462.8543780.0085X-1.4566130.734838-1.9822230.0585X20.0002450.0001541.5863420.1252R-square
26、d0.201002Mean dependent var425.0258Adjusted R-squared0.137082S.D. dependent var1198.210S.E. of regression1113.057Akaike info criterion16.96857Sum squared residSchwarz criterion17.11130Log likelihood-234.5599F-statistic3.144597Durbin-Watson stat2.559506Prob(F-statistic)0.060509由上看出,n= 5.628058 ,由White检验知,在=0,05下,查分布表,得临界值:(2)=5.99147。比较计算统计量与临界值,因为n= 5.628058 (2)=5.99147 ,所以接受原假设,这说明修正后模型不存在异方差。教师评阅意见: