异方差案例分析doc

1、1.图示法。首先做出Y与人、X2的散点图，如下:图2可见Xi基本在其均值附近上下波动，而X2散点存在较为 明显的增大趋势。再做残差平方项er与lnXi、I11X2的散点图：口 Graph; UNTITLED Workfib: UNTITLED;Untitled、百II 回苗VfevvHpouObjed Print(Name Ad(fl&tLine/Sh&de REmoxre "Template Options|Zoom.20-*.16-.12-*.08-* *案.04 -* *%*井糸*.00 Jtill5.56.06.57.07.58.08.59.0LOG(X2)图

2、4可见图1中离群点相对较少而图2呈现较为明显的单调递增的异方差性。故初步判断异方差性主要是X2引起的。2. G-Q检验根据上述分析，首先将原始数据按X2升序排序，去掉中间7个 数据，得到两个容量为12的子样本，记数据较小的样本为子 样本数据较大的为子样本2。对子样本1进行OLS回归, 结果如下: Equation: UNTITLED Workfile: UNnTLED:Untitled I 丁|茴£|viesa|Prod|objECt|Print血诳慣“涸 |Estim3te ForEcast|tatsResidsDependent Variable: LOG(Y)Method: L

3、eastSquaresDate: 06/02/09 Time: 21:35Sample: 1 12Included observations: 12VariableCoefficient Std. Error t-Statistic Prob.C4.0606601.2753163.1840420.0111LOG(X1)0.3434720.0831034.1330900.0025LOG(X2)0.1196580.1277860.9363960.3735R-squared0.706831Mean dependent var7.212597Adjusted R-squared0.641682S.D.

4、 dependent var0.U1759S.E. o 仃 egessi on0.084857Akaike info criterion-1.883390Sum squared resid0.064806Schwarz criterion-1.762164Log likelihood14.30034Han nanQ uinn crite r.-1.928273F-statistic10.84949Durbin-Watson stat2.314157Prob(F-statistic)0.004000图5得到子样本1的残差平方和RSSfO. 064806;再对子样本2进行0LS回归，结果如下：口

5、Equation; UNTULED Wo水file; UNTITLED;Untitled百1回 II 8S IVi£wPrcKObjc:t prir±Nam£Frwzw EstimateXForeicasMstatsXREsidsDependent Variable: LOG(Y)Method: Least SquaresDate: 06/02709 Time: 21:38Sample: 20 31Included observations: 12VariableCoefficientStd. Errort-StatisticProb.C0.7907881.827

6、6890.4326710.6754LOG(X1)0.1380370.1883460.7328900.4823LOG(X2)0.7762420.1189086.5281060.0001R-squared0.833949Mean dependentvar7.744334Adjusted R-squared0.797049S.D. dependentvar0.390930S.E. of regression0.176114Aka ike info criterion-0.423052Sum squared resid0.279145Schwarz criterion-0.301825Log like

7、lihood5.538312Hannan-Quinn criter.-0.467934F-statistic22.60016Durbin-Watson stat2.341788Prob(F-statistic)0.000310得到子样本2的残差平方和RSS2=0. 279145c 计算F统计量：= °-279145 . 4.30820.064806在5%的显著水平下，Fo.o5 (9, 9) =3. 18 < F,故应拒绝同方差 假设，表明该总体随机干扰项存在单调递增的异方差。3. white 检验记原模型残差平方项为"，将其与人，怡及其平方项与交叉项做辅助回归，结果

8、如下： Equation: QIAN01 Workfile: UNTITLED:Untitledvfewprocobject PrinthtemeFnegze EstinonteIporscaststats RwskEHeteroskedasticity Test: White4.324625 Prob. F(5,25)Prob. Chi-SquareC5)11.68495 Prob. Chi-Square(5)0.00570.01340.0394F-statisticObs *R-squ a red14.37735Scaled explained SSTest Equation:Depend

9、ent Variable: RESIDE Method: Least SquaresDate: 06/03/09 Time: 18:47Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.C-0.17J27S4.576151-0.0378660.9701LOG(X1)0.1022851.0762610.0950380.9250(LOG(X1)F20.014-5910.0692680.2106430.8349(LOG(X1)>*(LOGCX2)-0.0432770.039001-

10、1.1096340.2777LOG(X2)-0.0554970.476727-0.1164120.9083(LOG(X2)r20.0257870.0176021.4650400.1554R-squared0.463785hlean depende0.026553Adjusted R-squared0.356542S.D.dependentvar0.038100S.E. of regression0.030562Akai Ke info criterion-3.966115Sum squared resid0.023351Schwarz criterion3688569Log likelihoo

11、d67.47479Hannan-Quinn criier.-3.875642F-statistfc4.324625Durbin-Watson stat2.390463Prob(F-statistic)0.005679e_由各参数的t值可见各项都不是很显著，而且可决系数值也比 较小，但white统计量nR2=31 x 0.464=14. 38该值大于5%显著 水平下自由度为5的*分布相应的临界值005=1 1.07,因此应 拒绝同方差假设。去掉交叉项后的辅助回归结果如下： Equation: UNTITLED Workfile: UNlTrLED:Untitled亘倉壓皿创胡丹0Object【P

12、rint【Name尸reez 【Estim吕te任orecastitatsR皀sickDependent Variable: E2Method: Least SquaresDate: 06/04/09 Time: 15:45Sample: 1 31Included observations: 31VariableCoefficient Std. Error t-Statistic Prob.C3.8426122.8129961.3660210.1836LOG(X1)-0.5703190.893284-0.6384520.5288LOGQ(irLOG(X1)0.0415080.0651690.6

13、369220.5297LOG(X2)-0.5385980.195084-27608550.0104LOG(X2fLOG(X2)0.0386420.0133112.9029400.0074R-squared0.437376Mean dependent var0.026553Adjusted R-squ a red0.350819S.D. dependent var0.038100S.E. of regression0.030698Akai Ke info criteri on-3.982554Sum squared resid0.024501Schwarz criterion-3.751266L

14、og likelihood66.72959-Quinn criter.-3.907160F-statistic5.053009DurbirvWmtson stat2.262924Prob(F-statistic)0.003784显然，X2和X2的平方项的参数的t检验是显著的，并且white 统计量nR2二31 x 0.437376二门.58656大于5%显著水平下自由度 为5的力2分布相应的临界值才（）.05二门07,因此应拒绝同方差假 设。4.异方差的修正加权最小二乘法我们以1/X2为权重进行异方差的修正。加权后的估计结果如下： Equation: UNTITLED Workfile: UN

15、TITLED;Untitled目叵I |1View|Prod|objEUt |print|Namm|FrEezE| Estimate|卜0胆3或|stats|Rms;ids|Dependent Variable: LOG(Y) Method: Least Squares Date: 06/04709 Time: 16:47 Sample: 1 31Included observations: 31Weighting series: 1/X2VariableCoefficientStd. Errort-StatisticProb.C2.3252710.582093'3.9946700.0

16、004LOG(X1)0.44-06880.0558057.8969060.0000LOG(X2)0.2838660.0440506.4441730.0000Weighted StatisticsR-squared0.721871【屁日门depende ntva7.315886Adjusted R-squared0.702004S.D. dependentvar3.932411S.E. of regression0.102630Aka ike info criterion-1.623609Sum squared resid0.294921Schwarz criterion-1.484836Log

17、 likelihood28.16594nan-Quinn enter.-1.578373F-statistic36.33630Durbin-Watson stat1.724818Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.550255【Sean depende7.440815Adjusted R-squared0.518130S.D. depe nden tvar0.355636S.E. otregression0.246871Sum squared resitf1.706473Durbin-Watson stat0.593

18、183可见修正后各解释变量的显著性总体相对提高。其white检验结果如下: Equation: UNTITLED Workfile: UNTITLED:Untitled|fevv|pQG|Qbject|尸代亡ze| estimntglporexastllstatsIlRgsidsHeteroskedasticity Test: WhiteF-statistic0.433666Prob.F(6,24>0.S491Obs*R-squared3.032175Prob.Chi-Square(6)0.8048Scaled explained SS2.259474Prob.Chi-Square(6)

19、0.8944Test Equation:Dependent Variable: WGT_RESIDA2 Method: Least SquaresDate: 06/04/09 Time: 17:06Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.C0.0233250.0117071.9924860.0578WGTA2-1.0753693.693815-0.2911270.7735(LOG(X1)r2*WGTA2-0.0096770.027862-0.34730307314(LOGCWWGT 人 20.0