Eviews异方差性实验报告

1、实验一异方差性【实验目的】掌握异方差性问题出现的来源、后果、检验及修正的原理，以及相关的Eviews操作方法。【实验内容】以计量经济学学习指南与练习补充习题4-16为数据，练习检查和克服模型的异方差的操作方法。【4-16】表4-1给出了美国18个行业1988年研究开发（R&D）费用支出丫与 销售收入X的数据。请用帕克（Park）检验、戈里瑟（Gleiser）检验、G-Q检 验与怀特（White）检验来检验丫关于X的回归模型是否存在异方差性？若存在 异方差性，请尝试消除它。表4-1单位：百万美元序号研究开发费用丫销售收入X162.56375.3292.911626.43178.31465

2、5.14258.421869.25494.726408.361083.032405.671620.635107.78421.740295.49509.270761.6106620.180522.8113918.695294.0121595.3101314.1136107.5116141.3144454.1122315.7153163.8141649.91613210.7175025.8171703.8230614.5【实验步骤】一检查模型是否存在异方差性1、图形分析检验（1）散点相关图分析做出销售收入X与研究开发费用丫的散点相关图（SCAT X 丫）。观察相关图 可以看出，随着销售收入的增加，

3、研究开发费用的平均水平不断提高， 但离散程 度也逐步扩大。这说明变量之间可能存在递增的异方差性。14,00012,000 -10,000 -e.ooo -6,000 -4,000 -2,000 -050,000 100,000 150,000 200.000 250,000(2)残差图分析首先对数据按照解释变量X由小至大进行排序(SORT X )，然后建立一元线 性回归方程(LS 丫 C X )。Dependentvariable: YMethod: Least SquaresDate: 12/06/11 Time： 23:08Sample: 1 17Included obseivations

4、: 17VariableCo EfficientStd. Errort-Stall SticProbC187.50681106.6810.1694320.8677X0.0319930.0111112 8793580.0115R-squared0.355966Mean dependent var2676.188Adjusted R-squared0.313031S.D. dependent var3438.207S.E. of regression2849711Aka ike Info criterion13.85795Sum squared resid1 22E+O0Schwarz crite

5、rion18.95698Log likelihood-158.2926Hannan-Quinn criter.18.86770F-statistic8.290703Durbin-Watson stat2.738533Prob(F-statistic)0.011464因此，模型估计式为：Y =187.507 0.032* X (*)2(0.17)(2.88)R2=0.31s.e.=2850F=0.011建立残差关于X的散点图，可以发现随着X增加，残差呈现明显的扩大 趋势，表明存在递增的异方差。8,000 6.000 4.000 -2.000 -0-2.000-4,000 -*e(ooo 1111

6、_7050,000 100,000 150,000 200.000 250.0002、Park检验建立回归模型(LS 丫 C X ),结果如(*)式。生成新变量序列：GENR LNE2 = LOG(RESIDT)GENR LNX = LOG(X)生成新残差序列对解释变量的回归模型(LS LNE2 C LNX )。从下图所示的 回归结果中可以看出，LNX的系数估计值不为0且能通过显著性检验，即随机 误差项的方差与解释变量存在较强的相关关系，即认为存在异方差性。Dependent Variable: LNE2Method: Least SquaresDate: 12/04/11 Tme： 13:2

7、7Sample: 1 17Included observations: 17VariableCoefficientStd Errort-StatisticProbC-2.5472734.379817-0.5815930.5695LNX1.5019570.4019423.7365000 0020R-squared0 482070Mean dependentvar13.74855Adjusted R-squared0 4475418,0. dependentvar2.234574S E. of regrEssion1,660905Aka ike info criterion3 962733Sum

8、squared re si J41.37907Schwarz criterion<060758Log likelihood-31.68323Hannan-Quinn criter3.972477F-statistic13.96143Durbin-Watson stat1.585766ProbfF-statistic)0.0019853、Gleiser 检验建立回归模型（LS 丫 C X ）,结果如（*）式。生成新变量序列：GENR E = ABS（RESID）1 1分别建立新残差序列 E对各解释变量X/X2/X 2/X J/X/X_2的回归模 型（LS E C X），回归结果如各图所示。

9、Dependent Variable: EMethod: Least SquaresDate: 12/04/11 Time： 13:38Sample: 1 11Included observations: 11VariableCoefficientStd Errort-StatisticProbC221.7507530.9000-0.4176880.6821X0 0252790.00533047425350.0003R-squareJ0.599911Mean dependent ver1744.661Adjusted R-squared0.5732388.D. dependent var209

10、2 658S.E. of regression1367.071Akaike Info criterion17 38836Sum squared resid29033236Schwarz criterion1748688Log likelihood!-145.8053Hannan-Quinn criter.17.39860F-statistic22.49164Durbin-Watson stat1 996727Probf-statistlc）0 000262Dependent Variable: EMethod: Least SquaresDate： 12/04/11 Time: 13:40Sa

11、mple: 1 17Included obsen/ations: 17VariableCoefficientStd. Errort-StatisticProbC571.7499393.64191 4524S201670XA21.18E-072.33B0850661580.0001R-squared0.631141Mean dependent var1744.601Adjusted R-squared0.606550s D dependentvar2092.658S E of regression1312.631Aka ike info criterion17.30759Sum squared

12、resid25845008Schwarz criterion17.40561Log likelihood-145J145Hannan-Quin n criter.17.31733F-statistic25.06595Durbin-Watson stat2 352964Prob （F-statistic）0.000139DependentVariable: EMethod: Least SquaresDate: 12/04/11 Time: 13:41Sample: 1 17Included observations: 17VariableCoefficientStd. Error t-Stat

13、isticProb.C1549.666886.3886-1.7482910.1008XA(1/2)12.935363.1781184.0701310.0010R-squared0.524805Mean dependentvar1744.661Adjusted R-squared0.493125S.D. dependent var2092.658SE of regression1489.871Aka ike info criteri on17.56090Sum squared resid33295728Schwarz criterion17.65892Log likelihood-147.267

14、6Hannan-Quinn criter.17.57064F-statistic16.56597Durbin-Watson stat1.669125Prob(F-statistic)0.001005Dependent Variable: E Method: Least Squares Date: 12/04/11 Time: 13:42 Sample: 1 17Included observations: 17VariableCoefficientStd. Error t-StatisticProb.C2486.909625.55473.9755250.0012XA(-1)-225460181

15、2385595-1.8203420.0887R-squared0.180939Mean dependent var1744.661Adjusted R-squared0.126334S.D. dependent var2092.658S.E. of regression1956.009Aka ike info criterion18.10533Sum squared resid57389553Schwarz criterio n18.20336Log likelihood-151.8953Hannan-Quinn criter.18.11507F-statistic3.313645Durbin

16、-Wats on stat1.052473Prob(F-statistic)0.088716Dependentvariable: EMethod: Least SquaresDate: 12/04/11 Time: 13:42Sample: 1 17In eluded observations: 17VariableCoefficientStd. Errort-StatisticProb.C1995.1 4154S.74453.6358300.0024Xrt(-2)-9.82E+108.61 E+10-1.1401860.2721R-squared0.079756Mean dependent

17、var1744.601Adjust Ed R-squared0.018406S O. dependent var2092.658S.E. of regression2073.309Akaike info criterion18.22181Sum squared resid64479157Schwarz criterion10.31984Log likelihood152.8854Hannan-Quinn criter18.23155F-statistic1.300025Durbiin-Watson stat0 944698Prob(F-statistic0.272088Dependent Va

18、riable. E Method: Least Squares Date: 12/04/11 Time: 13:43 Sample: 1 17Included observations: 17VariableCoefficientStd. Errort-StatisticProb.C3711.103918.831 S 4.0389370.0011XA(-1/2)-391281.2160138.7-2.4433090 0274R-squared0.284698Mean dependent var1744.661Adjusted R-squared0.237011S D dependentvar2

19、092.658S.E, ofregressio n1827.921Akaike info criterion17.96988Sum squared resid50119421Schwarz criterion18 06790Log likelihood-1507440Hannan-Quinn criter.17.97962F-statistic5.970152Durbin-Watson start1 176271ProbfF-statistic)0 027395由上述各回归结果可知，各回归模型中解释变量的系数估计值显著不为0,且除了 X的系数，均能通过10%的显著性检验。所以认为存在异方差性。

20、4、G-Q检验将样本按解释变量排序(SORT X)并分成两部分，分别为1到7和11到 17,各7个样本。利用样本1建立回归模型1( SMPL 1 7 LS Y C X)，其残差平方和为 412586.0Dependent Variable: YMethod: Least SquaresDate： 12/06/11 Time: 20:32Sample: 1 7Included observations: 7VariableCoefficientStd. Errort-StatisticProb.C*499.9132254.4416-1.9647460.1056X0.0491070 0108514

21、.5255820 0063R-squared0 803775Meain deperidentvar541.4857Adjusted R-squared0.7645298 D dependentvar591 9758S.IE. of regression287.2581Akaike info criterion14.39360Sum squared resid412586.0Schwarz criterion14.37814Log likelihood-4S.37758HannaivQuinn criter14.20258F-statistic20 48090Durbin-Watson stat

22、0 924315Prob(F-statl3tilc)0.006251利用样本2建立回归模型2 (SMPL 11 17 LS Y C X ),其残差平方和为94219377 。Dependent Variable: YMethod: Least SquaresDate: 12706/11 Time: 20:35Sample: 11 17Included observations; 7VariableCoefficientStd Errort-StatisticProbC3361 2005436 1400 6183060.5634X0.0108160.0369300.2928850.7814R-s

23、quared0.016867Mean dependent var4879 114Adjusted R-squared-0.179760S.D. dependent var3996.578S.E. of regression4340.953Akaike info criterion19.82453Sum squared resid94219377Schwarz criterion19.80908Log likelihood-67.38586H自nnan-Qumn criter.19.63352F-statistic0 085782Durbiin-Watson stat2.868565Prab(F

24、-statistic)0.781376计算 F 统计量：F=RSS/RSS = 91219377 / 412586 = 221.09 , RSS和RSS>分别是模型1和模型2的残差平方和。取 a =0.05 时，查 F 分 布表得 F°.05(7-1-1,7-1-1) = 5.05，而F =221.09 a F°.05 =5.05，所以存在异方差性。5、White 检验建立回归模型(LS 丫 C X )Dependent Variable: YMethod: Least SquaresDate: 12J06/11 Time: 20:44Sample: 1 11Incl

25、uded observations: 17VariableCoefficientStd. ErrorV StatisticProbC187.50681106.6310J 694320.8677X0.0319930.0111112.8793580.0115R'Squared0.355966Mean dependent var2676.188Adjusted R-squred0.313031S D, dependent var3438.207S.E, of regression2849.711Aka ike info criterion18,85795Sum squared resid1.

26、22E+08Schwarz criterion16.95598Log likelihood-160.2926Hannan-Quinri criter18.86770F-statistlc9.290703Durbin-Watson stat2739533Prob(F-statistic)0.011464在窗口菜单中选择 Heteroskedasticity Test: White，检验结果如下:Heteroskedasticity Test: WhiteF*statistic9793067Prob. F(2,1 4)0.0022Obs*R'Squared9.913742Prob. Chk

27、Bquare(2)0.0070Scaled explained SS16.01775Prob. Chi-Square(2)0.0003其中F值为辅助回归模型的 F统计量值。取显著水平二0.05，由于0.05=5.99： nR2 =17*9.9137 = 168.533，所以存在异方差性。同时可以直接观察相伴概率P值的大小，这里P = 0.0022，小于0.05的显著水平，认为存在 异方差性。二克服异方差1、确定权数变量根据Park检验生成权数变量：GENR W1=1/XA1.5019根据Gleiser检验生成权数变量：GENR W2=1/XA2 另外生成：GENR W3=1/ABS(RESID

28、)GENR W4=1/RESIDA2其中RESID为最初回归模型LS 丫 C X的残差序列。2、利用加权最小二乘法估计模型在Eviews命令窗口中依次键入命令 LS(W= W ) 丫 C X，或在回归的权数变量栏里依次输入 W1、W2、W3、W4，得到回归结果。并对所估计的模型再分 别进行White检验，观察异方差的调整情况。W1 :Dependent Variable: YMethod: Least SquaresDate 12/06/11 Time： 21:01Sample: 1 17Included observations: 17Weighting series: W1Variable

29、CoefficientStd Errort-StatisticProbC-154.316364.55461-2.3904770.0304X0.029B020 0061364 85712B0 0002Weighted StatisticsR-squared0.611315Mean dependent var434.5284Adjusted R-squared0.585403S.D. dependent var280.0751S E. ofregression311.2520AkalkB info criterion14.42921Sum squared resid1453167.Schwarz

30、criterion14.52724Log likelihood-120.6483Hannan-Quinni criter.14.43396F-statistic23.59167Ourbin-Watson stat2.116089Prob(F-statistic)0.000209Heteroskedasticity Test: WhiteF-statistic0.081299Prob. F(3,13)0.9690Obs*R-squared0 313067Prob. Chi-Square(3)0.9576Scaled explained S30.221476Prob. Chi-Square(3)0

31、.9741W2 :DependentVariable: YMethod: Least SquaresDate: 12/06/11 Time: 21:03Sample: 1 11Included observations: 17Weighting series: W2VariableCoefficientStd. Errort-StatisticProb.C-79.6884S37.29966-21364450.0495X0.0211240.0047064.4S91100 0004Weighted StatisticsR-scuuared0.573283Mean dependentvar230.4

32、072Adjusted R-squared0.544835s.D. dependent var171 9140S E. of regression149 5192Akaike info criteri口n12.96286Sum squared resid335339 9Schwarz criterion13.06088Log liikelihood-108 1843Hannan-Quinn criter.12.37260F-statistic20.15210Durbin-Wats on stat1 659831Prob (Fatalistic)0.000433Heteroskedasticlt

33、y Test: WhiteF-statistic0.151263Prob.F(3,13)0.9270Obs*H-squared0,573473Prob. Chi-Square Q)0.9025Scaled explained ss0.476239Prob. Chi'Square(3)0.9241W3 :Dependent Variable: ¥Method： Least SquaresDate： 12/06/11 Time: 21:04Sample: 1 17Included observations: 11Weighting series: W3VariableCoeffi

34、cientStd. Errort-BtatlsticProb.C-1537640148.0721-1.038445Qi.3155X0.0376660.00304312.377490.0000Weighted StatisticsR-squared0.910822Mean dependent var1493.934Adjusted R-squared0.904S76S.D dependentvar2005.197S.E of regression536.2098Aka ike imfo criterion15.51706Sum squared resid4312814Schwarz criterion15 61500Log likelihood-129,8950Hannan-Qui