实验四异方差性【实验目的】掌握异方差性的检验及处理方法【实验内容】建立并检验我国制造业利润函数模型【实验步骤】【例1】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。

一、检验异方差性⒈图形分析检验⑴观察销售利润（Y）与销售收入（X）的相关图(图1)：SCAT X Y图1 我国制造工业销售利润与销售收入相关图从图中可以看出，随着销售收入X的增加，销售利润Y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。

⑵残差分析首先将数据排序（命令格式为：SORT X解释变量），然后建立回归方程。

在方程窗口中点击Resids按钮就可以得到模型的残差分布图（或建立方程后在Eviews工作文件窗口中点击resid对象来观察）。

View,Actual,Residuai图2 我国制造业销售利润回归模型残差分布图2显示回归方程的残差分布有明显的扩大趋势，即表明存在异方差性。

⒉Goldfeld-Quant检验⑴将样本安解释变量排序（SORT X）并分成两部分（分别有1到10共11个样本合19到28共10个样本）⑵利用样本1建立回归模型1（回归结果如图3），其残差平方和为2579.587。

SMPL 1 10LS Y C X图3 样本1回归结果Dependent Variable: YMethod: Least SquaresDate: 11/14/13 Time: 13:37Sample: 1 10Included observations: 10Variable Coefficient Std. Error t-Statistic Prob.C 15.76466 14.82022 1.063727 0.3185X 0.085894 0.019182 4.477937 0.0021R-squared 0.714814 Mean dependent var 77.06400Adjusted R-squared 0.679166 S.D. dependent var 31.70225S.E. of regression 17.95685 Akaike info criterion 8.790677Sum squared resid 2579.587 Schwarz criterion 8.851194Log likelihood -41.95338 F-statistic 20.05192Durbin-Watson stat 2.280129 Prob(F-statistic) 0.002061⑶利用样本2建立回归模型2（回归结果如图4），其残差平方和为63769.67。

SMPL 19 28LS Y C X图4 样本2回归结果Dependent Variable: YMethod: Least SquaresDate: 11/14/13 Time: 13:39Sample: 19 28Included observations: 10Variable Coefficient Std. Error t-Statistic Prob.C -11.99687 138.6642 -0.086517 0.9332 X0.1105520.0393672.8082090.0229R-squared 0.496413 Mean dependent var 369.2440 Adjusted R-squared 0.433465 S.D. dependent var 118.6175 S.E. of regression 89.28163 Akaike info criterion 11.99833 Sum squared resid 63769.67 Schwarz criterion 12.05884 Log likelihood -57.99163 F-statistic 7.886037 Durbin-Watson stat2.489267 Prob(F-statistic)0.022906⑷计算F 统计量：12/RSS RSS F =＝63769.67/2579.59=24.72，21RSS RSS 和( Sum squaredresid )分别是模型1和模型2的残差平方和。

取05.0=α时，查F 分布表得44.3)1110,1110(05.0=----F ，而44.372.2405.0=>=F F ，所以存在异方差性.(原假设为同方差，大于临界值，则拒绝原假设)⒊White 检验⑴建立回归模型：LS Y C X ，回归结果如图5。

图5 我国制造业销售利润回归模型Dependent Variable: Y Method: Least Squares Date: 11/14/13 Time: 13:42Sample: 1 28Included observations: 28VariableCoefficientStd. Error t-Statistic Prob.C 12.03349 19.51809 0.616530 0.5429X 0.104394 0.008442 12.36658 0.0000R-squared 0.854694 Mean dependent var 213.4639Adjusted R-squared 0.849105 S.D. dependent var 146.4905S.E. of regression 56.90455 Akaike info criterion 10.98938Sum squared resid 84191.34 Schwarz criterion 11.08453Log likelihood -151.8513 F-statistic 152.9322Durbin-Watson stat 2.497440 Prob(F-statistic) 0.000000 ⑵在方程窗口上点击View\Residual\Test\White Heteroskedastcity,检验结果如图6。

图6 White检验结果White Heteroskedasticity Test:F-statistic 3.607090 Probability 0.042040Obs*R-squared 6.270439 Probability 0.043490Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 11/14/13 Time: 13:43Sample: 1 28Included observations: 28Variable Coefficient Std. Error t-Statistic Prob.C -3279.669 2857.119 -1.147894 0.2619X 5.670687 3.109366 1.823744 0.0802X^2 -0.000871 0.000653 -1.334033 0.1942R-squared 0.223944 Mean dependent var 3006.833Adjusted R-squared 0.161860 S.D. dependent var 5144.454S.E. of regression 4709.748 Akaike info criterion 19.85361Sum squared resid 5.55E+08 Schwarz criterion 19.99635Log likelihood -274.9506 F-statistic 3.607090Durbin-Watson stat2.576402 Prob(F-statistic)0.042040其中F 值为辅助回归模型的F 统计量值。

取显著水平05.0=α，由于2704.699.5)2(2205.0=<=nR χ,所以存在异方差性。

实际应用中可以直接观察相伴概率p 值的大小，若p 值较小，则认为存在异方差性。

反之，则认为不存在异方差性。

⒋Park 检验⑴建立回归模型（结果同图5所示）。

⑵生成新变量序列：GENR LNE2=log(RESID^2)GENR LNX=log （X ）⑶建立新残差序列对解释变量的回归模型：LS LNE2 C LNX ，回归结果如图7所示。

图7 Park 检验回归模型Dependent Variable: LNE2 Method: Least Squares Date: 11/14/13 Time: 14:12Sample: 1 28Included observations: 28Variable Coefficient Std. Error t-Statistic Prob. C -5.554862 2.585463 -2.148497 0.0412 LNX1.6743090.3518834.7581420.0001R-squared 0.465460 Mean dependent var 6.679331 Adjusted R-squared 0.444900 S.D. dependent var 1.925320 S.E. of regression 1.434460 Akaike info criterion 3.628203 Sum squared resid 53.49953 Schwarz criterion 3.723360 Log likelihood -48.79484 F-statistic 22.63991 Durbin-Watson stat2.315009 Prob(F-statistic)0.000064从图7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，即随即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。

⒌Gleiser检验（Gleiser检验与Park检验原理相同）（重新数据）⑴建立回归模型（结果同图5所示）。

⑵生成新变量序列：GENR E=ABS(RESID)⑶分别建立新残差序列（E）对各解释变量（X/ X^2/ X^(1/2)/ X^(－1)/ X^(－2)/ X^(－1/2)）的回归模型：LS E C X，回归结果如图8、9、10、11、12、13所示。

图8Dependent Variable: EMethod: Least SquaresDate: 11/14/13 Time: 14:20Sample: 1 28Included observations: 28Variable Coefficient Std. Error t-Statistic Prob.C 12.23936 10.61881 1.152612 0.2596X 0.015267 0.004593 3.324123 0.0026R-squared 0.298242 Mean dependent var 41.69654Adjusted R-squared 0.271251 S.D. dependent var 36.26573S.E. of regression 30.95889 Akaike info criterion 9.771947Sum squared resid 24919.78 Schwarz criterion 9.867104Log likelihood -134.8073 F-statistic 11.04980Durbin-Watson stat 1.727735 Prob(F-statistic) 0.002644图9Dependent Variable: EMethod: Least SquaresDate: 11/14/13 Time: 14:21Sample: 1 28Included observations: 28Variable Coefficient Std. Error t-Statistic Prob.C 27.05837 8.232528 3.286763 0.0029X^2 2.74E-06 1.02E-06 2.689852 0.0123R-squared 0.217699 Mean dependent var 41.69654 Adjusted R-squared 0.187611 S.D. dependent var 36.26573 S.E. of regression 32.68726 Akaike info criterion 9.880597 Sum squared resid 27779.88 Schwarz criterion 9.975755 Log likelihood -136.3284 F-statistic 7.235303 Durbin-Watson stat 1.690469 Prob(F-statistic) 0.012319图10Dependent Variable: EMethod: Least SquaresDate: 11/14/13 Time: 14:22Sample: 1 28Included observations: 28Variable Coefficient Std. Error t-Statistic Prob.C -15.67683 17.09642 -0.916965 0.3676X^(1/2) 1.386178 0.389207 3.561545 0.0015R-squared 0.327898 Mean dependent var 41.69654 Adjusted R-squared 0.302048 S.D. dependent var 36.26573 S.E. of regression 30.29767 Akaike info criterion 9.728768 Sum squared resid 23866.67 Schwarz criterion 9.823926 Log likelihood -134.2028 F-statistic 12.68460 Durbin-Watson stat 1.748726 Prob(F-statistic) 0.001450图11Dependent Variable: EMethod: Least SquaresDate: 11/14/13 Time: 14:22Sample: 1 28Included observations: 28Variable Coefficient Std. Error t-Statistic Prob.C 59.38997 8.966462 6.623568 0.0000X^(-1) -19128.96 7040.358 -2.717044 0.0116R-squared 0.221145 Mean dependent var 41.69654 Adjusted R-squared 0.191189 S.D. dependent var 36.26573 S.E. of regression 32.61520 Akaike info criterion 9.876183 Sum squared resid 27657.53 Schwarz criterion 9.971341Log likelihood -136.2666 F-statistic 7.382327 Durbin-Watson stat 1.846972 Prob(F-statistic) 0.011561图12Dependent Variable: EMethod: Least SquaresDate: 11/14/13 Time: 14:23Sample: 1 28Included observations: 28Variable Coefficient Std. Error t-Statistic Prob.C 46.93599 7.198811 6.519964 0.0000X^(-2) -3230227. 1793010. -1.801566 0.0832R-squared 0.110979 Mean dependent var 41.69654 Adjusted R-squared 0.076785 S.D. dependent var 36.26573 S.E. of regression 34.84559 Akaike info criterion 10.00848 Sum squared resid 31569.59 Schwarz criterion 10.10364 Log likelihood -138.1187 F-statistic 3.245641 Durbin-Watson stat 1.768049 Prob(F-statistic) 0.083222图13Dependent Variable: EMethod: Least SquaresDate: 11/14/13 Time: 14:23Sample: 1 28Included observations: 28Variable Coefficient Std. Error t-Statistic Prob.C 86.80755 15.09094 5.752297 0.0000X^(-1/2) -1611.111 496.1991 -3.246904 0.0032R-squared 0.288497 Mean dependent var 41.69654Adjusted R-squared 0.261132 S.D. dependent var 36.26573S.E. of regression 31.17309 Akaike info criterion 9.785737Sum squared resid 25265.81 Schwarz criterion 9.880894Log likelihood -135.0003 F-statistic 10.54239Durbin-Watson stat 1.830876 Prob(F-statistic) 0.003206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且均能通过显著性检验。