实验六共线性.docx

实验六、计量经济学多重共线性模型实验一、 实验目的与要求：掌握多重共线性模型的检验及处理方法，了解辅助回归检验和掌握R2值和t值检验及 解释变量相关系数检验，了解变量变换法和掌握先验信息法，熟悉逐步回归法能运用计量 经济学软件包Eviews对多重共线性模型进行检验及处理二、 实验内容与步骤：1. 选择多重共线性模型实际经济问题从本实验提供的参考选题中或从其它途径选择合适的实际经济问题2. 回归模型的理论形式设定针对所选的实际经济问题，依据有关的经济理论设定恰当的回归模型的理论形式3. 模型多重共线性检验应用计量经济学软件包Eviews对已设定的回归模型进行初步估计并进行多重共线性 检验4. 模型多重共线性处理应用计量经济学软件包Eviews对多重共线性模型进行处理三、 实验例题：某地区服装市场需求问题下表给出了某地区在1981年至1990年的有关统计数据年份(年)服装支出(白力兀)Y可支配收 入(百万 元)X流动资产(白力元)K服装类物价指数PC(1985 年为 100)总物价指数P0(1985 年为100)19818.482.917.1929419829.688.021.39396198310.499.925.19697198411.4105.329.09497198512.2117.734.0100100198614.2131.040.0101101198715.8148.044.0105104198817.9161.849.0112109198919.3174.251.0112111199020.8184.753.0112111试建立该地区服装市场需求模型。

实验步骤及内容如下：1. 回归模型的理论形式设定以服装支出(Y)作为被解释变量，可支配收入(X)、流动资产(K)、服装类物价指数(PC) 和总物价指数(P0)作为解释变量因此回归模型的理论形式设定为 丫=%+%乂+%虬+%?尸+以】0+出t U .L t Z/ t J t \J t tt=1981,1982,“・19902. 用OLS法初步估计模型参数并进行多重共线性检验(1)用OLS法初步估计参数，结果如下：Y =-13.20442+0.097836X +0.014448K -0.197220P +0.334132Pt t t Ct 0tDependent Variable: YMethod: Least SquaresDate: 08/2W7 Time: 16:26Sample: 1981 1990Included observations: 10VariableCoefficientStd. Errort-StatisticProb.C-13.204427.496429-1.7614280.13E5X0.0978360.0263883.7076350.0139K0.0144480.0489570.2951160.7798PC-0.1972200.089447-2.2048780.0786P00.3341320.1492292.2390560.0753R-squared0.998046Mean dependent var14.00000.Adjusted R-squared0.996482S.D. dependent var4.301163S.E. of regression0.255104Akaike info criterion0.412559Sum squared resid0.325389Schwarz criterion0.563852Log likelihood2.937205F-statistic638.3684Durbin-VVatson stat3.359692Prob(F-statistic)0 000001 图 1由以上结果可知，回归方程显著成立，但有些解释变量不够显著，可能存在多重共线性。

2)多重共线性检验1)R2值和t值检验法由以上初步回归结果可知，R2=0.998046，F= 638.3684，方程的显著性极高，但解释变量K、PC及P0的t检验值均小于显著性水平0.05时的临界值2.571这是存在多重共线性的典型特征2)解释变量相关系数检验法解释变量之间简单相关系数如下图:Correlation MatrixXKPCP0X1.0000000.9882640.9804160.987785K0.9882641.0000000.9699620.969477PC0.9804160.9699621.0000000.991796P00.9877850.9694770.9917961.000000由上图可知解释变量之间存在高度线性相关3)辅助回归检验法①X对K、PC、P0做OLS回归，得到如下结果:Dependent Variable: X Method: Least Squares Date: 08/24..107 Time: 22:10 Sample: 1981 1990 Included observations: 10VariableCoefficientStd. Errort-StatisticProb.C-221.503672.61994-3.0501750.0225K1.5263610.4305773.5449210.0121PC-1.0539731.315256-0.8013440.4535P03.9466611.6535582.3867690.0543R-squared0.992164Mean dependent var129.3500.Adjusted R-squared0.988246S.D. dependent var36.40443S.E. of repression3.946743.Akaike info criterion5.872833Sum squared resid93.46068Schwarz criterion5.993867Loq likelihood-25.36416F-statistic253.2420Durbin-VVatson stat2.251510Prob(F-statistic)坐驾图3②K对X、PC、P0做OLS回归，得到如下结果:Dependent Variable: KMethod: Least SquaresDate: 08/24/07 Time: 22:14Sample: 1981 1990Included observations: 10VariableCoefficientStd. Error t-StatisticProb.C52.5175158.71992 0.8943730.4056X0.4434310.125089 3.5449210.0121PC0.7331290.683205 1.0730730.3245P0-1.4518101.094182 -1.3268440.2328R-squared0.981982Mean dependent var36.35000.Adjusted R-squared0.972972S.D. dependent var12.93954S.E. of repression2.127274.Ak:aik:e info criterion4.636734Sum squared resid27.15176Schwarz criterion4.757768Loq likelihood-19.18367F-statistic108.9972Durbin-VVatson stat1.640034Prob(F-statistic)0.000013③PC对X、K、P0做OLS回归，得到如下结果:Dep end ent Variable: PC Method: Least Squares Date: 08/24/07 Time: 22:17 Sample: 1981 1990 Included observations: 10VariableCoefficientStd. Error t-StatisticProb.C-31.2520731.74680 -0.9844170.3629X-0.0917280.114467 -0.8013440.4535K0.2196250.204669 1.0730730.3245P01.3415070.404914 3.3130630.0161R-squared0.986309Mean dependent var101.7000.Adjusted R-squared0.979463S.D. dependent var8.124722S.E. of repression1.164325.Akaike info criterion3.431334Sum squared resid8.133911Schwarz criterion3.552368Loq likelihood-13.15667F-statistic144.0798Durbin-VVatson stat2.818167Prob(F-statistic)0.000006④P0对X、K、PC做OLS回归，得到如下结果:Dep end ent Variable: PO Method: Least Squares Date: 08..124/07 Time: 22:20Sample: 1981 1990Included observations: 10VariableCoefficientStd. Errort-Statist! cProb.C42.7011510.802113.9530380.0075X0.1234040.0517032.3867690.0543K-0.1562570.117766-1.3268440.2328PC0.4819720.1454763.3130630.0161R-squared0.992102Mean dependent var102.0000.Adjusted R-squared0.988153S.D. dependent var6.411795S.E. of regressio。