计量经济学实验报告4.doc

实 验 报 告课程名称： 计量经济学 实验项目： 多重共线性模型的检验和处理 实验类型：综合性 设计性 验证性专业班别： 09本国际经济与贸易3班 姓 名： 陈春丽 学 号： 409010304 实验课室： 创新楼E506 指导教师： 石立 实验日期： 2012年4月19日 广东商学院华商学院教务处 制 一、实验项目训练方案小组合作：是 否小组成员：陈春丽实验目的：掌握多重共线性模型的检验和处理方法实验场地及仪器、设备和材料实验场地：创新楼E506使用EViews软件进行操作实验。实验训练内容（包括实验原理和操作步骤）：1、直观判断法（R2值、t值检验）根据广东数据（见附件1），先分别建立以下模型：【模型1】财政收入CS对第一产业产值GDP1、第二产业产值GDP2和第三产业产值GDP3的多元线性回归模型；Dependent Variable: CSMethod: Least SquaresDate: 04/19/12 Time: 14:20Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.GDP10.0287740.0541140.5317300.5998GDP2-0.0451410.030055-1.5019380.1462GDP30.2251210.0306417.3469830.0000C34.5239016.901002.0427140.0522R-squared0.993169Mean dependent var449.5546Adjusted R-squared0.992315S.D. dependent var509.5465S.E. of regression44.66975Akaike info criterion10.56803Sum squared resid47889.28Schwarz criterion10.75835Log likelihood-143.9525Hannan-Quinn criter.10.62621F-statistic1163.070Durbin-Watson stat2.056993Prob(F-statistic)0.000000【模型2】固定资产投资TZG对固定资产折旧ZJ、营业盈余YY和财政支出CZ的多元线性回归模型。Dependent Variable: TZGMethod: Least SquaresDate: 04/19/12 Time: 14:23Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.ZJ1.1118640.2431524.5727160.0001YY0.4316920.0525668.2123520.0000CZ0.1432100.4053080.3533380.7269C31.2762527.825171.1240270.2721R-squared0.997573Mean dependent var1628.997Adjusted R-squared0.997270S.D. dependent var2003.852S.E. of regression104.7010Akaike info criterion12.27166Sum squared resid263095.1Schwarz criterion12.46197Log likelihood-167.8032Hannan-Quinn criter.12.32984F-statistic3288.646Durbin-Watson stat1.298515Prob(F-statistic)0.000000观察模型结果，初步判断模型自变量之间是否存在多重共线性问题。观察模型结果，初步判断模型自变量之间存在多重共线性问题。2、简单相关系数检验法分别计算【模型1】和【模型2】的自变量的简单相关系数，进一步判断模型是否存在多重共线性。根据广东数据，CS对GDP1、GDP2和GDP3的回归中，解释变量GDP1、GDP2和GDP3之间的相关系数为可以看出三个解释变量、和之间高度相关，必然存在严重的多重共线性。根据广东数据，对、和之间的相关系数为：可以看出三个解释变量、和之间也高度相关，特别是和之间高度相关，必然也存在严重的多重共线性。3、方差扩大因子法（辅助回归检验）；分别建立【模型1】和【模型2】的辅助回归。计算各模型各个自变量的方差扩大因子。并将计算的结果，以表格形式列出。确定模型是否存在严重的多重共线性。Dependent Variable: GDP1Method: Least SquaresDate: 04/19/12 Time: 14:39Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.GDP20.2262730.1014462.2304870.0349GDP3-0.1087260.111141-0.9782700.3373C233.540441.475275.6308340.0000R-squared0.861095Mean dependent var569.4539Adjusted R-squared0.849983S.D. dependent var426.2507S.E. of regression165.0958Akaike info criterion13.15189Sum squared resid681415.5Schwarz criterion13.29462Log likelihood-181.1264Hannan-Quinn criter.13.19552F-statistic77.48953Durbin-Watson stat0.125127Prob(F-statistic)0.000000Dependent Variable: GDP2Method: Least SquaresDate: 04/19/12 Time: 14:40Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.GDP10.7335090.3288562.2304870.0349GDP30.9887830.04967319.905860.0000C-96.61529110.7935-0.8720300.3915R-squared0.991441Mean dependent var2584.440Adjusted R-squared0.990756S.D. dependent var3091.650S.E. of regression297.2502Akaike info criterion14.32798Sum squared resid2208941.Schwarz criterion14.47072Log likelihood-197.5918Hannan-Quinn criter.14.37162F-statistic1447.895Durbin-Watson stat0.553986Prob(F-statistic)0.000000Dependent Variable: GDP3Method: Least SquaresDate: 04/19/12 Time: 14:41Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.GDP1-0.3391030.346635-0.9782700.3373GDP20.9513230.04779119.905860.0000C23.49799110.21480.2132020.8329R-squared0.990116Mean dependent var2289.032Adjusted R-squared0.989325S.D. dependent var2821.962S.E. of regression291.5652Akaike info criterion14.28936Sum squared resid2125257.Schwarz criterion14.43210Log likelihood-197.0511Hannan-Quinn criter.14.33300F-statistic1252.134Durbin-Watson stat0.540826Prob(F-statistic)0.000000三个回归方程均高度显著，特别是第二、三个方程，显示存在严重的多重共线性，特别是和GDP3之间存在严重的多重共线性，解释变量之间的相关系数检验也证实了这一点。根据广东数据，TZG对ZJ、YY和CZ的回归中，解释变量ZJ、YY和CZ之间的辅助回归分别为：Dependent Variable: ZJMethod: Least SquaresDate: 04/19/12 Time: 14:45Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.YY-0.0014380.043236-0.0332680.9737CZ1.5524090.12141712.785740.0000C-9.31528022.81113-0.4083660.6865R-squared0.993332Mean dependent var846.0661Adjusted R-squared0.992798S.D. dependent var1014.824S.E. of regression86.11988Akaike info criterion11.85031Sum squared resid185415.8Schwarz criterion11.99305Log likelihood-162.9044Hannan-Quinn criter.11.89395F-statistic1862.101Durbin-Watson stat0.991139Prob(F-statistic)0.000000Dependent Variable: YYMethod: Least SquaresDate: 04/19/12 Time: 14:46Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.ZJ-0.0307770.925106-0.0332680.9737CZ2.7938701.4372891.9438470.0633C-178.113699.69398-1.7866040.0861R-squared0.956330Mean dependent var1338.742Adjusted R-squared0.952836S.D. dependent var1834.295S.E. of regression398.3588Akaike info criterion14.91354Sum squared resid3967244.Schwarz criterion15.05628Log likelihood-205.7896Hannan-Quinn criter.14.95718F-statistic273.7354Durbin-Watson stat0.547674Prob(F-statistic)0.000000Dependent Variable: CZMethod: Least SquaresDate: 04/19/12 Time: 14:47Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.ZJ0.5587160.04369812.785740.0000YY0.0469950.0241761.9438470.0633C16.6180413.322061.2474070.2238R-squared0.994207Mean dependent var552.2429Adjusted R-squared0.993744S.D. dependent var653.1881S.E. of regression51.66495Akaike info criterion10.82839Sum squared resid66731.67Schwarz criterion10.97113Log likelihood-148.5975Hannan-Quinn criter.10.87203F-statistic2145.335Durbin-Watson stat1.188416Prob(F-statistic)0.000000三个回归方程均高度显著，特别是第一、三个方程，显示存在严重的多重共线性，特别是ZJ和CZ之间存在严重的多重共线性，解释变量之间的相关系数检验也证实了这一点。（二）多重共线性的处理1、先验信息法、变量变换法已知【模型1】有一先验信息：GDP3对CS的贡献是GDP1贡献的3倍。根据该先验信息，我们可以将变量CS和GDP2作变量取对数变换，作出回归模型，判断是否消除了多重共线性。根据该先验信息，请提出一个对模型变量变换的方法，消除模型多重共线性。假设知道已知信息，对的贡献是贡献的倍，并结合变量交换法，进行如下回归：Dependent Variable: LOG(CS)Method: Least SquaresDate: 04/19/12 Time: 15:00Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.LOG(GDP2)0.6930370.03025722.904930.0000GDP1+3*GDP32.38E-055.55E-064.2826050.0002C0.4329670.1745942.4798440.0202R-squared0.991675Mean dependent var5.369302Adjusted R-squared0.991009S.D. dependent var1.319281S.E. of regression0.125097Akaike info criterion-1.218493Sum squared resid0.391233Schwarz criterion-1.075757Log likelihood20.05890Hannan-Quinn criter.-1.174857F-statistic1488.955Durbin-Watson stat1.002599Prob(F-statistic)0.000000得到回归方程为：LOG（CS）=0.693037*2.38E-05*（GDP1+3*GDP3）+0.432967基本消除了多重共线性，当然，假设是否正确有待探讨。已知【模型2】有一先验信息：在企业折旧资金和营业盈余资金主要是会计账面对区别，资金常常是混在一起用的，不区分折旧资金和营业盈余资金的使用，因此我们可以将ZJ和YY加起来作为一个大的变量使用。使用该先验信息，作回归模型，根据模型结果，判断是否消除了多重共线性。实际上，在企业折旧资金和营业盈余资金主要是会计账面的区别，资金常常是混在一起使用的，不区分折旧资金营业盈余资金的使用。据此，把ZJ和YY加在一起 ，进行如下回归：Dependent Variable: TZGMethod: Least SquaresDate: 04/19/12 Time: 15:07Sample: 1978 2005Included observations: 28CoefficientStd. Errort-StatisticProb.ZJ+YY0.4612080.0577487.9866040.0000CZ1.0696670.2504134.2716160.0002C30.6306331.230660.9807870.3361R-squared0.996815Mean dependent var1628.997Adjusted R-squared0.996561S.D. dependent var2003.852S.E. of regression117.5195Akaike info criterion12.47204Sum squared resid345270.5Schwarz criterion12.61478Log likelihood-171.6086Hannan-Quinn criter.12.51568F-statistic3912.553Durbin-Watson stat0.908575Prob(F-statistic)0.000000得到回归方程为：TZG=0.461208*(ZJ+YY)+1.069667*CZ+30.63063基本消除了多重共线性。2、逐步回归方法现研究中国的能源消费需求问题：理论上认为影响能源消费需求总量的因素主要有经济发展水平、收入水平、产业发展、人民生活水平提高、能源转换技术等因素。为此，收集了中国能源消费总量Y (万吨标准煤)、国内生产总值(亿元)X1(代表经济发展水平)、国民总收入(亿元)X2(代表收入水平)、工业增加值(亿元)X3、建筑业增加值(亿元)X4、交通运输邮电业增加值(亿元)X5(代表产业发展水平及产业结构)、人均生活电力消费 (千瓦小时)X6(代表人民生活水平提高)、能源加工转换效(%)X7(代表能源转换技术)等在1985-2002年期间的统计数据（见附件2：中国的能源消费需求相关数据）。 建立中国能源消费需求的多元回归模型。Y=-80155.52+36.84232X1-28.23350X2-10.32637X3-17.52643X4-34.49995X5+336.4866X6+1952.573 根据建立的模型，判断是否有多重共线性的问题。并使用直观判断法（R2值、t值检验）、简单相关系数检验法、方差扩大因子法（辅助回归检验）对模型多重共线性问题进行检验。 如果存在多重共线性的问题，使用逐步回归法处理模型的多重共线性问题。Dependent Variable: YMethod: Stepwise RegressionDate: 04/19/12 Time: 15:42Sample: 1985 2002Included observations: 18Number of always included regressors: 1Number of search regressors: 1Selection method: Stepwise forwardsStopping criterion: p-value forwards/backwards = 0.5/0.5CoefficientStd. Errort-StatisticProb.*C85243.953524.48124.186240.0000X10.6249740.06154510.154810.0000R-squared0.865682Mean dependent var114898.3Adjusted R-squared0.857287S.D. dependent var22162.37S.E. of regression8372.365Akaike info criterion21.00770Sum squared resid1.12E+09Schwarz criterion21.10663Log likelihood-187.0693Hannan-Quinn criter.21.02134F-statistic103.1201Durbin-Watson stat0.253364Prob(F-statistic)0.000000Selection SummaryAdded X1*Note: p-values and subsequent tests do not account for stepwiseselection.如果存在多重共线性的问题，使用逐步回归法处理模型的多重共线性问题。Dependent Variable: YMethod: Stepwise RegressionDate: 04/19/12 Time: 15:42Sample: 1985 2002Included observations: 18Number of always included regressors: 1Number of search regressors: 1Selection method: Stepwise forwardsStopping criterion: p-value forwards/backwards = 0.5/0.5CoefficientStd. Errort-StatisticProb.*C85243.953524.48124.186240.0000X10.6249740.06154510.154810.0000R-squared0.865682Mean dependent var114898.3Adjusted R-squared0.857287S.D. dependent var22162.37S.E. of regression8372.36