多重共线性实验报告-lucas

1《计量经济学》实验报告四开课实验室：崇德楼3152013年5月19日姓名金超龙成绩年级专业2010级国贸专业学号20102811课程名称计量经济学实验名称多重共线性实验一、实验内容依据经济学理论，以实际数据（实验数据五）为基础，①建立反映天津市粮食市场需求状况的粮食需求函数。②检验所建立的粮食需求函数是否存在多重共线性。③如果存在多重共线性，使用恰当的方法加以解决。二、实验目的熟练使用EViews软件进行计量分析，理解多重共线性的检验和估计的基本方法。三、实验步骤STEP1：参数估计STEP2：检验STEP3：消除多重共线性四、实验结果及分析（附上必要的回归分析报告，并作以分析）经分析，影响天津粮食需求的主要因素，除了市常住人口和人均收入以外，还可能与相关其他农畜产品有关。为此，考虑的影响因素主要有市常住人口X1，人均收入X2、肉销售量X3、蛋销售量X4和鱼虾销售量X5。为此设定如下的对数形式的计量经济模型：tttttttXXXXXY54321543210Y=粮食销售量（万吨/年）；X1=市常住人口数（万人）；X2=人均收入（元/年）；X3=肉销售量（万吨/年）；X4=蛋销售量（万吨/年）；X5=鱼虾销售量（万吨/年）。数据见实验指导数据五，来源于《中国统计年鉴年》STEP1：参数估计在Eviews中点击NEW项，建立Workfile输入Y、X1、X2、X3、X4、X5的数据。点击Quick，选EstimateEquation项，在OLS对话框中，键入YCX1X2X3X4X5，输出结果。见图6.4.1。2图6.4.1Eviews输出的回归结果分析：模型R2=0.9703910.9518852R可决系数很高，F检验值52.43740，显著。但当α=5%时，t统计值=1.7613，X4和X5系数的t检验不显著，同时X5的系数为负号不符合实际，这表明很可能存在多重共线性。STEP2：检验计算各解释变量的相关系数，选择X1、X2、X3、X4、X5数据，点击“quick\groupstatistics\correlation”的相关系数矩阵，见表6.4.1。有相关系数矩阵可以看出：各解释变量相关之间的相关系数较高，证实存在严重多重共线性。表6.4.1自变量相关系数矩阵STEP3：消除多重共线性采用逐步回归的办法，检验和解决多重共线性问题。分别作Y对X1、X2、X3、X4、X5的一元回归，结果如表6.4.2。DependentVariable:YMethod:LeastSquaresDate:05/12/03Time:13:56Sample:19741987Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.C-90.9207419.32929-4.7037810.0005X10.3169250.02608112.151610.0000R-squared0.924841Meandependentvar142.71293AdjustedR-squared0.918578S.D.dependentvar26.09805S.E.ofregression7.446964Akaikeinfocriterion6.985054Sumsquaredresid665.4873Schwarzcriterion7.076347Loglikelihood-46.89537F-statistic147.6617Durbin-Watsonstat1.536885Prob(F-statistic)0.000000DependentVariable:YMethod:LeastSquaresDate:05/12/03Time:13:59Sample:19741987Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.C99.552516.42336415.498500.0000X20.0815190.0107187.6055060.0000R-squared0.828188Meandependentvar142.7129AdjustedR-squared0.813870S.D.dependentvar26.09805S.E.ofregression11.25942Akaikeinfocriterion7.811851Sumsquaredresid1521.294Schwarzcriterion7.903145Loglikelihood-52.68296F-statistic57.84372Durbin-Watsonstat0.642278Prob(F-statistic)0.000006DependentVariable:YMethod:LeastSquaresDate:05/12/03Time:14:00Sample:19741987Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.C74.648248.2889899.0057110.0000X34.8927120.5635788.6815140.0000R-squared0.862651Meandependentvar142.7129AdjustedR-squared0.851205S.D.dependentvar26.09805S.E.ofregression10.06704Akaikeinfocriterion7.587974Sumsquaredresid1216.144Schwarzcriterion7.679268Loglikelihood-51.11582F-statistic75.36868Durbin-Watsonstat0.813884Prob(F-statistic)0.000002DependentVariable:Y4Method:LeastSquaresDate:05/12/03Time:14:01Sample:19741987Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.C108.86475.93433018.344900.0000X45.7397520.8387566.8431750.0000R-squared0.796019Meandependentvar142.7129AdjustedR-squared0.779021S.D.dependentvar26.09805S.E.ofregression12.26828Akaikeinfocriterion7.983475Sumsquaredresid1806.129Schwarzcriterion8.074769Loglikelihood-53.88433F-statistic46.82904Durbin-Watsonstat0.769006Prob(F-statistic)0.000018DependentVariable:YMethod:LeastSquaresDate:05/12/03Time:14:02Sample:19741987Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.C113.37476.07713318.655960.0000X53.0808110.5123006.0136880.0001R-squared0.750854Meandependentvar142.7129AdjustedR-squared0.730091S.D.dependentvar26.09805S.E.ofregression13.55865Akaikeinfocriterion8.183490Sumsquaredresid2206.044Schwarzcriterion8.274784Loglikelihood-55.28443F-statistic36.16444Durbin-Watsonstat0.593639Prob(F-statistic)0.000061表6.4.2回归结果变量X1X2X3X4X5参数估计值0.3169250.0815194.8927125.7397523.080811t统计值12.151617.6055068.6815146.8431756.013688R20.9248410.8281880.8626510.7960190.750854按R2的大小排序为：X1、X3、X2、X4、X5。以X1为基础，顺次加入其他变量逐步回归。首先加入X3回归结果为：DependentVariable:Y5Method:LeastSquaresDate:05/12/03Time:14:05Sample:19741987Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.C-39.7947925.01570-1.5907930.1400X10.2115430.0453024.6695810.0007X31.9092460.7241532.6365230.0231R-squared0.953945Meandependentvar142.7129AdjustedR-squared0.945571S.D.dependentvar26.09805S.E.ofregression6.088671Akaikeinfocriterion6.638146Sumsquaredresid407.7910Schwarzcriterion6.775087Loglikelihood-43.46702F-statistic113.9220Durbin-Watsonstat1.655554Prob(F-statistic)0.000000tttXXY390924.11211543.079479.39ˆt(-1.590793)(4.669581)（2.636523）R2=0.953945当α=5%时，2010.2)1214()1(025.02/tknt，X3参数的t检验显著，不予剔除，加入X2回归得：DependentVariable:YMethod:LeastSquaresDate:05/12/03Time:14:10Sample:19741987Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.C-34.6287927.82151-1.2446770.2416X10.2063280.0480164.2970540.0016X31.4486691.1753251.2325690.2459X20.0096050.0188750.5088970.6219R-squared0.955107Meandependentvar142.7129AdjustedR-squared0.941640S.D.dependentvar26.09805S.E.ofregression6.304735Akaikeinfocriterion6.755435Sumsquaredresid397.4968Schwarzcriterion6.938023Loglikelihood-43.28805F-statistic70.91803Durbin-Watsonstat1.682728Prob(F-statistic)0.0000006ttttXXXY2009605.03448669.11206328.062879.34ˆt(4.297054)(1.232569)(0.508897)R2=0.955107当α=5%时，2281.2)1314()1(