计量经济学实验五-多重共线性的检验与修正

1多重共线性的检验与修正【实验目的】掌握多重共线性的检验与修正方法并能运用Eviews软件进行实现【实验要求】能根据OLS的估计结果判断是否存在多重共线性，熟悉逐步回归法修正模型的基本操作步骤，读懂各项上机榆出结果的含义并能进行分析【实验软件】Eviews软件【实验内容】根据给定的案例数据按实验要求进行操作【实验方案与进度】实验：设某地区蔬菜销售量Y与人口（X1）、价格（X2）、粮食价格（X3）、收入（X4）、副食价格（X5）和储蓄（X6）等资料如下：obsYX1X2X3X4X5X619887.450425.58.1217.517.80185.8521.6819897.605422.38.3222.919.51185.3521.0819907.855418.08.3623.718.93185.1021.0319917.805419.28.2021.119.05184.8020.7319926.900384.28.8623.319.57184.6021.9319937.470372.57.7019.119.95184.2522.4919947.385372.98.4618.220.89181.3523.2619957.225380.88.8822.223.27179.3024.3919968.130401.79.0027.626.06178.1025.0419978.720406.58.8028.828.55176.2525.5319989.145410.59.2627.830.12174.3526.64199910.105447.08.6224.432.78174.2527.53200010.170452.88.4424.132.21179.3528.12200110.540467.19.6627.833.57173.8531.35200210.635495.29.6819.534.86179.5034.58200310.455500.011.3225.436.60166.8541.78200410.995525.012.3028.440.35158.2542.85200512.380550.012.8835.445.00155.0046.75200611.770561.014.0234.849.87141.0549.21要求：（1）将Y关于其他变量线性回归DependentVariable:YMethod:LeastSquaresDate:06/03/13Time:16:48Sample:19882006Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.2C-1.5302606.006901-0.2547500.8032X10.0146490.0029235.0121070.0003X2-0.7027750.254521-2.7611690.0172X30.0603210.0275752.1875450.0492X40.1198250.0369913.2392900.0071X50.0180810.0260220.6948160.5004X60.0922660.0542651.7003020.1148R-squared0.986169Meandependentvar9.091579AdjustedR-squared0.979254S.D.dependentvar1.717935S.E.ofregression0.247442Akaikeinfocriterion0.322027Sumsquaredresid0.734730Schwarzcriterion0.669979Loglikelihood3.940740F-statistic142.6067Durbin-Watsonstat2.292164Prob(F-statistic)0.000000123456-1.5300.0150.7030.0600.120.0180.092ttttttttYXXXXXXu（2）经济意义检验：与预期符号相符（3）方程线性显著性检验由（1）表中的数据可知F统计量的值为142.6067，查表得0.05(6,12)F=3，显然142.60670.05(6,12)F=3，说明方程具有线性显著性。（4）解释变量的变量显著性检验。在0.05的显著水平条件下，查表得0.025,(197)t=2.179，由（1）表中数据可知，5X、6X的t检验值明显小于临界值，则接受原假设：0:06050HH和：,说明5X、6X对Y的影响不显著，对方程没有意义。（5）用直观判断法判断模型是否有多重共线性？由（1）表中数据可知，该模型判定系数2R=0.986169,调整的判定系数2R=0.979254，数值都接近于1，解释变量对被解释变量的解释程度很高，而F统计值为142.6067，明显显著。但是如果给定0.05的显著性水平，0.025,(197)t=2.179，显然5X与6X系数不能通过t检验，5X的与预期符号不符，这表明很可能存在严重的多重共线性。（6）对解释变量之间的相关系数进行检查，是否可怀疑自变量之间存在严重的多重共线性。X1X2X3X4X5X6X110.8849650.6545300.898947-0.8416170.929992X20.88496510.7827340.897952-0.9627260.963175X30.6545300.78273410.783237-0.8288400.7166813X40.8989470.8979520.7832371-0.9278430.953896X5-0.841617-0.962726-0.82884-0.9278431-0.936253X60.9299920.9631750.7166810.953896-0.9362531由相关系数矩阵可以看出，除1X与3X和3X与4X的相关系数较低，（但也达0.6以上）其他各解释变量之间的相关系数都很高，证实确实存在较严重的多重共线性。（7）利用逐步回归法拟合一个较为理想的回归模型。分别作Y对1X，2X，3X，4X，5X，6X的一元回归，整理数据结果如下：变量1X2X3X4X5X6X参数估计值0.0271530.7801630.2425010.171860-0.1176250.168005t统计量10.235275.6792424.13597113.90115-6.0119288.8274992R0.8521690.6345460.4722380.9143840.6612930.810376以4X为解释变量的一元线性回归方程拟合最好，修正的判定系数值最大，以这个模型为基础，分别加入1X，2X，3X，5X，6X进行回归分析整理数据结果如下：1X2X3X4X5X6X2R41,XXt0.0100270.1166620.9343632.4848254.72101942,XXt-0.2571300.2147910.924533-1.8127478.14391643,XXt-0.0378230.1873690.914339-0.9954989.42009045,XXt0.2494030.0664960.9430489.2251373.09128546,XXt0.187951-0.0174500.9099314.448634-0.399277加入5X的二元方程2R=0.943048，改进最大，且4X、5X的t统计量都大于临界值0.025,(197)t=2.179，检验显著，保留5X，结果如下表：变量1X2X3X4X5X6X2R451,,XXXt统计量0.0105850.1943890.0692890.9692983.8314117.9346194.382464452,,XXXt统计量0.1155490.2486780.0824180.9405100.5632798.9901972.301523453,,XXXt统计量0.0053990.2491140.0681460.9393440.1516028.9079912.7560734456,,XXXt统计量0.2256920.0778300.0400460.9432396.3531063.2231901.026534加入1X的二元方程2R=0.969298，改进最大，而且4X、5X、1X的t统计量都大于临界值0.025,(197)t=2.179，检验显著，保留1X结果如下表：变量1X2X3X4X5X6X2R4512,,,XXXXt统计量0.014468-0.3461750.1763810.0226120.9748744.638504-2.0806657.4132450.8498954513,,,XXXXt统计量0.0112930.0287540.1891760.0782680.9697864.0141091.1146037.6437584.4389274516,,,XXXXt统计量0.0128680.2060420.058650-0.0397170.9698103.7685737.7964913.199514-1.120068经比较，加入2X的二元方程2R=0.974874，改进最大，但他的t统计量不是显著的，而加入3X，6X，不但2R没有改进，而且他们的t统计量也不是显著的，说明2X，3X，6X引起严重的多重共线性。