多重共线的检验与修正.doc

附件二：实验报告格式（首页） 山东轻工业学院实验报告 成绩 课程名称 计量经济学 指导教师 实验日期 2013-5-25 院（系） 商学院 专业班级 实验地点 二机房 学生姓名 学号 同组人 无 实验项目名称 多重共线性的检验与修正 一、 实验目的和要求 掌握Eviews软件的操作和多重共线性的检验与修正二、 实验原理 Eviews软件的操作和多重共线性的检验修正方法三、 主要仪器设备、试剂或材料 Eviews软件，计算机四、 实验方法与步骤 （1）准备工作：建立工作文件，并输入数据： CREATE EX-7-1 A 1974 1981; TATA Y X1 X2 X3 X4 X5 ; (2)OLS估计： LS Y C X1 X2 X3 X4 X5; (3)计算简单相关系数 COR X1 X2 X3 X4 X5 ; (4)多重共线性的解决 LS Y C X1; LS Y C X2;LS Y C X3;LS Y C X4;LS Y C X5;LS Y C X1 X3;LS Y C X1 X3 X2;LS Y C X1 X3 X4;LS Y C X1 X3 X5; 五、 实验数据记录、处理及结果分析 （1）建立工作组，输入以下数据： 98.45560.20 153.20 6.53 1.23 1.89 100.70 603.11 190.00 9.12 1.30 2.03 102.80 668.05 240.30 8.10 1.80 2.71 133.95 715.47 301.12 10.10 2.09 3.00 140.13 724.27 361.00 10.93 2.39 3.29 143.11 736.13 420.00 11.85 3.90 5.24 146.15 748.91 491.76 12.28 5.13 6.83 144.60 760.32 501.00 13.50 5.47 8.36 148.94 774.92 529.20 15.29 6.09 10.07 158.55 785.30 552.72 18.10 7.97 12.57 169.68 795.50 771.16 19.61 10.18 15.12 162.14 804.80 811.80 17.22 11.79 18.25 170.09 814.94 988.43 18.60 11.54 20.59 178.69 828.73 1094.65 23.53 11.68 23.37 （2）OLS估计 Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:10Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C-3.49656330.00659-0.1165260.9101X10.1253300.0591392.1192450.0669X20.0736670.0378771.9448970.0877X32.6775891.2572932.1296460.0658X43.4534482.4508501.4090820.1965X5-4.4911172.214862-2.0277190.0771R-squared0.970442Mean dependent var142.7129Adjusted R-squared0.951968S.D. dependent var26.09805S.E. of regression5.719686Akaike info criterion6.623232Sum squared resid261.7185Schwarz criterion6.897114Log likelihood-40.36262F-statistic52.53086Durbin-Watson stat1.972755Prob(F-statistic)0.000007 用Eviews进行最小二乘估计得，=-3.497+0.125X1+0.074X2+2.678X3+3.453X4-4.491X5(-0.1) (2.1) (1.9) (2.1) (1.4) (-2.0)R=0.970, =0.952, DW=1.97, F=52.53其中括号内的数字是t值。给定显著水平=0.05，回归系数估计值都没有显著性。查F分布表，得临界值为F0.05（5,8）=3.69，故F=52.533.69，回归方程显著。(3)计算简单相关系数 COR X1 X2 X3 X4 X5 ; X1X2X3X4X5X110.866551867279170.8822931086064990.8524491353193940.821305444858646X20.8665518672791710.9458956983200270.9647730220121920.98253206329193X30.8822931086064990.94589569832002710.9405058208239960.948361346495427X40.8524491353193940.9647730220121920.94050582082399610.98197917741363X50.8213054448586460.982532063291930.9483613464954270.981979177413631 r12=0.867， r13=0.882， r14=0.852， r15=0.821，r23=0.946， r24=0.965,r25=0.983， r34=0.941，r35=0.948， r45=0.982可见解释变量之间是高度相关的。(4)多重共线性的解决, 采用Frisch法。&1.对Y关于X1，X2，X3，X4，X5作最小二乘回归: 1) LS Y C X1Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:12Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C-90.9207419.32929-4.7037810.0005X10.3169250.02608112.151610.0000R-squared0.924841Mean dependent var142.7129Adjusted R-squared0.918578S.D. dependent var26.09805S.E. of regression7.446964Akaike info criterion6.985054Sum squared resid665.4873Schwarz criterion7.076347Log likelihood-46.89537F-statistic147.6617Durbin-Watson stat1.536885Prob(F-statistic)0.000000 得回归方程为：=-90.921+0.317X1（-4.7） （12.2)R=0.925, =0.919, DW=1.537, F=147.6192) LS Y C X2Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:14Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C99.613496.43124215.489000.0000X20.0814700.0107387.5871190.0000R-squared0.827498Mean dependent var142.7129Adjusted R-squared0.813123S.D. dependent var26.09805S.E. of regression11.28200Akaike info criterion7.815858Sum squared resid1527.403Schwarz criterion7.907152Log likelihood-52.71101F-statistic57.56437Durbin-Watson stat0.638969Prob(F-statistic)0.000006 得回归方程为：=99.614+0.0815X2（15.5） （7.6）R=0.828, =0.813, DW=0.639，F=57.5643）LS Y C X3Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:14Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C74.648248.2889899.0057110.0000X34.8927120.5635788.6815140.0000R-squared0.862651Mean dependent var142.7129Adjusted R-squared0.851205S.D. dependent var26.09805S.E. of regression10.06704Akaike info criterion7.587974Sum squared resid1216.144Schwarz criterion7.679268Log likelihood-51.11582F-statistic75.36868Durbin-Watson stat0.813884Prob(F-statistic)0.000002得回归方程为：=74.648+4.893X3（9.0） （8.7）R=0.863, =0.851, DW=0.814，F=75.3694) LS Y C X4Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:15Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C108.86475.93433018.344900.0000X45.7397520.8387566.8431750.0000R-squared0.796019Mean dependent var142.7129Adjusted R-squared0.779021S.D. dependent var26.09805S.E. of regression12.26828Akaike info criterion7.983475Sum squared resid1806.129Schwarz criterion8.074769Log likelihood-53.88433F-statistic46.82904Durbin-Watson stat0.769006Prob(F-statistic)0.000018 得回归方程为：=108.865+5.740X4（18.3） （6.8）R=0.796, =0.779, DW=0.769，F=46.8295) LS Y C X5Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:16Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C113.37476.07713318.655960.0000X53.0808110.5123006.0136880.0001R-squared0.750854Mean dependent var142.7129Adjusted R-squared0.730091S.D. dependent var26.09805S.E. of regression13.55865Akaike info criterion8.183490Sum squared resid2206.044Schwarz criterion8.274784Log likelihood-55.28443F-statistic36.16444Durbin-Watson stat0.593639Prob(F-statistic)0.000061得回归方程为：=113.375+3.081X5（18.7） （6.0）R=0.75, =0.73, DW=0.59，F=36.16选第一个方程为基本回归方程。&2. 加入肉销售量X3，对Y关于X1，X3作最小二乘回归1) LS Y C X1 X3Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:17Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C-39.7947925.01570-1.5907930.1400X10.2115430.0453024.6695810.0007X31.9092460.7241532.6365230.0231R-squared0.953945Mean dependent var142.7129Adjusted R-squared0.945571S.D. dependent var26.09805S.E. of regression6.088671Akaike info criterion6.638146Sum squared resid407.7910Schwarz criterion6.775087Log likelihood-43.46702F-statistic113.9220Durbin-Watson stat1.655554Prob(F-statistic)0.000000 得回归方程为：=-39.795+0.212X1+1.909X3（-1.6） （4.7）(2.6)R=0.954, =0.946, DW=1.656，F=113.922可以看出，加入X3后，拟合优度R和均有所增加，参数估计值的符号也正确，并且没有影响X1系数的显著性，所以在模型中保留X3.2)加入人均收入X2，对Y关于X1,X2,X3作最小二乘回归 LS Y C X1 X3 X2Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:18Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C-34.7768327.80679-1.2506600.2395X10.2065350.0480004.3028100.0016X31.4555201.1801891.2332940.2457X20.0094250.0189230.4980370.6292R-squared0.955060Mean dependent var142.7129Adjusted R-squared0.941577S.D. dependent var26.09805S.E. of regression6.308098Akaike info criterion6.756502Sum squared resid397.9210Schwarz criterion6.939090Log likelihood-43.29551F-statistic70.83889Durbin-Watson stat1.682584Prob(F-statistic)0.000000 得回归方程为：=-34.777+0.207X1+0.009X2+1.456X3(-1.3) (4.3) (0.5) (1.2)R=0.955, =0.942, DW=1.683, F=70.839可以看出，再加入X2后，拟合优度R增加不显著，有所减小，并且X2和X3系数均不显著，说明存在严重的共线性。比较X2和X3，肉销售量比人均收入对粮食销售量的影响大，所以在模型中保留X3，略去X2。3) 加入蛋销售量X4，对Y关于X1,X3,X4作最小二乘估计 LS Y C X1 X3 X4Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:19Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C-37.9988428.00654-1.3567850.2047X10.2103140.0479194.3889780.0014X31.7457671.1785901.4812340.1694X40.2347891.2958740.1811820.8598R-squared0.954096Mean dependent var142.7129Adjusted R-squared0.940324S.D. dependent var26.09805S.E. of regression6.375396Akaike info criterion6.777726Sum squared resid406.4568Schwarz criterion6.960314Log likelihood-43.44408F-statistic69.28123Durbin-Watson stat1.673512Prob(F-statistic)0.000001得回归方程为：=-37.999+0.210X1+1.746X3+0.235X4 (-1.4) （4.4） （1.5） （0.2） R=0.954, =0.940, DW=1.674, F=69.281 可以看出，在加入X4后，拟合优度R没有增加， 有所减小，并且X3和X4系数均不显著，说明存在严重的多重共线性。比较X3和X4，肉销售量比蛋销售量对粮食销售量的影响大，所以在模型中保留X3,略去X4。4) 加入鱼虾销售量X5，对Y关于X1,X3,X5作最小二乘回归 LS Y C X1 X3 X5Dependent Variable: YMethod: Least SquaresDate: 05/25