(整理)多重共线性的检验与修正

1、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

2、 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：98.45560.20153.206.531.231.89100.70603.11190.009.121.302.03102.80668.05240.308.101.802.71133.9571

3、5.47301.1210.102.093.00140.13724.27361.0010.932.393.29143.11736.13420.0011.853.905.24146.15748.91491.7612.285.136.83144.60760.32501.0013.505.478.36148.94774.92529.2015.296.0910.07158.55785.30552.7218.107.9712.57169.68795.50771.1619.6110.1815.12162.14804.80811.8017.2211.7918.25170.09814.94988.4318.60

4、11.5420.59178.69828.731094.6523.5311.6823.372) 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

5、.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 criterion6.89

6、7114Log likelihood-40.36262F-statistic52.53086Durbin-Watson stat1.972755Prob(F-statistic)0.000007用Eviews进行最小二乘估计得，Y?=-3.497+0.125X1+0.074X2+2.678X3+3.453X4-4.491X5(-0.1) (2.1) (1.9) (2.1) (1.4) (-2.0)R2 =0.970, R 2 =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(

7、5,8)=3.69 ，故F=52.53>3.69 ，回归方程显著。(3) 计算简单相关系数COR X1 X2 X3 X4 X5 ;X1X20.8665518672X30.8822931086X40.8524491353X50.8213054448X1179170649919394586460.86655186720.94589569830.96477302200.9825320632X279171200271219291930.88229310860.94589569830.94050582080.9483613464X30649920027123996954270.8524491353

8、0.96477302200.94050582080.9819791774X4193941219223996113630.82130544480.98253206320.94836134640.9819791774X55864691939542713631r12=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 X

9、1，X2， X3，X4，X5作最小二乘回归 :1)LS Y C X1Dependent Variable: Y Method: Least Squares Date: 05/25/13Time: 11:12Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C-90.9207419.32929-4.7037810.0005X10.3169250.02608112.151610.0000R-squared0.924841Mean dependent var142.7129Ad

10、justed R-squared0.918578 S.D. dependent var26.09805S.E. of regression7.446964 Akaike info criterion6.985054Sum squared resid665.4873 Schwarz criterion7.076347Log likelihood-46.89537 F-statistic147.6617Durbin-Watson stat1.536885 Prob(F-statistic)0.000000得回归方程为：Y?=-90.921+0.317X1(-4.7 ) (12.2)R2 =0.92

11、5, R 2 =0.919, DW=1.537, F=147.6192) LS Y C X2Dependent Variable: YMethod: Least Squares Date: 05/25/13Time: 11:14Sample: 1974 1987Included observations: 14VariableCoefficientStd. Error t-StatisticProb.C99.613496.431242 15.489000.0000X20.0814700.010738 7.5871190.0000R-squared0.827498Mean dependent v

12、ar142.7129Adjusted 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：Y?=99.614+0.0815X2（15.5 ） （7.6 ）R

13、2 =0.828, R 2 =0.813, DW=0.639 ，F=57.5643)LS Y C X3Dependent Variable: YMethod: Least SquaresDate: 05/25/13Time: 11:14Sample: 1974 1987Included observations: 14VariableCoefficientStd. Error t-StatisticProb.C74.648248.288989 9.0057110.0000X34.8927120.563578 8.6815140.0000R-squared0.862651Mean depende

14、nt 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：Y?=74.648+4.893X3 (9.0 ) (8.7

15、 )R2 =0.863, R 2 =0.851, DW=0.814 ，F=75.3694) LS Y C X4Dependent Variable: YMethod: Least SquaresDate: 05/25/13Time: 11:15Sample: 1974 1987Included observations: 14VariableCoefficientStd. Error t-StatisticProb.C108.86475.934330 18.344900.0000X45.7397520.838756 6.8431750.0000R-squared0.796019Mean dep

16、endent 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：Y?=108.865+5.740X4（18.3 ）

17、 （6.8 ）R2 =0.796,2R 2 =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. Error t-StatisticProb.C113.37476.077133 18.655960.0000X53.0808110.512300 6.0136880.0001R-squared0.750854Me

18、an 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：Y?=113.375+3.081X5（

19、18.7 ） （6.0 ）22R2 =0.75, R2 =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: 05/25/13Time: 11:17Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C-39.7947925.01570-1.5907930.

20、1400X10.2115430.045302 4.6695810.0007X31.9092460.724153 2.6365230.0231R-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-stati

21、stic113.9220Durbin-Watson stat1.655554Prob(F-statistic)0.000000得回归方程为：Y?=-39.795+0.212X1+1.909X3 (-1.6 ) (4.7 )(2.6)R2 =0.954, R 2 =0.946, DW=1.656 ，F=113.922可以看出，加入 X3后，拟合优度 R2和 R2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: YMetho

22、d: Least SquaresDate: 05/25/13 Time: 11:18Sample: 1974 1987Included observations: 14VariableCoefficientStd. Error t-StatisticProb.C-34.7768327.80679 -1.2506600.2395X10.2065350.048000 4.3028100.0016X31.4555201.180189 1.2332940.2457X20.0094250.018923 0.4980370.6292R-squared0.955060Mean dependent var14

23、2.7129Adjusted 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：Y?=-34.777+0.207X1+0.009X2+1.456X3(-1

24、.3) (4.3) (0.5) (1.2)R2 =0.955, R 2 =0.942, DW=1.683, F=70.839可以看出，再加入 X2后，拟合优度 R2 增加不显著， R 2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: 197

25、4 1987Included observations: 14VariableCoefficientStd. Error t-StatisticProb.C-37.9988428.00654 -1.3567850.2047X10.2103140.047919 4.3889780.0014X31.7457671.178590 1.4812340.1694X40.2347891.295874 0.1811820.8598R-squared0.954096Mean dependent var142.7129Adjusted R-squared0.940324S.D. dependent var26.

26、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：Y?=-37.999+0.210X1+1.746X3+0.235X4（-1.4）（4.4 ） （1.5） （0.2 ）R 2 =0.954, R 2 =0.940, DW=1.674, F=69.281可以看出，在加入 X4后，拟合优度 R2 没有增加， R 2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: 05/25/13Time: 11:20Sample: