实验报告6-多重共线性

1、浙江大学城市学院 实 验 报 告 纸编号： 2014-2015学年第 一 学期实 验 报 告实验课程名称 多重共线性的检验与修正 专 业 班 级 金融1204 学 生 学 号 31205382 学 生 姓 名 黄聪聪 实验指导教师 董美双 实验名称 多重共线性检验与修正 指导老师 董美双 成绩 专业 金融 班级 金融1204 姓名 黄聪聪 学号 31205382 一、实验目的目的：通过实验，理解并掌握多重共线性的原理，熟悉掌握对多元模型的多重共线性问题进行检验和修正的方法与步骤。要求：熟练掌握检验多重共线性检验的不显著系数法、系数符号判断法、相关系数矩阵法、拟合优度法、Frisch综合分析法；

2、消除多重共线性：可以综合应用各种方法。验证性部分用教材中的例题7.6的数据，按步骤做。或者自己收集数据按上面的步骤做一遍，把结果输出到word文档中。步骤： 1.模型的参数估计（至少有3个解释变量）； 2.检验是否存在多重共线性； 方法一：不显著系数法； 方法二：系数符号法 方法三：相关系数矩阵法 方法四：Frish综合分析法逐步回归法 3.多重共线性的修正：差分法、取对数法、逐步回归法等。 4.得出修正后的模型。 1.模型的参数估计（至少有3个解释变量）Dependent Variable: BUSTRAVLMethod: Least SquaresDate: 07/26/14 Time:

3、10:09Sample: 1 40Included observations: 40VariableCoefficientStd. Errort-StatisticProb. C2744.6802641.6721.0389940.3064FARE-238.6544451.7281-0.5283140.6008GASPRICE522.11322658.2280.1964140.8455INC-0.1947440.064887-3.0012940.0051POP1.7114420.2313647.3971760.0000DENSITY0.1164150.0595701.9542530.0592LA

4、NDAREA-1.1552301.802638-0.6408550.5260R-squared0.921026 Mean dependent var1933.175Adjusted R-squared0.906667 S.D. dependent var2431.757S.E. of regression742.9113 Akaike info criterion16.21666Sum squared resid18213267 Schwarz criterion16.51221Log likelihood-317.3332 F-statistic64.14338Durbin-Watson s

5、tat2.082671 Prob(F-statistic)0.000000估计方程为：2.检验是否存在多重共线性方法一：不显著系数法Dependent Variable: BUSTRAVLMethod: Least SquaresDate: 07/26/14 Time: 10:09Sample: 1 40Included observations: 40VariableCoefficientStd. Errort-StatisticProb. C2744.6802641.6721.0389940.3064FARE-238.6544451.7281-0.5283140.6008GASPRICE5

6、22.11322658.2280.1964140.8455INC-0.1947440.064887-3.0012940.0051POP1.7114420.2313647.3971760.0000DENSITY0.1164150.0595701.9542530.0592LANDAREA-1.1552301.802638-0.6408550.5260R-squared0.921026 Mean dependent var1933.175Adjusted R-squared0.906667 S.D. dependent var2431.757S.E. of regression742.9113 Ak

7、aike info criterion16.21666Sum squared resid18213267 Schwarz criterion16.51221Log likelihood-317.3332 F-statistic64.14338Durbin-Watson stat2.082671 Prob(F-statistic)0.000000由表格可知，样本整体拟合优度达到92.1%，意味着模型解释变量整理能够解释因变量的92.1%，即说服力相对较强。但是个别变量如FARE，GASPRICE，DENSITY ，LANDAREA，它们系数的p值分别为0.6008，0.8455，0.0592，0

8、.5260，大于0.01，0.05，0.1的显著水平，因此可以判断本模型存在多重共线性。方法二：系数符号法Dependent Variable: BUSTRAVLMethod: Least SquaresDate: 07/26/14 Time: 10:09Sample: 1 40Included observations: 40VariableCoefficientStd. Errort-StatisticProb. C2744.6802641.6721.0389940.3064FARE-238.6544451.7281-0.5283140.6008GASPRICE522.11322658.2

9、280.1964140.8455INC-0.1947440.064887-3.0012940.0051POP1.7114420.2313647.3971760.0000DENSITY0.1164150.0595701.9542530.0592LANDAREA-1.1552301.802638-0.6408550.5260R-squared0.921026 Mean dependent var1933.175Adjusted R-squared0.906667 S.D. dependent var2431.757S.E. of regression742.9113 Akaike info cri

10、terion16.21666Sum squared resid18213267 Schwarz criterion16.51221Log likelihood-317.3332 F-statistic64.14338Durbin-Watson stat2.082671 Prob(F-statistic)0.000000根据我们的经验以及常识判断：城市公交需求（BUSTRAVL）与公交车费（FARE）应该成负相关，城市公交需求（BUSTRAVL）与汽油价格（GASPRICE）成正相关，城市公交需求（BUSTRAVL）与人均收入（INC）成负相关，城市公交需求（BUSTRAVL）与城市人口规模（P

11、OP）成正相关，城市公交需求（BUSTRAVL）与城市人口密度（DENSITY）成正相关，城市公交需求（BUSTRAVL）与城市面积（LANDAREA）成正相关。观察分析上面的表格，发现城市公交需求（BUSTRAVL）与城市面积（LANDAREA）成负相关，符号的经济意义不符合常理。方法三：相关系数矩阵法DENSITYFAREGASPRICEINCLANDAREAPOPDENSITY1-0.1406476848190.4553300597540.459093713333-0.2274655405970.63623436455FARE-0.14064768481910.0509688156425

12、-0.07545364014580.2620763434980.0149309080982GASPRICE0.4553300597540.050968815642510.136417782013-0.1082887627370.326581135483INC0.459093713333-0.07545364014580.13641778201310.007598273482890.335116892976LANDAREA-0.2274655405970.262076343498-0.1082887627370.0075982734828910.484836661826POP0.63623436

13、4550.01493090809820.3265811354830.3351168929760.4848366618261根据上表格发现，相关系数没有大于0.8，但是最高的相关系数有0.636234（DENSITY与POP），所以由相关系数矩阵法可得解释变量有多重共线性。方法四：Frish综合分析法逐步回归法相关系数矩阵：DENSITYFAREGASPRICEINCLANDAREAPOPBUSTRAVLDENSITY1-0.1406476848190.4553300597540.459093713333-0.2274655405970.636234364550.721038213472FARE

14、-0.14064768481910.0509688156425-0.07545364014580.2620763434980.0149309080982-0.0479743950177GASPRICE0.4553300597540.050968815642510.136417782013-0.1082887627370.3265811354830.378669590619INC0.459093713333-0.07545364014580.13641778201310.007598273482890.3351168929760.228670500775LANDAREA-0.2274655405

15、970.262076343498-0.1082887627370.0075982734828910.4848366618260.303441237086POP0.636234364550.01493090809820.3265811354830.3351168929760.48483666182610.93129085757BUSTRAVL0.721038213472-0.04797439501770.3786695906190.2286705007750.3034412370860.931290857571观察发现BUSTRAVL与POP的相关系数最高，为0.9313，所以我们选择BUSTR

16、AVL与POP的回归方程为基本回归方程。逐步回归：以BUSTRAVL与POP的回归方程为基本回归方程，逐个加入其他变量，寻找最佳回归方程。Dependent Variable: BUSTRAVLMethod: Least SquaresDate: 07/26/14 Time: 11:07Sample: 1 40Included observations: 40VariableCoefficientStd. Errort-StatisticProb. C259.5720177.23211.4645880.1513POP1.8205980.11552315.759630.0000R-squared

17、0.867303 Mean dependent var1933.175Adjusted R-squared0.863811 S.D. dependent var2431.757S.E. of regression897.4119 Akaike info criterion16.48561Sum squared resid30603227 Schwarz criterion16.57006Log likelihood-327.7123 F-statistic248.3660Durbin-Watson stat1.697039 Prob(F-statistic)0.000000加入DENSITY，

18、输出结果如图：Dependent Variable: BUSTRAVLMethod: Least SquaresDate: 07/26/14 Time: 11:08Sample: 1 40Included observations: 40VariableCoefficientStd. Errort-StatisticProb. C-275.3904234.0197-1.1767830.2468POP1.5520350.13495211.500640.0000DENSITY0.1151610.0368183.1278750.0034R-squared0.895053 Mean dependent

19、 var1933.175Adjusted R-squared0.889380 S.D. dependent var2431.757S.E. of regression808.7919 Akaike info criterion16.30100Sum squared resid24203340 Schwarz criterion16.42766Log likelihood-323.0200 F-statistic157.7793Durbin-Watson stat1.781685 Prob(F-statistic)0.000000模拟的拟合优度增加，两个变量的显著性都很强，符号的经济意义也符合常

20、理，因此保留自变量DENSITY。继续加入GASPRICE，回归结果如图：Dependent Variable: BUSTRAVLMethod: Least SquaresDate: 07/26/14 Time: 11:14Sample: 1 40Included observations: 40VariableCoefficientStd. Errort-StatisticProb. C-1388.2212538.754-0.5468120.5879POP1.5488050.13664411.334610.0000DENSITY0.1092460.0395762.7604320.0090GA

21、SPRICE1264.3772871.9310.4402530.6624R-squared0.895615 Mean dependent var1933.175Adjusted R-squared0.886916 S.D. dependent var2431.757S.E. of regression817.7498 Akaike info criterion16.34563Sum squared resid24073728 Schwarz criterion16.51452Log likelihood-322.9126 F-statistic102.9590Durbin-Watson sta

22、t1.806759 Prob(F-statistic)0.000000模拟的拟合优度增加，符号的经济意义也符合常理，但是GASPRICE的显著性不强，所以不保留GASPRICE。继续加入LANDAREA，回归结果如图：Dependent Variable: BUSTRAVLMethod: Least SquaresDate: 07/26/14 Time: 11:24Sample: 1 40Included observations: 40VariableCoefficientStd. Errort-StatisticProb. C210.7973483.24260.4362140.6653DE

23、NSITY0.0601220.0603390.9964090.3257LANDAREA-2.1455831.868280-1.1484270.2584POP1.7890170.2462487.2650980.0000R-squared0.898762 Mean dependent var1933.175Adjusted R-squared0.890325 S.D. dependent var2431.757S.E. of regression805.3290 Akaike info criterion16.31502Sum squared resid23347972 Schwarz crite

24、rion16.48391Log likelihood-322.3004 F-statistic106.5324Durbin-Watson stat1.942799 Prob(F-statistic)0.000000模拟的拟合优度增加，但是符号的经济意义不符合常理，而且显著性也不高，所以不保留LANDAREA。继续加入INC，回归结果如图：Dependent Variable: BUSTRAVLMethod: Least SquaresDate: 07/26/14 Time: 11:31Sample: 1 40Included observations: 40VariableCoefficien

25、tStd. Errort-StatisticProb. C2815.703976.30072.8840530.0066POP1.5765750.12061213.071480.0000DENSITY0.1534210.0348984.3963110.0001INC-0.2012730.062101-3.2410760.0026R-squared0.918759 Mean dependent var1933.175Adjusted R-squared0.911989 S.D. dependent var2431.757S.E. of regression721.4228 Akaike info

26、criterion16.09497Sum squared resid18736228 Schwarz criterion16.26386Log likelihood-317.8993 F-statistic135.7080Durbin-Watson stat1.878671 Prob(F-statistic)0.000000模拟的拟合优度增加，三个变量的显著性都很强，符号的经济意义也符合常理，因此保留自变量INC。继续加入FARE，回归结果如图：Dependent Variable: BUSTRAVLMethod: Least SquaresDate: 07/26/14 Time: 11:33

27、Sample: 1 40Included observations: 40VariableCoefficientStd. Errort-StatisticProb. C3111.1811071.0672.9047490.0063POP1.5883370.12265412.949730.0000DENSITY0.1490270.0357134.1729250.0002INC-0.2021970.062564-3.2318210.0027FARE-295.7306424.8354-0.6961060.4910R-squared0.919868 Mean dependent var1933.175A

28、djusted R-squared0.910710 S.D. dependent var2431.757S.E. of regression726.6434 Akaike info criterion16.13122Sum squared resid18480373 Schwarz criterion16.34233Log likelihood-317.6243 F-statistic100.4449Durbin-Watson stat1.995180 Prob(F-statistic)0.000000模拟的拟合优度增加，符号的经济意义也符合常理，但是FARE的显著性不高，所以不保留FARE。

29、设BUSTRAVL为YCFAREGASPRICE INCLANDAREAPOPDENSITYDWY=f(pop)259.571.820.861.70T值1.46(15.8)*Y=f(pop,density) -275.39041.550.120.901.78T值-1.18(11.50)*(3.13)*Y=f(pop,density,gasprice)-1388.221264.381.550.110.891.81T值-0.550.44(11.33)*(2.76)*Y=f(pop,density,Landarea)210.80-2.151.790.060.891.94T值0.44-1.15(7.27)*0.996Y=f(pop,density,Inc)2815.70-0.201.580.150.911.88T值(2.88)*(-3.24)*(13.07)*(4.40)*Y=f(pop,de