多重共线性实验报告-lucas

多重共线性实验报告-lucas

-CAL-FENGHAI.-(YICAI)-Company One1

《计量经济学》实验报告 四

开课实验室： 崇德楼315 2013年 5月19日 姓 名 成 绩 金超龙 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：Yt01X1t2X2t3X3t4X4t5X5tt Y=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Estimate Equation项，在OLS对话框中，键入Y C X1 X2 X3 X4 X5，输出结果。见图6.4.1。 2

图6.4.1 Eviews输出的回归结果 分析：模型R2=0.970391 R20.951885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\\group statistics\\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。 Dependent Variable: Y Method: Least Squares Date: 05/12/03 Time: 13:56 Sample: 1974 1987 Included observations: 14 Variable Coefficient Std. Error t-Statistic Prob. C -90.92074 19.32929 -4.703781 0.0005 X1 0.316925 0.026081 12.15161 0.0000 R-squared 0.924841 Mean dependent var 142.7129 Adjusted R-squared 0.918578 S.D. dependent var 26.09805 3

S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 7.446964 Akaike info criterion 665.4873 Schwarz criterion -46.89537 F-statistic 1.536885 Prob(F-statistic) 6.985054 7.076347 147.6617 0.000000 Prob. 0.0000 0.0000 142.7129 26.09805 7.811851 7.903145 57.84372 0.000006 Prob. 0.0000 0.0000 142.7129 26.09805 7.587974 7.679268 75.36868 0.000002 Prob. Dependent Variable: Y Method: Least Squares Date: 05/12/03 Time: 13:59 Sample: 1974 1987 Included observations: 14 Variable Coefficient Std. Error t-Statistic C 99.55251 6.423364 15.49850 X2 0.081519 0.010718 7.605506 R-squared 0.828188 Mean dependent var Adjusted R-squared 0.813870 S.D. dependent var S.E. of regression 11.25942 Akaike info criterion Sum squared resid 1521.294 Schwarz criterion Log likelihood -52.68296 F-statistic Durbin-Watson stat 0.642278 Prob(F-statistic) Dependent Variable: Y Method: Least Squares Date: 05/12/03 Time: 14:00 Sample: 1974 1987 Included observations: 14 Variable Coefficient Std. Error t-Statistic C 74.64824 8.288989 9.005711 X3 4.892712 0.563578 8.681514 R-squared 0.862651 Mean dependent var Adjusted R-squared 0.851205 S.D. dependent var S.E. of regression 10.06704 Akaike info criterion Sum squared resid 1216.144 Schwarz criterion Log likelihood -51.11582 F-statistic Durbin-Watson stat 0.813884 Prob(F-statistic) Dependent Variable: Y Method: Least Squares Date: 05/12/03 Time: 14:01 Sample: 1974 1987 Included observations: 14 Variable Coefficient t-Statistic Std. Error 4

C X4 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 108.8647 5.934330 18.34490 5.739752 0.838756 6.843175 0.796019 Mean dependent var 0.779021 S.D. dependent var 12.26828 Akaike info criterion 1806.129 Schwarz criterion -53.88433 F-statistic 0.769006 Prob(F-statistic) 0.0000 0.0000 142.7129 26.09805 7.983475 8.074769 46.82904 0.000018 Prob. 0.0000 0.0001 142.7129 26.09805 8.183490 8.274784 36.16444 0.000061 Dependent Variable: Y Method: Least Squares Date: 05/12/03 Time: 14:02 Sample: 1974 1987 Included observations: 14 Variable Coefficient Std. Error t-Statistic C 113.3747 6.077133 18.65596 X5 3.080811 0.512300 6.013688 R-squared 0.750854 Mean dependent var Adjusted R-squared 0.730091 S.D. dependent var S.E. of regression 13.55865 Akaike info criterion Sum squared resid 2206.044 Schwarz criterion Log likelihood -55.28443 F-statistic Durbin-Watson stat 0.593639 Prob(F-statistic) 变 量 X1 X4 X5 参数估计0.081519 4.892712 5.739752 3.080811 0.316925 值 t统计值 7.605506 8.681514 6.843175 6.013688 12.15161 0.828188 0.862651 0.796019 0.750854 R2 0.924841 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： Dependent Variable: Y Method: Least Squares Date: 05/12/03 Time: 14:05 Sample: 1974 1987 Included observations: 14 Variable Coefficient C -39.79479 X1 0.211543 X3 1.909246 t-Statistic -1.590793 4.669581 2.636523 Prob. 0.1400 0.0007 0.0231 表6.4.2 回归结果 X2 X3 Std. Error 25.01570 0.045302 0.724153 5

ˆ39.794790.211543X11.90924X3 Yttt2 t (-1.590793) (4.669581) （2.636523） R=0.953945 当α=5%时，t/2(nk1)t0.025(1421)2.2010，X3参数的t检验显著，不予剔除，加入X2回归得： Dependent Variable: Y Method: Least Squares Date: 05/12/03 Time: 14:10 Sample: 1974 1987 Included observations: 14 Variable Coefficient Std. Error t-Statistic C -34.62879 27.82151 -1.244677 X1 0.206328 0.048016 4.297054 X3 1.448669 1.175325 1.232569 X2 0.009605 0.018875 0.508897 R-squared 0.955107 Mean dependent var Adjusted R-squared 0.941640 S.D. dependent var S.E. of regression 6.304735 Akaike info criterion Sum squared resid 397.4968 Schwarz criterion Log likelihood -43.28805 F-statistic Durbin-Watson stat 1.682728 Prob(F-statistic) Prob. 0.2416 0.0016 0.2459 0.6219 142.7129 26.09805 6.755435 6.938023 70.91803 0.000000 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 0.953945 Mean dependent var 0.945571 S.D. dependent var 6.088671 Akaike info criterion 407.7910 Schwarz criterion -43.46702 F-statistic 1.655554 Prob(F-statistic) 142.7129 26.09805 6.638146 6.775087 113.9220 0.000000 ˆ34.628790.206328X11.448669X30.009605X2 Ytttt2 t (4.297054) (1.232569) (0.508897) R=0.955107 当α=5%时，t/2(nk1)t0.025(1431)2.2281，X3、X2参数的t检验均不显著，但单独对x1、x2进行回归得： Dependent Variable: Y Method: Least Squares Date: 05/13/13 Time: 23:05 Sample: 1974 1987 Included observations: 14 Variable Coefficient C X1 X2 Std. Error t-Statistic -1.4 -40.78385 28.00819 6140 0.229149 0.045337 5.054381 0.027520 0.012323 2.233229 0.948287 Mean dependent var 0.938885 S.D. dependent var 6.451819 Akaike info criterion Prob. 0.1733 0.0004 0.0473 142.7129 26.09805 6.754010 R-squared Adjusted R-squared S.E. of regression 6

Yˆt40.783850.229149X1t0.027520X2t t (5.054381) （2.233229） R=0.948287 R=0.938885 22Sum squared resid Log likelihood F-statistic Prob(F-statistic) 457.8856 Schwarz criterion -44.27807 Hannan-Quinn criter. 100.8568 Durbin-Watson stat 0.000000 6.890951 6.741334 1.803344 因为R=0.938885<0.941640，X2参数不显著，需要剔除x2 保留X1和X3并加入X4回归得： Dependent Variable: Y Method: Least Squares Date: 05/12/0 Time: 14:16 Sample: 1974 1987 Included observations: 14 Variable Coefficient Std. Error t-Statistic C -37.99884 28.00654 -1.356785 X1 0.210314 0.047919 4.388978 X3 1.745767 1.178590 1.481234 X4 0.234789 1.295874 0.181182 R-squared 0.954096 Mean dependent var Adjusted R-squared 0.940324 S.D. dependent var S.E. of regression 6.375396 Akaike info criterion Sum squared resid 406.4568 Schwarz criterion Log likelihood -43.44408 F-statistic Durbin-Watson stat 1.673512 Prob(F-statistic) Prob. 0.2047 0.0014 0.1694 0.8598 142.7129 26.09805 6.777726 6.960314 69.28123 0.000001 2 ˆ37.998840..210314X11.745767X30.234789X4 Yttttt (4.388978) (1.481234) (0.181182) R2=0.954096 当α=5%时，t/2(nk1)t0.025(1431)2.2281，X3和X4参数的t检验不显著，但单独对X1和X4做回归得 Dependent Variable: Y Method: Least Squares Date: 05/13/13 Time: 23:25 Sample: 1974 1987 Included observations: 14 Variable Coefficient Std. Error t-Statistic C -46.10792 28.91860 -1.594404 X1 0.242503 0.044966 5.393027 X4 1.704287 0.877794 1.941557 R-squared 0.944024 Mean dependent var Adjusted R-squared 0.933846 S.D. dependent var S.E. of regression 6.712509 Akaike info criterion Prob. 0.1392 0.0002 0.0782 142.7129 26.09805 6.833232 7

Yˆt46.107920.242503X1t1.70428X4t t (5.393027) （1.941557） R=0.944024 R=0.933846 22Sum squared resid Log likelihood F-statistic Prob(F-statistic) 495.6355 Schwarz criterion -44.83262 Hannan-Quinn criter. 92.75612 Durbin-Watson stat 0.000000 6.970173 6.820556 1.915578 因为R=0.933846<0.940324，X4参数不显著，需要剔除x4 加入X5回归得： Dependent Variable: Y Method: Le st Squares Date: 05/12/03 Time: 14:19 Sample: 1974 1987 Included observations: 14 Variable Coefficient Std. Error t-Statistic C -40.82333 26.65152 -1.531745 X1 0.210527 0.047668 4.416536 X3 2.144798 1.370441 1.565042 X5 -0.157438 0.763156 -0.206298 R-squared 0.954140 Mean dependent var Adjusted R-squared 0.940382 S.D. dependent var S.E. of regression 6.372306 Akaike info criterion Sum squared resid 406.0629 Schwarz criterion Log likelihood -43.43729 F-statistic Durbin-Watson stat 1.634831 Prob(F-statistic) Prob. 0.1566 0.0013 0.1486 0.8407 142.7129 26.09805 6.776756 6.959344 69.35167 0.000001 2 ˆ40.823330.210527X12.144798X30.157438X5 Yttttt (4.416536) (1.565042) (-0.206298) R2=0.954140 当α=5%时，t/2(nk1)t0.025(1431)2.2281，X3和X5参数的t检验不显著，通过对X1和X5做回归得： Dependent Variable: Y Method: Least Squares Date: 05/13/13 Time: 23:30 Sample: 1974 1987 Included observations: 14 Variable Coefficient Std. Error t-Statistic C -51.88754 27.33731 -1.898049 X1 0.253155 0.041617 6.082992 X5 0.837671 0.448988 1.865687 R-squared 0.942907 Mean dependent var Adjusted R-squared 0.932527 S.D. dependent var S.E. of regression 6.779127 Akaike info criterion Prob. 0.0842 0.0001 0.0890 142.7129 26.09805 6.852983 8

YˆX5t t51.887540.253155X1t0.837671 t (6.082992) （1.865687） R=0.942907 R=0.932527 22Sum squared resid Log likelihood F-statistic Prob(F-statistic) 505.5222 Schwarz criterion -44.97088 Hannan-Quinn criter. 90.83449 Durbin-Watson stat 0.000000 6.989924 6.840307 1.877452 因为R=0.932527<0.940382，X5参数不显著，需要剔除x5 结论：在其他因素不变的情况下，当市常住人口X1和肉销售量X3分别增长1%时，国内旅游收入Y分别增长0.211543%与1.909246%。 29