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1、习题1.下表给出了中国商品进口额Y、国内生产总值GDP、消费者价格指数CPI。年份商品进口额（亿元）国内生产总值（亿元）居民消费价格指数（1985=100）19851257.88964.410019861498.310202.2106.519871614.211962.5114.319882055.114928.3135.819892199.916909.2160.219902574.318547.9165.219913398.721617.8170.819924443.326638.1181.719935986.234634.4208.419949960.146759.4258.619951
2、1048.158478.1302.8199611557.467884.6327.9199711806.574462.6337.1199811626.178345.2334.4199913736.482067.5329.7200018638.889468.1331.0200120159.297314.8333.3200224430.3105172.3330.6200334195.6117251.9334.6资料来源：中国统计年鉴，中国统计出版社2000年、2004年。请考虑下列模型：lnY = P +P lnGDP + P lnCPI + ut 12t 3t i(1) 利用表中数据估计此模型的参
3、数。解：Dependent Variable: LOG(YMethoc Least SquaresDate: 06/13/U Time: 16:44Sample 1985 003Included observations: 19VariableCoefficientStd Errort-StatisticrobC-3.64894U0.322308-11 32129D UUUULOG(GDP)1.7961740 1808699 9313630.0000LOGfCPI；-1.2076110.363594-3.4149610 0036R-squared0 989725Mean dependent v
4、ar8 771863Adjusted R-squared0 988441S C dependent var1 045337S E of regress on0 112388Aka ike info criterion-1 389779Sum squared resid0.202097Schv/arz crterion-1 2+0657Log likelihood16.20290F-statistic770.6017Durbin-Watson stat0 939369Prob(F-stat stic：o toooooIn Y = 3.6489+1.796ln GDP - 1.2075ln CPI
5、t=(-11.32)(9.93)(-3.415)R 2 = 0.988 F = 770.6 S .E = 0.1124(2) 你认为数据中有多重共线性吗？多重共线性的检验1) 综合统计检验法若 在OLS法下：R2与F值较大，但t检验值较小，则可能存在多重共线性。2) 简单相关系数检验在Eviews软件命令窗口中键入：COR GDP CPI或在包含所有解释变量的数组窗口中点击ViewCorrelations,其结果如图 所示。由相关系数矩阵可以看出，解释变量之间的相关系数均为0.93以上，即 解释变量之间是高度相关的。GDPCPIGDP1.0000000.941303CPI0.9413031.0
6、000003) 判定系数检验法当解释变量多余两个且变量之间呈现出较复杂的相关关系时，可以通过建立 辅助回归模型来检验多重共线性。在Eviews软件命令窗口中键入：LS GDP C CPI得到相应的回归结果，分析方程对应的F值和T值，来检验这些变量间是否 相关以及相关联程度。对应的回归结果如下图所示。Dependent Variable GDPMethod Least SquaresDate 06/13/14 Time: 16:51Sample: 1386 2003ncluded oljservations 19Variable-CoefficientStd Errort-StatisticPr
7、ohC-36059 89S1E0 G47-4.418764(J 0004CPI3G5.282431 7707611 49744(J 0000-squared0 886062M&an d&pendent war61GG3.65Adjusted R-squared0 879349S.D. dependent var3S331 34S E of regression12619 62Akaike info criterion21.82319Sum squared resid2.71E409Schv/arz criterion21.92261_ocj likeliho-od-205.3203F-stat
8、istic132 1911Durbin-Watsor stat0 180834ProbiF-statistic：o oooooa上述回归方程的F检验值非常显著，方程回归系数的T检验值表明：GDP与 CPI的T检验值较大，变量之间相关。(3)进行以下回归：ln Y = A +A ln GDP + vIn Y = B+B In CPI + v :In GdP = C + C In CPI + vt 12t 3i根据这些回归你能对数据中多重共线性的性质说些什么？解：进行ls检验，得到如下的三个结果:Dependent Variable: LOG(Y)Method Least SquaresDate:
9、 05/13/14 Time: 16:55Sample 1966 2003Included obsenations: 19VariableCoefficientStd Errort-StatisticProbC-3.7448650.409574-9.1433260 0000LOG(GDP)1 1873120 03872630 659400 0000R-squared0 982236Mean dependent var8.771063Adjusted R-squared0 9B1131S.D. dependent var1 045337S E of regression0 143363Aka i
10、ke info criterion-0 947673Sum squared resid0 349400Schwarz criterion-0.846158Lag likelihood11 00194F-statistic939 9986Durhin-Watson stat0 629351Pral(F-statistic0 000000In Y = 3.745+1.187ln GDPttt=(-9.143)(30.6594)R 2 = 0.981 F = 939.999 S.E = 0.1434Dependent Variabls: LOG(Y) Method Least Squares Dat
11、s: 06/13/14 Time: 16:57Sample-: 1906 2003Included obseRations: 19VariableCoefficientSid Error t-StatisticProbC33904160.8342164.0G41990 0008LOGCPI2.2543350 16412714.G26490 0000R-squared0 926386Ilean dependent var8.771963Adjusted R-squared0 92205GS D. dependent var1 045337S E of regression0.291842Aka
12、ike infc criierion0.474096Sliiti squared resid1 447925Schv/arz criterion0.673610Log likelihood-2.S03908F-statistic213.9343Durbin-Watson stat0 374991ProbiF-statistic ；0 000000In Y = 3.39+2.254ln CPIttt= (-4.064)(14.63)R 2 = 0.922 F = 213.93 S.E = 0.2918Dependent Variable: LOGiGDP) Method Least Square
13、s Date; 05/13/14 Tiiine; 16却Sainpls; 19S5 2003Included chservaticns;19VariableCoefficientStd Error t-StatisticProbC0 1439300.4308100 3340920.7424LOG(CPI1 9273440.07959524.214390 0000R-squared0 971823Iean dependent var10.54207Adjusted R-squared0 970166S D. dependent var0.872569S E of regression0 1507
14、15Aka ike infc criterion-0.847664Sum squared resid0.386154Schv/arz criterion-0.748139Log likelihood10 05176F-st atistic686.3366Durhin-Watson stat0.326231ProbfF -statistic：0 000000In GDP = 0.1439+1.9273ln CPIt=(0.334)(24.21)R 2 = 0.97 F = 586.337 S .E = 0.15数据中多重共线性的性质：单个解释变量也可以解释被解释变量，但是本题的 两个解释变量之间的相关性较大，若在同一个线性方程中使用就会造成多重共线 性。一一-1*1 A一（4）假设数据有多重共线性
