计量经济学庞皓第三版课后答案.pdf

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1、第二章简单线性回归模型第二章简单线性回归模型2.1（1）首先分析人均寿命与人均GDP 的数量关系，用 Eviews分析：Dependent Variable:YMethod:Least SquaresDate:12/27/14Time:21:00Sample:1 22Included observations:22VariableCoefficientStd.Errort-StatisticProb.C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001R-squared0.526082 Mean dependent va

2、r62.50000Adjusted R-squared0.502386 S.D.dependent var10.08889S.E.of regression7.116881 Akaike info criterion6.849324Sum squared resid1013.000 Schwarz criterion6.948510Log likelihood-73.34257 Hannan-Quinn criter.6.872689F-statistic22.20138 Durbin-Watson stat0.629074Prob(F-statistic)0.000134有上可知，关系式为

3、y=56.64794+0.128360 x1关于人均寿命与成人识字率的关系，用Eviews分析如下：Dependent Variable:YMethod:Least SquaresDate:11/26/14Time:21:10Sample:1 22Included observations:22VariableCoefficientStd.Errort-StatisticProb.C38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825 Mean dependent var62.50000A

4、djusted R-squared0.702666 S.D.dependent var10.08889S.E.of regression5.501306 Akaike info criterion6.334356Sum squared resid605.2873 Schwarz criterion6.433542Log likelihood-67.67792 Hannan-Quinn criter.6.357721F-statistic50.62761 Durbin-Watson stat1.846406Prob(F-statistic)0.000001由上可知，关系式为 y=38.79424

5、+0.331971x2关于人均寿命与一岁儿童疫苗接种率的关系，用Eviews 分析如下：Dependent Variable:YMethod:Least SquaresDate:11/26/14Time:21:14Sample:1 22Included observations:22VariableCoefficientStd.Errort-StatisticProb.C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001R-squared0.537929 Mean dependent var62.50000Adjuste

6、d R-squared0.514825 S.D.dependent var10.08889S.E.of regression7.027364 Akaike info criterion6.824009Sum squared resid987.6770 Schwarz criterion6.923194Log likelihood-73.06409 Hannan-Quinn criter.6.847374F-statistic23.28338 Durbin-Watson stat0.952555Prob(F-statistic)0.000103由上可知，关系式为 y=31.79956+0.387

7、276x3（2）关于人均寿命与人均 GDP 模型，由上可知，可决系数为 0.526082，说明所建模型整体上对样本数据拟合较好。对于回归系数的 t 检验：t（1）=4.711834t0.025(20)=2.086，对斜率系数的显著性检验表明，人均 GDP 对人均寿命有显著影响。关于人均寿命与成人识字率模型，由上可知，可决系数为 0.716825，说明所建模型整体上对样本数据拟合较好。对于回归系数的 t 检验：t（2）=7.115308t0.025(20)=2.086，对斜率系数的显著性检验表明，成人识字率对人均寿命有显著影响。关于人均寿命与一岁儿童疫苗的模型，由上可知，可决系数为 0.5379

8、29，说明所建模型整体上对样本数据拟合较好。对于回归系数的 t 检验：t（3）=4.825285t0.025(20)=2.086，对斜率系数的显著性检验表明，一岁儿童疫苗接种率对人均寿命有显著影响。2.2（1）对于浙江省预算收入与全省生产总值的模型，用Eviews 分析结果如下：Dependent Variable:YMethod:Least SquaresDate:12/03/14Time:17:00Sample(adjusted):1 33Included observations:33 after adjustmentsVariableCoefficientStd.Errort-Stat

9、isticProb.X0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004R-squared0.983702 Mean dependent var902.5148Adjusted R-squared0.983177 S.D.dependent var1351.009S.E.of regression175.2325 Akaike info criterion13.22880Sum squared resid951899.7 Schwarz criterion13.31949Log likelihood-216.2751

10、Hannan-Quinn criter.13.25931F-statistic1871.115 Durbin-Watson stat0.100021Prob(F-statistic)0.000000由上可知，模型的参数：斜率系数0.176124，截距为154.3063关于浙江省财政预算收入与全省生产总值的模型，检验模型的显著性：1）可决系数为 0.983702，说明所建模型整体上对样本数据拟合较好。2）对于回归系数的t 检验：t（2）=43.25639t0.025(31)=2.0395，对斜率系数的显著性检验表明，全省生产总值对财政预算总收入有显著影响。用规范形式写出检验结果如下：=0.176

11、124X154.3063(0.004072)(39.08196)=(43.25639)（-3.948274）2=0.983702F=1871.115n=33经济意义是：全省生产总值每增加1 亿元，财政预算总收入增加0.176124 亿元。（2）当 x=32000 时，进行点预测，由上可知Y=0.176124X154.3063，代入可得：Y=Y=0.176124*32000154.3063=5481.6617进行区间预测：先由 Eviews 分析：Mean Median Maximum Minimum Std.Dev.Skewness Kurtosis Jarque-Bera Probabili

12、ty Sum Sum Sq.Dev.ObservationsX 6000.441 2689.280 27722.31 123.7200 7608.021 1.432519 4.010515 12.69068 0.001755 198014.5 1.85E+09 33Y 902.5148 209.3900 4895.410 25.87000 1351.009 1.663108 4.590432 18.69063 0.000087 29782.99 58407195 33由上表可知，x2=（XiX）2=2x(n1)=7608.0212 x(331)=1852223.473(XfX)2=(32000

13、 6000.441)2=675977068.2当 Xf=32000 时，将相关数据代入计算得到：5481.66172.0395x175.2325x1/33+1852223.473/675977068.2Yf5481.6617+2.0395x175.2325x1/33+1852223.473/675977068.2即 Yf 的置信区间为（5481.661764.9649,5481.6617+64.9649）(3)对于浙江省预算收入对数与全省生产总值对数的模型，由Eviews 分析结果如下：Dependent Variable:LNYMethod:Least SquaresDate:12/03/1

14、4Time:18:00Sample(adjusted):1 33Included observations:33 after adjustmentsVariableCoefficientStd.Errort-StatisticProb.LNX0.9802750.03429628.582680.0000C-1.9182890.268213-7.1521210.0000R-squared0.963442 Mean dependent var5.573120Adjusted R-squared0.962263 S.D.dependent var1.684189S.E.of regression0.3

15、27172 Akaike info criterion0.662028Sum squared resid3.318281 Schwarz criterion0.752726Log likelihood-8.923468 Hannan-Quinn criter.0.692545F-statistic816.9699 Durbin-Watson stat0.096208Prob(F-statistic)0.000000模型方程为：lnY=0.980275lnX-1.918289由上可知，模型的参数：斜率系数为0.980275，截距为-1.918289关于浙江省财政预算收入与全省生产总值的模型，检验

16、其显著性：1）可决系数为 0.963442，说明所建模型整体上对样本数据拟合较好。2）对于回归系数的 t 检验：t（2）=28.58268t0.025(31)=2.0395，对斜率系数的显著性检验表明，全省生产总值对财政预算总收入有显著影响。经济意义：全省生产总值每增长1%，财政预算总收入增长0.980275%2.4（1）对建筑面积与建造单位成本模型，用Eviews分析结果如下：Dependent Variable:YMethod:Least SquaresDate:12/01/14Time:12:40Sample:1 12Included observations:12VariableCoe

17、fficientStd.Errort-StatisticProb.X-64.184004.809828-13.344340.0000C1845.47519.2644695.796880.0000R-squared0.946829 Mean dependent var1619.333Adjusted R-squared0.941512 S.D.dependent var131.2252S.E.of regression31.73600 Akaike info criterion9.903792Sum squared resid10071.74 Schwarz criterion9.984610L

18、og likelihood-57.42275 Hannan-Quinn criter.9.873871F-statistic178.0715 Durbin-Watson stat1.172407Prob(F-statistic)0.000000由上可得：建筑面积与建造成本的回归方程为：Y=1845.475-64.18400X（2）经济意义：建筑面积每增加1 万平方米，建筑单位成本每平方米减少64.18400 元。（3）首先进行点预测，由 Y=1845.475-64.18400X 得，当 x=4.5，y=1556.647再进行区间估计：用 Eviews 分析：Mean Median Maximu

19、m Minimum Std.Dev.Skewness Kurtosis Jarque-Bera ProbabilityY 1619.333 1630.000 1860.000 1419.000 131.2252 0.003403 2.346511 0.213547 0.898729X 3.523333 3.715000 6.230000 0.600000 1.989419-0.060130 1.664917 0.898454 0.638121 Sum Sum Sq.Dev.Observations 19432.00 189420.7 12 42.28000 43.53567 12由上表可知，x

20、2=（XiX）2=2x(n1)=1.9894192 x(121)=43.5357(XfX)2=(4.5 3.523333)2=0.95387843当 Xf=4.5 时，将相关数据代入计算得到：1556.6472.228x31.73600 x1/12+43.5357/0.95387843Yf1556.647+2.228x31.73600 x1/12+43.5357/0.95387843即 Yf 的置信区间为（1556.647478.1231,1556.647+478.1231）3.1（1）对百户拥有家用汽车量计量经济模型，用Eviews 分析结果如下：Dependent Variable:YMe

21、thod:Least SquaresDate:11/25/14Time:12:38Sample:1 31Included observations:31VariableCoefficientStd.Errort-StatisticProb.X25.9968651.4060584.2650200.0002X3-0.5240270.179280-2.9229500.0069X4-2.2656800.518837-4.3668420.0002C246.854051.975004.7494760.0001R-squared0.666062 Mean dependent var16.77355Adjus

22、ted R-squared0.628957 S.D.dependent var8.252535S.E.of regression5.026889 Akaike info criterion6.187394Sum squared resid682.2795 Schwarz criterion6.372424Log likelihood-91.90460 Hannan-Quinn criter.6.247709F-statistic17.95108 Durbin-Watson stat1.147253Prob(F-statistic)0.000001得到模型得：Y=246.8540+5.99686

23、5X2-0.524027 X3-2.265680 X4对模型进行检验：1）可决系数是 0.666062，修正的可决系数为0.628957，说明模型对样本拟合较好2）F 检验，F=17.95108F（3,27）=3.65，回归方程显著。3）t 检验，t 统计量分别为 4.749476，4.265020，-2.922950，-4.366842，均大于t（27）=2.0518，所以这些系数都是显著的。依据：1）可决系数越大，说明拟合程度越好2）F 的值与临界值比较，若大于临界值，则否定原假设，回归方程是显著的；若小于临界值，则接受原假设，回归方程不显著。3）t 的值与临界值比较，若大于临界值，则否定

24、原假设，系数都是显著的；若小于临界值，则接受原假设，系数不显著。（2）经济意义：人均增加万元，百户拥有家用汽车增加 5.996865 辆，城镇人口比重增加个百分点，百户拥有家用汽车减少0.524027 辆，交通工具消费价格指数每上升，百户拥有家用汽车减少2.265680 辆。（3）用 EViews 分析得：Dependent Variable:YMethod:Least SquaresDate:12/08/14Time:17:28Sample:1 31Included observations:31VariableCoefficientStd.Errort-StatisticProb.X25.

25、1356701.0102705.0834650.0000LNX3-22.810056.771820-3.3683780.0023LNX4-230.848149.46791-4.6666240.0001C1148.758228.29175.0319740.0000R-squared0.691952 Mean dependent var16.77355Adjusted R-squared0.657725 S.D.dependent var8.252535S.E.of regression4.828088 Akaike info criterion6.106692Sum squared resid6

26、29.3818 Schwarz criterion6.291723Log likelihood-90.65373 Hannan-Quinn criter.6.167008F-statistic20.21624 Durbin-Watson stat1.150090Prob(F-statistic)0.000000模型方程为：Y=5.135670 X2-22.81005 LNX3-230.8481 LNX4+1148.758此分析得出的可决系数为0.6919520.666062，拟合程度得到了提高，可这样改进。3.2（）对出口货物总额计量经济模型，用Eviews 分析结果如下：Dependent

27、Variable:YMethod:Least SquaresDate:12/01/14Time:20:25Sample:1994 2011Included observations:18VariableCoefficientStd.Errort-StatisticProb.X20.1354740.01279910.584540.0000X318.853489.7761811.9285120.0729C-18231.588638.216-2.1105730.0520R-squared0.985838 Mean dependent var6619.191Adjusted R-squared0.98

28、3950 S.D.dependent var5767.152S.E.of regression730.6306 Akaike info criterion16.17670Sum squared resid8007316.Schwarz criterion16.32510Log likelihood-142.5903 Hannan-Quinn criter.16.19717F-statistic522.0976 Durbin-Watson stat1.173432Prob(F-statistic)0.000000由上可知，模型为：Y=0.135474X2+18.85348X3-18231.58对

29、模型进行检验：1）可决系数是 0.985838，修正的可决系数为 0.983950，说明模型对样本拟合较好2）F 检验，F=522.0976F（2,15）=4.77，回归方程显著3）t 检验，t 统计量分别为 X2 的系数对应 t 值为 10.58454，大于t（15）=2.131，系数是显著的，X3 的系数对应 t 值为 1.928512，小于 t（15）=2.131，说明此系数是不显著的。（2）对于对数模型，用 Eviews分析结果如下：Dependent Variable:LNYMethod:Least SquaresDate:12/01/14Time:20:25Sample:1994

30、2011Included observations:18VariableCoefficientStd.Errort-StatisticProb.LNX21.5642210.08898817.577890.0000LNX31.7606950.6821152.5812290.0209C-20.520485.432487-3.7773630.0018R-squared0.986295 Mean dependent var8.400112Adjusted R-squared0.984467 S.D.dependent var0.941530S.E.of regression0.117343 Akaik

31、e info criterion-1.296424Sum squared resid0.206540 Schwarz criterion-1.148029Log likelihood14.66782 Hannan-Quinn criter.-1.275962F-statistic539.7364 Durbin-Watson stat0.686656Prob(F-statistic)0.000000由上可知，模型为：LNY=-20.52048+1.564221 LNX2+1.760695 LNX3对模型进行检验：1）可决系数是 0.986295，修正的可决系数为 0.984467，说明模型对样本

32、拟合较好。2）F 检验，F=539.7364 F（2,15）=4.77，回归方程显著。3）t 检验，t 统计量分别为-3.777363，17.57789，2.581229，均大于t（15）=2.131，所以这些系数都是显著的。（3）（1）式中的经济意义：工业增加 1 亿元，出口货物总额增加 0.135474 亿元，人民币汇率增加 1，出口货物总额增加 18.85348 亿元。（2）式中的经济意义：工业增加额每增加1%，出口货物总额增加1.564221%，人民币汇率每增加1%，出口货物总额增加1.760695%3.3（1）对家庭书刊消费对家庭月平均收入和户主受教育年数计量模型，由Eviews分析

33、结果如下：Dependent Variable:YMethod:Least SquaresDate:12/01/14Time:20:30Sample:1 18Included observations:18VariableCoefficientStd.Errort-StatisticProb.X0.0864500.0293632.9441860.0101T52.370315.20216710.067020.0000C-50.0163849.46026-1.0112440.3279R-squared0.951235 Mean dependent var755.1222Adjusted R-squ

34、ared0.944732 S.D.dependent var258.7206S.E.of regression60.82273 Akaike info criterion11.20482Sum squared resid55491.07 Schwarz criterion11.35321Log likelihood-97.84334 Hannan-Quinn criter.11.22528F-statistic146.2974 Durbin-Watson stat2.605783Prob(F-statistic)0.000000模型为：Y=0.086450X+52.37031T-50.0163

35、8对模型进行检验：1）可决系数是 0.951235，修正的可决系数为 0.944732，说明模型对样本拟合较好。2）F 检验，F=539.7364 F（2,15）=4.77，回归方程显著。3）t 检验，t 统计量分别为 2.944186，10.06702，均大于 t（15）=2.131，所以这些系数都是显著的。经济意义：家庭月平均收入增加1 元，家庭书刊年消费支出增加0.086450 元，户主受教育年数增加 1 年，家庭书刊年消费支出增加52.37031 元。（2）用 Eviews 分析：Dependent Variable:YMethod:Least SquaresDate:12/01/14

36、Time:22:30Sample:1 18Included observations:18VariableCoefficientStd.Errort-StatisticProb.T63.016764.54858113.85416C-11.5817158.02290-0.199606R-squared0.923054 Mean dependent varAdjusted R-squared0.918245 S.D.dependent varS.E.of regression73.97565 Akaike info criterionSum squared resid87558.36 Schwar

37、z criterionLog likelihood-101.9481 Hannan-Quinn criter.F-statistic191.9377 Durbin-Watson statProb(F-statistic)0.000000Dependent Variable:XMethod:Least SquaresDate:12/01/14Time:22:34Sample:1 18Included observations:18VariableCoefficientStd.Errort-StatisticT123.151631.841503.867644C444.5888406.17861.0

38、94565R-squared0.483182 Mean dependent varAdjusted R-squared0.450881 S.D.dependent varS.E.of regression517.8529 Akaike info criterionSum squared resid4290746.Schwarz criterionLog likelihood-136.9753 Hannan-Quinn criter.F-statistic14.95867 Durbin-Watson statProb(F-statistic)0.001364以上分别是 y 与 T，X 与 T 的

39、一元回归模型分别是：Y=63.01676T-11.58171X=123.1516T+444.5888（3）对残差进行模型分析，用Eviews分析结果如下：Dependent Variable:E1Method:Least SquaresDate:12/03/14Time:20:39Sample:1 18Included observations:18VariableCoefficientStd.Errort-StatisticE20.0864500.0284313.0407420.00000.8443755.1222258.720611.5497911.6487211.563432.13404

40、3Prob.0.00140.28991942.933698.832515.4417015.5406315.455341.052251Prob.0.0078C3.96E-1413.880832.85E-151.0000R-squared0.366239 Mean dependent var2.30E-14Adjusted R-squared0.326629 S.D.dependent var71.76693S.E.of regression58.89136 Akaike info criterion11.09370Sum squared resid55491.07 Schwarz criteri

41、on11.19264Log likelihood-97.84334 Hannan-Quinn criter.11.10735F-statistic9.246111 Durbin-Watson stat2.605783Prob(F-statistic)0.007788模型为：E1=0.086450E2+3.96e-14参数：斜率系数为 0.086450，截距为 3.96e-14（4）由上可知，2 与2 的系数是一样的。回归系数与被解释变量的残差系数是一样的，它们的变化规律是一致的。3.6（1）预期的符号是 X1，X2,X3,X4,X5的符号为正，X6的符号为负（2）根据 Eviews分析得到数据

42、如下：Dependent Variable:YMethod:Least SquaresDate:12/04/14Time:13:24Sample:1994 2011Included observations:18VariableCoefficientStd.Errort-StatisticProb.X20.0013820.0011021.2543300.2336X30.0019420.0039600.4905010.6326X4-3.5790903.559949-1.0053770.3346X50.0047910.0050340.9516710.3600X60.0455420.0955520.

43、4766210.6422C-13.7773215.73366-0.8756590.3984R-squared0.994869 Mean dependent var12.76667Adjusted R-squared0.992731 S.D.dependent var9.746631S.E.of regression0.830963 Akaike info criterion2.728738Sum squared resid8.285993 Schwarz criterion3.025529Log likelihood-18.55865 Hannan-Quinn criter.2.769662F

44、-statistic465.3617 Durbin-Watson stat1.553294Prob(F-statistic)0.000000与预期不相符。评价：1）可决系数为 0.994869，数据相当大，可以认为拟合程度很好。2）F 检验，F=465.3617F（5.12）=3,89，回归方程显著3）T 检验，X1，X2,X3,X4,X5，X6系数对应的 t 值分别为：1.254330，0.490501，-1.005377，0.951671，0.476621，均小于 t（12）=2.179，所以所得系数都是不显著的。（3）根据 Eviews分析得到数据如下：Dependent Variabl

45、e:YMethod:Least SquaresDate:12/03/14Time:11:12Sample:1994 2011Included observations:18VariableCoefficientStd.Errort-StatisticProb.X50.0010322.20E-0546.799460.0000X6-0.0549650.031184-1.7625810.0983C4.2054813.3356021.2607860.2266R-squared0.993601 Mean dependent var12.76667Adjusted R-squared0.992748 S.

46、D.dependent var9.746631S.E.of regression0.830018 Akaike info criterion2.616274Sum squared resid10.33396 Schwarz criterion2.764669Log likelihood-20.54646 Hannan-Quinn criter.2.636736F-statistic1164.567 Durbin-Watson stat1.341880Prob(F-statistic)0.000000得到模型的方程为：Y=0.001032 X5-0.054965 X6+4.205481评价：1）

47、可决系数为 0.993601，数据相当大，可以认为拟合程度很好。2）F 检验，F=1164.567F（5.12）=3,89，回归方程显著3）T 检验，X5系数对应的 t 值为 46.79946，大于t（12）=2.179，所以系数是显著的，即人均 GDP 对年底存款余额有显著影响。X6系数对应的 t 值为-1.762581，小于t（12）=2.179，所以系数是不显著的。4.3（1）根据 Eviews分析得到数据如下：Dependent Variable:LNYMethod:Least SquaresDate:12/05/14Time:11:39Sample:1985 2011Included

48、 observations:27VariableCoefficientStd.Errort-StatisticProb.LNGDP1.3385330.08861015.105820.0000LNCPI-0.4217910.233295-1.8079750.0832C-3.1114860.463010-6.7201260.0000R-squared0.988051 Mean dependent var9.484710Adjusted R-squared0.987055 S.D.dependent var1.425517S.E.of regression0.162189 Akaike info c

49、riterion-0.695670Sum squared resid0.631326 Schwarz criterion-0.551689Log likelihood12.39155 Hannan-Quinn criter.-0.652857F-statistic992.2582 Durbin-Watson stat0.522613Prob(F-statistic)0.000000得到的模型方程为：LNY=1.338533 LNGDPt-0.421791 LNCPIt-3.111486（2）该模型的可决系数为 0.988051，可决系数很高，F 检验值为 992.2582，明显显著。但当=0.

50、05 时，t（24）=2.064，LNCPI 的系数不显著，可能存在多重共线性。得到相关系数矩阵如下：LNYLNGDPLNCPILNY 1.000000 0.993189 0.935116LNGDP 0.993189 1.000000 0.953740LNCPI 0.935116 0.953740 1.000000LNGDP，LNCPI 之间的相关系数很高，证实确实存在多重共线性。（3）由 Eviews 得：a）Dependent Variable:LNYMethod:Least SquaresDate:12/03/14Time:14:41Sample:1985 2011Included ob