计量经济学第三版庞皓课后习题答案.doc

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1、精品文档，仅供学习与交流，如有侵权请联系网站删除第二章 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: Y Method: Least Squares Date: 12/27/14 Time: 21:00 Sample: 1 22 Included observations: 22 Variable Coefficient Std. Error t-Statistic Prob. C 56.64794 1.960820 28.88992 0.0000 X1 0.128360 0.027242 4.711834

2、0.0001 R-squared 0.526082 Mean dependent var 62.50000 Adjusted R-squared 0.502386 S.D. dependent var 10.08889 S.E. of regression 7.116881 Akaike info criterion 6.849324 Sum squared resid 1013.000 Schwarz criterion 6.948510 Log likelihood -73.34257 Hannan-Quinn criter. 6.872689 F-statistic 22.20138 D

3、urbin-Watson stat 0.629074 Prob(F-statistic) 0.000134 有上可知，关系式为y=56.64794+0.128360x1关于人均寿命与成人识字率的关系，用Eviews分析如下：Dependent Variable: Y Method: Least Squares Date: 11/26/14 Time: 21:10 Sample: 1 22 Included observations: 22 Variable Coefficient Std. Error t-Statistic Prob. C 38.79424 3.532079 10.98340

4、 0.0000 X2 0.331971 0.046656 7.115308 0.0000 R-squared 0.716825 Mean dependent var 62.50000 Adjusted R-squared 0.702666 S.D. dependent var 10.08889 S.E. of regression 5.501306 Akaike info criterion 6.334356 Sum squared resid 605.2873 Schwarz criterion 6.433542 Log likelihood -67.67792 Hannan-Quinn c

5、riter. 6.357721 F-statistic 50.62761 Durbin-Watson stat 1.846406 Prob(F-statistic) 0.000001 由上可知，关系式为y=38.79424+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: 11/26/14 Time: 21:14Sample: 1 22Included observations: 22 Variable Coefficient Std. Error t-Statis

6、tic Prob. C 31.79956 6.536434 4.864971 0.0001X3 0.387276 0.080260 4.825285 0.0001 R-squared 0.537929 Mean dependent var 62.50000Adjusted R-squared 0.514825 S.D. dependent var 10.08889S.E. of regression 7.027364 Akaike info criterion 6.824009Sum squared resid 987.6770 Schwarz criterion 6.923194Log li

7、kelihood -73.06409 Hannan-Quinn criter. 6.847374F-statistic 23.28338 Durbin-Watson stat 0.952555Prob(F-statistic) 0.000103 由上可知，关系式为y=31.79956+0.387276x3（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，

8、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0.537929，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: YMeth

9、od: Least SquaresDate: 12/03/14 Time: 17:00Sample (adjusted): 1 33Included observations: 33 after adjustments Variable Coefficient Std. Error t-Statistic Prob. X 0.176124 0.004072 43.25639 0.0000C -154.3063 39.08196 -3.948274 0.0004 R-squared 0.983702 Mean dependent var 902.5148Adjusted R-squared 0.

10、983177 S.D. dependent var 1351.009S.E. of regression 175.2325 Akaike info criterion 13.22880Sum squared resid 951899.7 Schwarz criterion 13.31949Log likelihood -216.2751 Hannan-Quinn criter. 13.25931F-statistic 1871.115 Durbin-Watson stat 0.100021Prob(F-statistic) 0.000000由上可知，模型的参数：斜率系数0.176124，截距为

11、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：Y=0.176124X154.3063(0.004072) (39.08196)t= (43.25639) （-3.948274）R2=0.983702 F=1871.115 n=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）

12、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：由上表可知，x2=（XiX）2=2x(n1)= 7608.0212 x (331)=1852223.473(XfX)2=(32000 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+18

13、52223.473/675977068.2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: 12/03/14 Time: 18:00Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob.LNX 0

14、.980275 0.034296 28.58268 0.0000C -1.918289 0.268213 -7.152121 0.0000R-squared 0.963442 Mean dependent var 5.573120Adjusted R-squared 0.962263 S.D. dependent var 1.684189S.E. of regression 0.327172 Akaike info criterion 0.662028Sum squared resid 3.318281 Schwarz criterion 0.752726Log likelihood -8.9

15、23468 Hannan-Quinn criter. 0.692545F-statistic 816.9699 Durbin-Watson stat 0.096208Prob(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

16、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: 12/01/14 Time: 12:40Sample: 1 12Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X -64.18400 4.809828 -13.34434 0.0000C 1845.475 19.26446

17、 95.79688 0.0000 R-squared 0.946829 Mean dependent var 1619.333Adjusted R-squared 0.941512 S.D. dependent var 131.2252S.E. of regression 31.73600 Akaike info criterion 9.903792Sum squared resid 10071.74 Schwarz criterion 9.984610Log likelihood -57.42275 Hannan-Quinn criter. 9.873871F-statistic 178.0

18、715 Durbin-Watson stat 1.172407Prob(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：由上表可知，x2=（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

19、计算得到：1556.6472.228x31.73600x1/12+43.5357/0.95387843 Yf1556.647+2.228x31.73600x1/12+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建立计量经济模型，用Eviews分析如下：Dependent Variable: YMethod: Least SquaresDate: 05/24/15 Time: 22:28Sample: 1 31Included observations: 31C246.85405

20、1.975004.7494760.0001X25.9968651.4060584.2650200.0002X3-0.5240270.179280-2.9229500.0069X4-2.2656800.518837-4.3668420.0002R-squared0.666062Mean dependent var16.77355Adjusted R-squared0.628957S.D. dependent var8.252535S.E. of regression5.026889Akaike info criterion6.187394Sum squared resid682.2795Schw

21、arz criterion6.372424Log likelihood-91.90460Hannan-Quinn criter.6.247709F-statistic17.95108Durbin-Watson stat1.147253Prob(F-statistic)0.000001得到模型为Y=246.8540+5.996865X20.524027X32.265680X4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

22、,4.265050，-2.922950，-4.366843，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GDP增加一万元，百户拥有家用汽车增加5.996865辆，城镇人口比重增加一个百分点，百户拥有家用汽车减少0.524047辆，交通工具消费价格指数每上升1，百户拥有家用汽车减少2.265680辆。

23、（3） 模型改进:收集其他年份的截面数据进行分析3.2（）对出口货物总额计量经济模型，用Eviews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 20:25Sample: 1994 2011Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. X2 0.135474 0.012799 10.58454 0.0000X3 18.85348 9.776181 1.928512 0.0729C -18231.5

24、8 8638.216 -2.110573 0.0520 R-squared 0.985838 Mean dependent var 6619.191Adjusted R-squared 0.983950 S.D. dependent var 5767.152S.E. of regression 730.6306 Akaike info criterion 16.17670Sum squared resid 8007316. Schwarz criterion 16.32510Log likelihood -142.5903 Hannan-Quinn criter. 16.19717F-stat

25、istic 522.0976 Durbin-Watson stat 1.173432Prob(F-statistic) 0.000000 由上可知，模型为：Y = 0.135474X2 + 18.85348X3 - 18231.58对模型进行检验：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。

26、（2）对于对数模型，用Eviews分析结果如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/01/14 Time: 20:25Sample: 1994 2011Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. LNX2 1.564221 0.088988 17.57789 0.0000LNX3 1.760695 0.682115 2.581229 0.0209C -20.52048 5.432487 -3.777363 0.0018

27、 R-squared 0.986295 Mean dependent var 8.400112Adjusted R-squared 0.984467 S.D. dependent var 0.941530S.E. of regression 0.117343 Akaike info criterion -1.296424Sum squared resid 0.206540 Schwarz criterion -1.148029Log likelihood 14.66782 Hannan-Quinn criter. -1.275962F-statistic 539.7364 Durbin-Wat

28、son stat 0.686656Prob(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

29、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)用Eviews分析得Dependent Variable: YMethod: Least SquaresDate: 05/26/15 Time: 13:13Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.C-50.4868549.44365-1.0210990.3234X0.0862140.0

30、291982.9527250.0099T52.436075.17660310.129430.0000R-squared0.951338Mean dependent var755.1222Adjusted R-squared0.944850S.D. dependent var258.7206S.E. of regression60.75813Akaike info criterion11.20269Sum squared resid55373.25Schwarz criterion11.35109Log likelihood-97.82422Hannan-Quinn criter.11.2231

31、5F-statistic146.6246Durbin-Watson stat2.606756Prob(F-statistic)0.000000模型为：Y=-50.48685+0.086214X+52.43607T对模型进行检验：1）可决系数是0.951338，修正的可决系数为0.944850，说明模型对样本拟合很好。2）F检验，F=146.6246 F（2,15）=4.77，回归方程显著。3）t检验，t统计量分别为2.952725，10.12943，均大于t（15）=2.131，所以这些系数都是显著的。经济意义检验：模型估计结果说明，在假定其他变量不变的情况下，家庭月平均收入每增长1元，平均说

32、来家庭书刊年消费支出会增长0.086214元;户主受教育年数每增长1年，平均说来家庭书刊年消费支出增加52.43607元。（2）用Eviews分析：Dependent Variable: YMethod: Least SquaresDate: 05/28/15 Time: 22:30Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.T63.016764.54858113.854160.0000C-11.5817158.02290-0.1996060.8443R-squared0.9

33、23054Mean dependent var755.1222Adjusted R-squared0.918245S.D. dependent var258.7206S.E. of regression73.97565Akaike info criterion11.54979Sum squared resid87558.36Schwarz criterion11.64872Log likelihood-101.9481Hannan-Quinn criter.11.56343F-statistic191.9377Durbin-Watson stat2.134043Prob(F-statistic

34、)0.000000Dependent Variable: XMethod: Least SquaresDate: 05/28/15 Time: 22:34Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.T123.151631.841503.8676440.0014C444.5888406.17861.0945650.2899R-squared0.483182Mean dependent var1942.933Adjusted R-squared0.450881S.D. depen

35、dent var698.8325S.E. of regression517.8529Akaike info criterion15.44170Sum squared resid4290746.Schwarz criterion15.54063Log likelihood-136.9753Hannan-Quinn criter.15.45534F-statistic14.95867Durbin-Watson stat1.052251Prob(F-statistic)0.001364以上分别是Y与T，X与T的一元回归模型分别是：Y = 63.01676T - 11.58171X = 123.151

36、6T + 444.5888(3)用Eviews分析结果如下：Dependent Variable: E1Method: Least SquaresDate: 05/29/15 Time: 20:39Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.E20.0864500.0284313.0407420.0078C3.96E-1413.880832.85E-151.0000R-squared0.366239Mean dependent var2.30E-14Adjusted R-sq

37、uared0.326629S.D. dependent var71.76693S.E. of regression58.89136Akaike info criterion11.09370Sum squared resid55491.07Schwarz criterion11.19264Log likelihood-97.84334Hannan-Quinn criter.11.10735F-statistic9.246111Durbin-Watson stat2.605783Prob(F-statistic)0.007788模型为：E1 = 0.086450E2 + 3.96e-14参数估计：

38、斜率系数为0.086450，截距v为3.96e-14（4）由上分析可知，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）预期估计各个参数的符号是X1，X2，X3，X4，X5的符号为正，X6的符号为负（2）根据Eviews分析得到数据如下：Dependent Variable: YMethod: Least SquaresDate: 05/27/15 Time: 22:40Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-StatisticProb.X

39、20.0013820.0011021.2543300.2336X30.0019420.0039600.4905010.6326X4-3.5790903.559949-1.0053770.3346X50.0047910.0050340.9516710.3600X60.0455420.0955520.4766210.6422C-13.7773215.73366-0.8756590.3984R-squared0.994869Mean dependent var12.76667Adjusted R-squared0.992731S.D. dependent var9.746631S.E. of reg

40、ression0.830963Akaike info criterion2.728738Sum squared resid8.285993Schwarz criterion3.025529Log likelihood-18.55865Hannan-Quinn criter.2.769662F-statistic465.3617Durbin-Watson stat1.553294Prob(F-statistic)0.000000与预期不相符。评价：可决系数为0.994869，可以认为拟合程度很好。F检验，F=465.3617F（5.12）=3,89，回归方程显著T检验，X2,X3,X4,X5，X

41、6 ，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)由Eviews分析得Dependent Variable: YMethod: Least SquaresDate: 05/27/15 Time: 22:42Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-StatisticProb.X50.0010322.20E-0546.799460.0000X6-0.0549650

42、.031184-1.7625810.0983C4.2054813.3356021.2607860.2266R-squared0.993601Mean dependent var12.76667Adjusted R-squared0.992748S.D. dependent var9.746631S.E. of regression0.830018Akaike info criterion2.616274Sum squared resid10.33396Schwarz criterion2.764669Log likelihood-20.54646Hannan-Quinn criter.2.636736F-statistic1164.567Durbin-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） 可决系数为0.993601，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。