计量经济学 庞皓 后答案

1、 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: 12/27/14 Time: 21:00Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.  C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001R-squared0.526082 &#

2、160;  Mean dependent var62.50000Adjusted 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 

3、   Hannan-Quinn criter.6.872689F-statistic22.20138    Durbin-Watson stat0.629074Prob(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: YMethod: Least SquaresDate: 11/26/14 Time: 21:10Sample: 1 22Included observations:

4、 22VariableCoefficientStd. Errort-StatisticProb.  C38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825    Mean dependent var62.50000Adjusted R-squared0.702666    S.D. dependent var10.08889S.E. of regression5.501306 &#

5、160;  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=3

6、8.79424+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: 22VariableCoefficientStd. Errort-StatisticProb.  C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001R-squared0.537929 &#

7、160;  Mean dependent var62.50000Adjusted 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 

8、   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+0.387276x3（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）=4.711834>t0.025(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

9、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）=7.115308>t0.025(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）=4.825285>t0.025(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

10、结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/03/14 Time: 17:00Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  X0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004R-squared0.983702    

11、;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   

12、60;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）=43.25639>t0.025(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

13、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）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：XY Mean 6000.441 902.5148

14、60;Median 2689.280 209.3900 Maximum 27722.31 4895.410 Minimum 123.7200 25.87000 Std. Dev. 7608.021 1351.009 Skewness 1.432519 1.663108 Kurtosis 4.010515 4.590432 Jarque-Bera 12.69068 18.69063 Pro

15、bability 0.001755 0.000087 Sum 198014.5 29782.99 Sum Sq. Dev. 1.85E+09 58407195 Observations 33 33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：5481.66172.0395x175.2325

16、x1/33+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: 12/03/14 Time: 18:00Sample (adjusted): 1 33Included observations: 33 after ad

17、justmentsVariableCoefficientStd. 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 regression0.32717

18、2    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

19、程为：lnY=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）=28.58268>t0.025(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 Squar

20、esDate: 12/01/14 Time: 12:40Sample: 1 12Included observations: 12VariableCoefficientStd. Errort-StatisticProb.  X-64.184004.809828-13.344340.0000C1845.47519.2644695.796880.0000R-squared0.946829    Mean dependent var1619.333Adjusted R-squared0.941512   

21、60;S.D. dependent var131.2252S.E. of regression31.73600    Akaike info criterion9.903792Sum squared resid10071.74    Schwarz criterion9.984610Log likelihood-57.42275    Hannan-Quinn criter.9.873871F-statistic178.0715    

22、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=（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=得，当x=4.5，y=1556.647再进行区间估计：用Eviews分析：YX Mean 1619.333 3.523333 Median 1630.000 3.715000 Maximum 1860.000 6.230000 Minim

23、um 1419.000 0.600000 Std. Dev. 131.2252 1.989419 Skewness 0.003403-0.060130 Kurtosis 2.346511 1.664917 Jarque-Bera 0.213547 0.898454 Probability 0.898729 0.638121 Sum 19432.00 42.28000 Sum Sq. Dev.

24、60;189420.7 43.53567 Observations 12 12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，将相关数据代入计算得到：1556.6472.228x31.73600x1/12+43.5357/0.95387843Yf1556.647+2.228x31.73600x1/12+43.5357/0.95387843即Yf的置信区间为（1556.647478.1231, 1556

25、.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: YMethod: Least SquaresDate: 11/25/14 Time: 12:38Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.  X25.9968651.4060584.2650200.0002X3-0.5240270.179280-2.9229500.0069X4-2.2656800.518837-4

26、.3668420.0002C246.854051.975004.7494760.0001R-squared0.666062    Mean dependent var16.77355Adjusted R-squared0.628957    S.D. dependent var8.252535S.E. of regression5.026889    Akaike info criterion6.187394Sum squared resid682.2795 

27、60;  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+5.996865X2-0.524027 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0.62895

28、7，说明模型对样本拟合较好2） F检验，F=17.95108>F（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

29、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: 12/08/14 Time: 17:28Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.  X25.1356701.0102705.0834650.0000LNX3-22.810056.771820-3

30、.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 criterion6.1066

31、92Sum squared resid629.3818    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+1148.75

32、8此分析得出的可决系数为0.691952>0.666062，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 Variable: YMethod: Least SquaresDate: 12/01/14 Time: 20:25Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-StatisticProb.  X20.1354740.01279910.584540.0000X318.853489.7761811

33、.9285120.0729C-18231.588638.216-2.1105730.0520R-squared0.985838    Mean dependent var6619.191Adjusted R-squared0.983950    S.D. dependent var5767.152S.E. of regression730.6306    Akaike info criterion16.17670Sum squared resid8007316. &

34、#160;  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

35、明模型对样本拟合较好2）F检验，F=522.0976>F（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: 12/01/14 Time: 20:25Sample: 1994 2011Included observations: 18VariableCoefficien

36、tStd. 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 regressio

37、n0.117343    Akaike 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

38、.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1，出口货物总额增加18.85348亿元。（2）式中的经济意义：工

39、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分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 20:30Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.  X0.0864500.0293632.9441860.0101T52

40、.370315.20216710.067020.0000C-50.0163849.46026-1.0112440.3279R-squared0.951235    Mean dependent var755.1222Adjusted R-squared0.944732    S.D. dependent var258.7206S.E. of regression60.82273    Akaike info criterion11.20482Sum squared resid

41、55491.07    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-50.01638对模型进行检验：1）可决系数是0.951235，修正的可决系数为0.94

42、4732，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 Time: 22:30Sample: 1 18Included observation

43、s: 18VariableCoefficientStd. Errort-StatisticProb.  T63.016764.54858113.854160.0000C-11.5817158.02290-0.1996060.8443R-squared0.923054    Mean dependent var755.1222Adjusted R-squared0.918245    S.D. dependent var258.7206S.E. of regression73.97565 

44、;   Akaike info criterion11.54979Sum squared resid87558.36    Schwarz criterion11.64872Log likelihood-101.9481    Hannan-Quinn criter.11.56343F-statistic191.9377    Durbin-Watson stat2.134043Prob(F-statistic)0.000000Dependent

45、 Variable: XMethod: Least SquaresDate: 12/01/14 Time: 22:34Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.  T123.151631.841503.8676440.0014C444.5888406.17861.0945650.2899R-squared0.483182    Mean dependent var1942.933Adjusted R-squared

46、0.450881    S.D. dependent var698.8325S.E. of regression517.8529    Akaike info criterion15.44170Sum squared resid4290746.    Schwarz criterion15.54063Log likelihood-136.9753    Hannan-Quinn criter.15.45534F-statistic14.

47、95867    Durbin-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 = 123.1516T + 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: 12/03/14 Time: 20:39Sample: 1 18Included observations: 18VariableCoeffici

48、entStd. Errort-StatisticProb.  E20.0864500.0284313.0407420.0078C3.96E-1413.880832.85E-151.0000R-squared0.366239    Mean dependent var2.30E-14Adjusted R-squared0.326629    S.D. dependent var71.76693S.E. of regression58.89136    Aka

49、ike info criterion11.09370Sum squared resid55491.07    Schwarz criterion11.19264Log 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

50、数：斜率系数为0.086450，截距为3.96e-14（3）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分析得到数据如下：Dependent Variable: YMethod: Least SquaresDate: 12/04/14 Time: 13:24Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-StatisticProb. &#

51、160;X20.0013820.0011021.2543300.2336X30.0019420.0039600.4905010.6326X4-3.5790903.559949-1.0053770.3346X50.0047910.0050340.9516710.3600X60.0455420.0955520.4766210.6422C-13.7773215.73366-0.8756590.3984R-squared0.994869    Mean dependent var12.76667Adjusted R-squared0.992731 &#

52、160;  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-statistic465.3617  

53、;  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=465.3617>F（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 Variable: YM

54、ethod: Least SquaresDate: 12/03/14 Time: 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 va

55、r12.76667Adjusted R-squared0.992748    S.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    Durbi