《计量经济学》(第三版)课后习题答案

《计量经济学》(第三版)课后习题答案第二章简单线性回归模型2.1(1)①首先分析人均寿命与人均GDP的数量关系，用Eviews分析：DependentVariable:YMethod:LeastSquaresDate:12/23/15Time:14:37Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C56.64794 1.96082028.889920.0000XI0.1283600.027242 4.7118340.0001R-squared0.526082Meandependentvar62.50000AdjustedR-squared0.502386S.D.dependentvar10.08889S.E.ofregression7.116881Akaikeinfocriterion6.849324Sumsquaredresid1013.000Schwarzcriterion6.948510Loglikelihood-73.34257Hannan-Quinncriter.6.872689F-statistic22.20138Durbin-Watsonstat0.629074Prob(F-statistic)0.000134有上可知，关系式为y=56.64794+0.128360xl②关于人均寿命与成人识字率的关系，用Eviews分析如下：DependentVariable:YMethod:LeastSquaresDate:12/23/15Time:15:01Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C38.79424 3.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825Meandependentvar62.50000AdjustedR-squared0.702666S.D.dependentvar10.08889S.E.ofregression5.501306Akaikeinfocriterion6.334356Sumsquaredresid605.2873Schwarzcriterion6.433542Loglikelihood-67.67792Hannan-Quinncriter.6.357721F-statistic50.62761Durbin-Watsonstat1.846406Prob(F-statistic)0.000001由上可知，关系式为y=38.79424+0.331971x2③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：DependentVariable:YMethod:LeastSquaresDate:12/23/14Time:15:20Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C31.79956 6.536434 4.8649710.0001X303872760.080260 4.8252850.0001R-squared0.537929Meandependentvar62.50000AdjustedR-squared0.514825S.D.dependentvar10.08889S.E.ofregression7.027364Akaikeinfocriterion6.824009Sumsquaredresid987.6770Schwarzcriterion6.923194Loglikelihood-73.06409Hannan-Quinncriter.6.847374F-statistic23.28338Durbin-Watsonstat0.952555Prob(F-statistic)0.000103由上可知，关系式为y=3L79956+0.387276x3(2)①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(|31)=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响。②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(|32)=7.115308X0.025(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。③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(|33)=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)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：DependentVariable:YMethod:LeastSquaresDate:12/23/15Time:17:46Sample(adjusted):133Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.X0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004R-squared0.983702Meandependentvar902.5148AdjustedR-squared0.983177S.D.dependentvar1351.009S.E.ofregression175.2325Akaikeinfocriterion13.22880Sumsquaredresid951899.7Schwarzcriterion13.31949Loglikelihood-216.2751Hannan-Quinncriter.13.25931F-statistic1871.115Durbin-Watsonstat0.100021Prob(F-statistic)0.000000②由上可知，模型的参数：斜率系数0.176124,截距为一154.3063③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(02)=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收入有显著影响。④用规范形式写出检验结果如下：Y=0.176124X-154.3063(0.004072)(39.08196)t=(43.25639)(-3.948274)R2=0.983702F=1871.115n=33⑤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，①进行点预测，由上可知丫=0.176124X-154.3063,代入可得：Y=丫=0.176124*32000-154.3063=5481.6617②进行区间预测：先由Eviews分析：由上表可知，Wx2=W(Xi-X)2=62x(n—1)=7608.0212x(33-1)=1852223.473(Xf—X)2=(32000-6000.441)2=675977068.2当Xf=32000时，将相关数据代入计算得到：5481.6617—2.0395xl75.2325xVl/33+1852223.473/675977068.2<Yf<5481.6617+2.0395xl75.2325xVl/33+1852223.473/675977068.2即Yf的置信区间为(5481.6617—64.9649,5481.6617+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：DependentVariable:LNYMethod:LeastSquaresDate:12/23/15Time:18:04Sample(adjusted):133Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.LNX0.9802750.03429628.582680.0000C-1.9182890.268213-7.1521210.0000R-squared0.963442Meandependentvar5.573120AdjustedR-squared0.962263S.D.dependentvar1.684189S.E.ofregression0.327172Akaikeinfocriterion0.662028Sumsquaredresid3.318281Schwarzcriterion0.752726Loglikelihood-8.923468Hannan-Quinncriter.0.692545F-statistic816.9699Durbin-Watsonstat0.096208Prob(F-statistic)0.000000①模型方程为：lnY=0.980275lnX-1.918289②由上可知，模型的参数：斜率系数为0.980275,截距为-1.918289③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(B2)=28.58268X0.025(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。④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：DependentVariable:YMethod:LeastSquaresDate:12/23/15Time:20:11Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.X-64.18400 4.809828-13.344340.0000C1845.47519.2644695.796880.0000R-squared0.946829Meandependentvar1619.333AdjustedR-squared0.941512S.D.d叩endentvar131.2252S.E.ofregression31.73600Akaikeinfocriterion9.903792Sumsquaredresid10071.74Schwarzcriterion9.984610Loglikelihood-57.42275Hannan-Quinncriter.9.873871F-statistic178.0715Durbin-Watsonstat1.172407Prob(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)①首先进行点预测，由Y=1845.475-64.18400X得，当x=4.5,y=1556.647②再进行区间估计：由上表可知，Wx2=E(Xi-X)2=62x(n-l)=1.9894192x(12-1)=43.5357(Xf-X)2=(4.5-3.523333)2=0.95387843当Xf=4.5时，将相关数据代入计算得到：1556.647-2.228x31.73600xVl/12+43.5357/0.95387843<Yf<1556.647+2.228x31.73600xVl/12+43.5357/0.95387843即Yf的置信区间为(1556.647—478.1231,1556.647+478.1231)3.1(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：DependentVariable:YMethod:LeastSquaresDate:12/23/15Time:20:59Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.X25.996865 1.406058 4.2650200.0002X3-0.5240270.179280-2.9229500.0069X4-2.2656800.518837-4.3668420.0002C246.854051.97500 4.7494760.0001R-squared0.666062Meandependentvar16.77355AdjustedR-squared0.628957S.D.dependentvar8.252535S.E.ofregression5.026889Akaikeinfocriterion6.187394Sumsquaredresid682.2795Schwarzcriterion6.372424Loglikelihood-91.90460Hannan-Quinncriter.6.247709F-statistic17.95108Durbin-Watsonstat1.147253Prob(F-statistic)0.000001②得到模型得：Y=246.8540+5.996865X2-0.524027X3-2.265680X4③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=17.95108>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。④依据：1)可决系数越大，说明拟合程度越好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。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1万元，百户拥有家用汽车增加5.996865辆，城镇人口比重增加1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1,百户拥有家用汽车减少2.265680辆。(3)用EViews分析得：DependentVariable:YMethod:LeastSquaresDate:12/23/15Time:21:09Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.X25.135670 1.010270 5.0834650.0000LNX3-22.81005 6.771820-3.3683780.0023LNX4-230.848149.46791-4.6666240.0001C1148.758228.2917 5.0319740.0000R-squared0.691952Meandependentvar16.77355AdjustedR-squared0.657725S.D.dependentvar8.252535S.E.ofregression4.828088Akaikeinfocriterion6.106692Sumsquaredresid629.3818Schwarzcriterion6.291723Loglikelihood-90.65373Hannan-Quinncriter.6.167008F-statistic20.21624Durbin-Watsonstat1.150090Prob(F-statistic)0.000000模型方程为：Y=5.135670X2-22.81005LNX3-230.8481LNX4+1148.758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(1)对出口货物总额计量经济模型，用Eviews分析结果如下：：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:08:23Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X20.1354740.01279910.584540.0000X318.853489.776181 1.9285120.0729C-18231.588638.216-2.1105730.0520R-squared0.985838Meandependentvar6619.191AdjustedR-squared0.983950S.D.dependentvar5767.152S.E.ofregression730,6306Akaikeinfocriterion16.17670Sumsquaredresid8007316.Schwarzcriterion16.32510Loglikelihood-142.5903Hannan-Quinncriter.16.19717F-statistic522.0976Durbin-Watsonstat1.173432Prob(F-statistic)0.000000①由上可知，模型为：Y=0.135474X2+18.85348X3-18231.58②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=522,0976>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：DependentVariable:LNYMethod:LeastSquaresDate:12/24/15Time:08:47Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.LNX21.5642210.08898817.577890.0000LNX31.7606950.682115 2.5812290.0209C-20.52048 5.432487-3.7773630.0018R-squared0.986295Meandependentvar8.400112AdjustedR-squared0.984467S.D.dependentvar0.941530S.E.ofregression0.117343Akaikeinfocriterion-1.296424Sumsquaredresid0.206540Schwarzcriterion-1.148029Loglikelihood14.66782Hannan-Quinncriter.-1.275962F-statistic539.7364Durbin-Watsonstat0.686656Prob(F-statistic)0.000000①由上可知，模型为：LNY=-20.52048+1.564221LNX2+1.760695LNX3②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。F检验，F=539.7364>F(2,15)=4.77,回归方程显著。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。①(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)(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分析结果如下：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:09:03Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X0.0864500.029363 2.9441860.0101T52.37031 5.20216710.067020.0000C-50.0163849.46026-1.0112440.3279R-squared0.951235Meandependentvar755.1222AdjustedR-squared0.944732S.D.dependentvar258.7206S.E.ofregression60.82273Akaikeinfocriterion11.20482Sumsquaredresid55491.07Schwarzcriterion11.35321Loglikelihood-97.84334Hannan-Quinncriter.11.22528F-statistic146.2974Durbin-Watsonstat2.605783Prob(F-statistic)0.000000①模型为：Y=0.086450X+5237031T-50.01638②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。③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：①DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:09:18Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.T63.01676 4.54858113.854160.0000C-11.5817158.02290-0.1996060.8443R-squared0.923054Meandependentvar755.1222AdjustedR-squared0.918245S.D.dependentvar258.7206S.E.ofregression73.97565Akaikeinfocriterion11.54979Sumsquaredresid87558.36Schwarzcriterion11.64872Loglikelihood-101.9481Hannan-Quinncriter.11.56343F-statistic191.9377Durbin-Watsonstat2.134043Prob(F-statistic)0.000000②DependentVariable:XMethod:LeastSquaresDate:12/24/15Time:09:34Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.T123.151631.84150 3.8676440.0014C444.5888406.1786 1.0945650.2899R-squared0.483182Meandependentvar1942.933AdjustedR-squared0.450881S.D.dependentvar698.8325S.E.ofregression517.8529Akaikeinfocriterion15.44170Sumsquaredresid4290746.Schwarzcriterion15.54063Loglikelihood-136.9753Hannan-Quinncriter.15.45534F-statistic14.95867Durbin-Watsonstat1.052251Prob(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：DependentVariable:ElMethod:LeastSquaresDate:12/24/15Time:09:39Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.E20.0864500.028431 3.0407420.0078C3.96E-1413.88083 2.85E-15 1.0000R-squared0.366239Meandependentvar2.30E-14AdjustedR-squared0.326629S.D.dependentvar71.76693S.E.ofregression58.89136Akaikeinfocriterion11.09370Sumsquaredresid55491.07Schwarzcriterion11.19264Loglikelihood-97.84334Hannan-Quinncriter.11.10735F-statistic9.246111Durbin-Watsonstat2.605783Prob(F-statistic)0.007788模型为：El=0.086450E2+3.96e-14参数：斜率系数a为0.086450,截距为3.96e-14(3)由上可知，B2与a2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XI,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：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:10:13Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X20.0013820.001102 1.2543300.2336X30.0019420.0039600.4905010.6326X4-3.579090 3.559949-1.0053770.3346X50.0047910.0050340.9516710.3600X60.0455420.0955520.4766210.6422C-13.7773215.73366-0.8756590.3984R-squared0.994869Meandependentvar12.76667AdjustedR-squared0.992731S.D.dependentvar9.746631S.E.ofregression0.830963Akaikeinfocriterion2.728738Sumsquaredresid8.285993Schwarzcriterion3.025529Loglikelihood-18.55865Hannan-Quinncriter.2.769662F-statistic465.3617Durbin-Watsonstat1.553294Prob(F-statistic)0.000000①与预期不相符。②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，XI,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：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:10:20Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X50.001032 2.20E-0546.799460.0000X6-0.0549650.031184-1.7625810.0983C4.205481 3.335602 1.2607860.2266R-squared0.993601Meandependentvar12.76667AdjustedR-squared0.992748S.D.dependentvar9.746631S.E.ofregression0.830018Akaikeinfocriterion2.616274Sumsquaredresid10.33396Schwarzcriterion2.764669Loglikelihood-20.54646Hannan-Quinncriter.2.636736F-statistic1164.567Durbin-Watsonstat1.341880Prob(F-statistic)0.000000①得到模型的方程为：Y=0.001032X5-0.054965X6+4.205481②评价：1)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=1164.567>F(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：DependentVariable:LNYMethod:LeastSquaresDate:12/24/15Time:10:39Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNGDP1.3385330.08861015.105820.0000LNCPI-0.4217910.233295-1.8079750.0832C-3.1114860.463010-6.7201260.0000R-squared0.988051Meandependentvar9.484710AdjustedR-squared0.987055S.D.dependentvar1.425517S.E.ofregression0.162189Akaikeinfocriterion-0.695670Sumsquaredresid0.631326Schwarzcriterion-0.551689Loglikelihood12.39155Hannan-Quinncriter.-0.652857F-statistic992.2582Durbin-Watsonstat0.522613Prob(F-statistic)0.000000得到的模型方程为：LNY=1.338533LNGDPt-0.421791LNCPIt-3.111486(2)①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a=0.05时，t(24)=2.064,LNCPI的系数不显著，可能存在多重共线性。②得到相关系数矩阵如下：LNGDP,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)DependentVariable:LNYMethod:LeastSquaresDate:12/24/15Time:10:41Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNGDP1.1857390.02782242.619330.0000C-3.7506700.312255-12.011560.0000R-squared0.986423Meandependentvar9.484710AdjustedR-squared0.985880S.D.dependentvar1.425517S.E.ofregression0.169389Akaikeinfocriterion-0.642056Sumsquaredresid0.717312Schwarzcriterion-0.546068Loglikelihood10.66776Hannan-Quinncriter.-0.613514F-statistic1816.407Durbin-Watsonstat0.471111Prob(F-statistic)0.000000b)DependentVariable:LNYMethod:LeastSquaresDate:12/24/15Time:10:55Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNCPI2.9392950.22275613.195110.0000C-6.854535 1.242243-5.5178710.0000R-squared0.874442Meandependentvar9.484710AdjustedR-squared0.869419S.D.dependentvar1.425517S.E.ofregression0.515124Akaikeinfocriterion1.582368Sumsquaredresid6.633810Schwarzcriterion1.678356Loglikelihood-19.36196Hannan-Quinncriter.1.610910F-statistic174.1108Durbin-Watsonstat0.137042Prob(F-statistic)0.000000DependentVariable:LNGDPMethod:LeastSquaresDate:12/24/15Time:11:07Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNCPI2.5110220.15830215.862270.0000C-2.7963810.882798-3.1676340.0040R-squared0.909621Meandependentvar11.16214AdjustedR-squared0.906005S.D.dependentvar1.194029S.E.ofregression0.366072Akaikeinfocriterion0.899213Sumsquaredresid3.350216Schwarzcriterion0.995201Loglikelihood-10.13938Hannan-Quinncriter.0.927755F-statistic251.6117Durbin-Watsonstat0.099623Prob(F-statistic)0.000000①得到的回归方程分别为1)LNY=1.185739LNGDPt-3.7506702)LNY=2.939295LNCPIt-6.8545353)LNGDPt=2.511022LNCPIt-2.796381②对多重共线性的认识：单方程拟合效果都很好，回归系数显著，判定系数较高，GDP和CPI对进口的显著的单一影响，在这两个变量同时引入模型时影响方向发生了改变，这只有通过相关系数的分析才能发现。(4)建议：如果仅仅是作预测，可以不在意这种多重共线性，但如果是进行结构分析，还是应该引起注意的。4.4(1)按照设计的理论模型，由Eviews分析得：DependentVariable:CZSRMethod:LeastSquaresDate:12/24/15Time:11:23Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.CZZC0.0901140.044367 2.0311290.0540GDP-0.0253340.005069-4.9980360.0000SSZE1.1768940.06216218.932710.0000C-221.8540130.6532-1.6980380.1030R-squared0.999857Meandependentvar22572.56AdjustedR-squared0.999838S.D.dependentvar27739.49S.E.ofregression353.0540Akaikeinfocriterion14.70707Sumsquaredresid2866884.Schwarzcriterion14.89905Loglikelihood-194.5455Hannan-Quinncriter.14.76416F-statistic53493.93Durbin-Watsonstat1.458128Prob(F-statistic)0.000000从回归结果可见，可决系数为0.999857,校正的可决系数为0.999838,模型拟合的很好。F的统计量为53493.93,说明在a=0.05,水平下，回归方程回归方程整体上是显著的。但是t检验结果表明，国内生产总值对财政收入的影响显著，但回归系数的符号为负，与实际不符合。由此可得知，该方程可能存在多重共线性。(2)得到相关系数矩阵如下：由上表可知，CZZC与GDP,CZZC与SSZE,GDP与SSZE之间的相关系数都非常高，说明确实存在多重共线性。(3)做辅助回归方差扩大因子均大于10,存在严重多重共线性。并且通过以上分析，两两被解释变量之间相关性都很高。(4)解决方式：分别作出财政收入与财政支出、国内生产总值、税收总额之间的一元回归。5.2(1)①用图形法检验绘制e2的散点图，用Eviews分析如下：由上图可知，模型可能存在异方差，②Goldfeld-Quanadt检验1)定义区间为1-7时，由软件分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:14:52Sample:17Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.T35.20664 4.9014927.1828430.0020X0.1099490.061965 1.7743800.1507C77.1258882.328440.9368070.4019R-squared0.943099Meandependentvar565.6857AdjustedR-squared0.914649S.D.dependentvar108.2755S.E.ofregression31.63265Akaikeinfocriterion10.04378Sumsquaredresid4002.499Schwarzcriterion10.02060Loglikelihood-32.15324Hannan-Quinncriter.9.757267F-statistic33.14880Durbin-Watsonstat1.426262Prob(F-statistic)0.003238得Eeli2=4002.4992)定义区间为12-18时，由软件分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:14:55Sample:1218Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.T52.40588 6.9233787.5694090.0016X0.0686890.053763 1.2776350.2705C-8.78926579.92542-0.1099680.9177R-squared0.984688Meandependentvar887.6143AdjustedR-squared0.977032S.D.dependentvar274.4148S.E.ofregression41.58810Akaikeinfocriterion10.59103Sumsquaredresid6918.280Schwarzcriterion10.56785Loglikelihood-34.06861Hannan-Quinncriter.10.30451F-statistic128.6166Durbin-Watsonstat2.390329Prob(F-statistic)0.000234得Ee2i2=6918.2803)根据Goldfeld-Quanadt检验，F统计量为:F=Ie2i2/2eli2=6918.280/4002.499=1.7285在a=0.05水平下，分子分母的自由度均为4,查分布表得临界值F0.05(4,4)=6.39,因为F=1.7285<F0.05(4,4)=6.39,所以接受原假设，此检验表明模型不存在异方差。(2)存在异方差，估计参数的方法：①可以对模型进行变换②使用加权最小二乘法进行计算，得出模型方程，并对其进行相关检验③对模型进行对数变换，进行分析(3)评价：3.3所得结论是可以相信的，随机扰动项之间不存在异方差。回归方程是显著的。5.3⑴由Eviews软件分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:16:00Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.X1.2442810.07903215.744110.0000C242.4488291.19400.8326020.4119R-squared0.895260Meandependentvar4443.526AdjustedR-squared0.891649S.D.dependentvar1972.072S.E.ofregression649.1426Akaikeinfocriterion15.85152Sumsquaredresid12220196Schwarzcriterion15.94404Loglikelihood-243.6986Hannan-Quinncriter.15.88168F-statistic247.8769Durbin-Watsonstat1.078581Prob(F-statistic)0.000000由上表可知，2007年我国农村居民家庭人均消费支出(x)对人均纯收入(y)的模型为:Y=1.244281X+242.4488(2)①由图形法检验由上图可知，模型可能存在异方差。(2)Goldfeld-Quanadt检验1)定义区间为1・12时，由软件分析得：DependentVariable:Y1Method:LeastSquaresDate:12/24/15Time:16:05Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.XI1.4852960.500386 2.9682970.0141C-550.54921220.063-0.4512470.6614R-squared0.468390Meandependentvar3052.950AdjustedR-squared0.415229S.D.dependentvar550.5148S.E.ofregression420.9803Akaikeinfocriterion15.07406Sumsquaredresid1772245.Schwarzcriterion15.15488Loglikelihood-88.44437Hannan-Quinncriter.15.04414F-statistic8.810789Durbin-Watsonstat2.354167Prob(F-statistic)0.014087得£eli2=1772245.2)定义区间为20.31时，由软件分析得：DependentVariable:Y1Method:LeastSquaresDate:12/24/15Time:16:16Sample:2031Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.XI1.0869400.1488637.3016230.0000C1173.307733.2520 1.6001410.1407R-squared0.842056Meandependentvar6188.329AdjustedR-squared0.826262S.D.dependentvar2133.692S.E.ofregression889.3633Akaikeinfocriterion16.56990Sumsquaredresid7909670.Schwarzcriterion16.65072Loglikelihood-97.41940Hannan-Quinncriter.16.53998F-statistic53.31370Durbin-Watsonstat2.339767Prob(F-statistic)0.000026得£e2i2=7909670.3)根据Goldfeld-Quanadt检验，F统计量为:F=Ie2i2/Ieli2=7909670./1772245=4.4631在a=0.05水平下，分子分母的自由度均为10,查分布表得临界值F0Q5(10,10)=2.98,因为F=4.4631>F0.05(10,10)=2.98,所以拒绝原假设，此检验表明模型存在异方差。(3)1)采用WLS法估计过程中，①用权数wl=l/X,建立回归得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:16:29Sample:131Includedobservations:31Weightingseries:W1VariableCoefficientStd.Errort-StatisticProb.X1.4258590.11910411.971570.0000C-334.8131344.3523-0.9722980.3389WeightedStatisticsR-squared0.831707Meandependentvar3946.082AdjustedR-squared0.825904S.D.dependentvar536.1907S.E.ofregression536.6796Akaikeinfocriterion15.47102Sumsquaredresid8352726.Schwarzcriterion15.56354Loglikelihood-237.8008Hannan-Quinncriter.15.50118F-statistic143.3184Durbin-Watsonstat1.369081Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.875855Meandependentvar4443.526AdjustedR-squared0.871574S.D.dependentvar1972.072S.E.ofregression706.7236Sumsquaredresid14484289Durbin-Watsonstat1.532908对此模型进行White检验得：HeteroskedasticityTest:WhiteF-statistic0.299395Prob.F(2,28)0.7436Obs*R-squared0.649065Prob.Chi-Square(2)0.7229ScaledexplainedSS1.798067Prob.Chi-Square(2)0.4070TestEquation:DependentVariable:WGT_RESIDA2Method:LeastSquaresDate:12/24/15Time:16:34Sample:131Includedobservations:31CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticProb.C61927.891045682.0.0592220.9532WGTA2-593927.91173622.-0.5060640.6168X*WGTA2282.4407747.97800.3776060.7086R-squared0.020938Meandependentvar269442.8AdjustedR-squared-0.048995S.D.dependentvar689166.5S.E.ofregression705847.6Akaikeinfocriterion29.86395Sumsquaredresid1.40E+13Schwarzcriterion30.00273Loglikelihood-459.8913Hannan-Quinncriter.29.90919F-statistic0.299395Durbin-Watsonstat1.922336Prob(F-statistic)0.743610从上可知,nR2=0.649065,比较计算的统计量的临界值，因为nR2=0.649065<0.05(2)=5.9915,所以接受原假设，该模型消除了异方差。估计结果为：Y=1.425859X-334.8131t=(11.97157)(-0.972298)R2=0.875855F=143.3184DW=1.369081②用权数w2=l/x2,用回归分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:16:40Sample:131Includedobservations:31Weightingseries:W2VariableCoefficientStd.Errort-StatisticProb.X1.5570400.14539210.709220.0000C-693.1946376.4760-1.8412720.0758WeightedStatisticsR-squared0.798173Meandependentvar3635.028AdjustedR-squared0.791214S.D.dependentvar1029.830S.E.ofregression466.8513Akaikeinfocriterion15.19224Sumsquaredresid6320554.Schwarzcriterion15.28475Loglikelihood-233.4797Hannan-Quinncriter.15.22240F-statistic114.6875Durbin-Watsonstat1.562975Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.834850Meandependentvar4443.526AdjustedR-squared0.829156S.D.dependentvar1972.072S.E.ofregression815.1229Sumsquaredresid19268334Durbin-Watsonstat1.678365对此模型进行White检验得：HeteroskedasticityTest:WhiteF-statistic0.299790Prob.F(3,27)0.8252Obs*R-squared0.999322Prob.Chi-Square(3)0.8014ScaledexplainedSS1.789507Prob.Chi-Square(3)0.6172TestEquation:DependentVariable:WGT_RESIDA2Method:LeastSquaresDate:12/24/15Time:16:45Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.C-111661.8549855.7-0.2030750.8406WGTA2426220.22240181.0.1902620.8505XA2*WGTA20.1948880.5163950.3774020.7088X*WGTA2-583.21512082.820-0.2800120.7816R-squared0.032236Meandependentvar203888.8AdjustedR-squared-0.075293S.D.dependentvar419282.0S.E.ofregression434780.1Akaikeinfocriterion28.92298Sumsquaredresid5.10E+12Schwarzcriterion29.10801Loglikelihood-444.3062Hannan-Quinncriter.28.98330F-statistic0.299790Durbin-Watsonstat1.835854Prob(F-statistic)0.825233从上可知，nR2=0.999322,比较计算的统计量的临界值，因为nR2=0.999322<0.05(2)=5.9915,所以接受原假设，该模型消除了异方差。估计结果为：Y=1.557040X-693.1946t=(10.70922)(-1.841272)R2=0.798173F=114.6875DW=1.562975③用权数w3=l/sqr(x),用回归分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:16:49Sample:131Includedobservations:31Weightingseries:W3VariableCoefficientStd.Errort-StatisticProb.X1.3301300.09834513.525070.0000C-47.40242313.1154-0.1513900.8807WeightedStatisticsR-squared0.863161Meandependentvar4164.118AdjustedR-squared0.858442S.D.dependentvar991.2079S.E.ofregression586.9555Akaikeinfocriterion15.65012Sumsquaredresid9990985.Schwarzcriterion15.74263Loglikelihood-240.5768Hannan-Quinncriter.15.68027F-statistic182.9276Durbin-Watsonstat1.237664Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.890999Meandependentvar4443.526AdjustedR-squared0.887240S.D.dependentvar1972.072S.E.ofregression662.2171Sumsquaredresid12717412Durbin-Watsonstat1.314859对此模型进行White检验得：HeteroskedasticityTest:WhiteF-statistic0.423886Prob.F(2,28)0.6586Obs*R-squared0.911022Prob.Chi-Square(2)0.6341ScaledexplainedSS2.768332Prob.Chi-Square(2)0.2505TestEquation:DependentVariable:WGT_RESIDA2Method:LeastSquaresDate:12/24/15Time:16:57Sample:131Includedobservations:31CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticProb.C1212308.2141958.0.5659810.5759WGTA2-715673.01301839.-0.5497400.5869XA2*WGTA2-0.0151940.082276-0.1846770.8548R-squared0.029388Meandependentvar322289.8AdjustedR-squared-0.039942S.D.dependentvar863356.7S.E.ofregression880429.8Akaikeinfocriterion30.30597Sumsquaredresid2.17E+13Schwarzcriterion30.44475Loglikelihood-466.7426Hannan-Quinncriter.30.35121F-statistic0.423886Durbin-Watsonstat1.887426Prob(F-statistic)0.658628,比较计算的统计量的临界值，因为=0.911022<0.05估计结果为：Y=1.330130X-47.40242t=(13.52507)(-0.151390)R2=0.863161F=182.9276DW=1.237664经过检验发现，用权数wl的效果最好，所以综上可知，即修改后的结果为:Y=1.425859X-334.8131t=(11.97157)(-0.972298)R2=0.875855F=143.3184DW=1.369081⑴a)用Eviews模型分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:19:16Sample:19782011Includedobservations:34VariableCoefficientStd.Errort-StatisticProb.X0.7462410.01