计量经济学第三版课后习题答案解析

专业资料整理分享专业资料整理分享完美完美WORD格式编辑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勺数量关系，用Eviews分析:DependentVariable:YMethod:LeastSquaresDate:12/23/15Time:14:37Sample:122Includedobservations:22CoefficienVariabletStd.Errort-StatisticProb.C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001MeandependentR-squared0.526082varS.D.dependent62.50000AdjustedR-squared0.502386varAkaikeinfo10.08889S.E.ofregression7.116881criterionSchwarz6.849324Sumsquaredresid1013.000criterionHannan-Quinn6.948510Loglikelihood-73.34257criter.Durbin-Watson6.872689F-statistic22.20138stat0.629074Prob(F-statistic)0.000134有上可知，关系式为y=56.64794+0.128360x1②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:22CoefficienVariabletStd.Errort-StatisticProb.C38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000MeandependentR-squared0.716825var62.50000

S.D.dependentAdjustedR-squared0.702666var10.08889AkaikeinfoS.E.ofregression5.501306criterion6.334356SchwarzSumsquaredresid605.2873criterion6.433542Hannan-QuinnLoglikelihood-67.67792criter.6.357721Durbin-WatsonF-statistic50.62761stat1.846406Prob(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.C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001MeandependentR-squared0.537929varS.D.dependent62.50000AdjustedR-squared0.514825varAkaikeinfo10.08889S.E.ofregression7.027364criterionSchwarz6.824009Sumsquaredresid987.6770criterionHannan-Quinn6.923194Loglikelihood-73.06409criter.Durbin-Watson6.847374F-statisticProb(F-statistic)23.28338stat0.0001030.952555由上可知，关系式为y=31.79956+0.387276x3(2)①关于人均寿命与人均GDP莫型，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寸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(S)=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。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:33afteradjustmentsCoefficienStd.Errort-StatisticProb.VariabletX0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004MeandependentR-squared0.983702varS.D.dependent902.5148AdjustedR-squared0.983177varAkaikeinfo1351.009S.E.ofregression175.2325criterionSchwarz13.22880Sumsquaredresid951899.7criterion13.31949

Hannan-QuinnLoglikelihoodF-statisticProb(F-statistic)13.25931LoglikelihoodF-statisticProb(F-statistic)13.259310.100021Durbin-Watson1871.115stat0.000000②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(32)=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Y=0.176124X—154.3063,代入可得：Y=Y=0.176124*32000—154.3063=5481.6617②进行区间预测：先由Eviews分析:XYMean6000.441902.5148Median2689.280209.3900Maximum27722.314895.410Minimum123.720025.87000Std.Dev.7608.0211351.009Skewness1.4325191.663108Kurtosis4.0105154.590432Jarque-Bera12.6906818.69063Probability0.0017550.000087Sum198014.529782.99SumSq.Dev.1.85E+0958407195Observations3333由上表可知，汇X2=E(X—X)2=82x(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—2.0395x175.2325x/1/33+1852223.473/675977068.2&YfW5481.6617+2.0395x175.2325x/1/33+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-1.9182890.268213-7.1521210.0000MeandependentR-squared0.963442varS.D.dependent5.573120AdjustedR-squared0.962263varAkaikeinfo1.684189S.E.ofregression0.327172criterionSchwarz0.662028Sumsquaredresid3.318281criterionHannan-Quinn0.752726Loglikelihood-8.923468criter.Durbin-Watson0.692545F-statistic816.9699stat0.096208Prob(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(32)=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。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:12CoefficienStd.Errort-StatisticProb.VariabletX-64.184004.809828-13.344340.0000C1845.47519.2644695.796880.0000MeandependentR-squared0.946829varS.D.dependent1619.333AdjustedR-squared0.941512varAkaikeinfo131.2252S.E.ofregression31.73600criterionSchwarz9.903792Sumsquaredresid10071.74criterionHannan-Quinn9.984610Loglikelihood-57.42275criter.Durbin-Watson9.873871F-statisticProb(F-statistic)178.0715stat0.0000001.172407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。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：

用Eviews分析:YXMean1619.3333.523333Median1630.0003.715000Maximum1860.0006.230000Minimum1419.0000.600000Std.Dev.131.22521.989419Skewness0.003403-0.060130Kurtosis2.3465111.664917Jarque-Bera0.2135470.898454Probability0.8987290.638121Sum19432.0042.28000SumSq.Dev.189420.743.53567Observations1212由上表可知，汇x2=E(X—X)2=82x(n—1)=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—2.228x31.73600x/1/12+43.5357/0.95387843《YfW1556.647+2.228x31.73600x/1/12+43.5357/0.95387843即Yf的置信区间为(1556.647—478.1231,1556.647+478.1231)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:丫Method:LeastSquaresDate:12/23/15Time:20:59Sample:131Includedobservations:31Coefficient-StatisticProb.VariabletStd.ErrorX25.9968651.4060584.2650200.0002X3-0.5240270.179280-2.9229500.0069X4-2.2656800.518837-4.3668420.0002C246.854051.975004.7494760.0001MeandependentR-squared0.666062varS.D.dependent16.77355AdjustedR-squared0.628957varAkaikeinfo8.252535S.E.ofregression5.026889criterionSchwarz6.187394Sumsquaredresid682.2795criterionHannan-Quinn6.372424Loglikelihood-91.90460criter.Durbin-Watson6.247709F-statistic17.95108stat1.147253Prob(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F检验，F=17.95108>F(3,27)=3.65,回归方程显著。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.X25.1356701.0102705.0834650.0000LNX3-22.810056.771820-3.3683780.0023LNX4-230.848149.46791-4.6666240.0001C1148.758228.29175.0319740.0000MeandependentR-squared0.691952varS.D.dependent16.77355AdjustedR-squared0.657725varAkaikeinfo8.252535S.E.ofregression4.828088criterionSchwarz6.106692Sumsquaredresid629.3818criterion6.291723Loglikelihood-90.65373Hannan-Quinn6.167008criter.Durbin-WatsonF-statistic20.21624stat1.150090Prob(F-statistic)0.000000Y=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.X20.1354740.01279910.584540.0000X318.853489.7761811.9285120.0729C-18231.588638.216-2.1105730.0520MeandependentR-squared0.985838var6619.191

S.D.dependentAdjustedR-squared0.983950varAkaikeinfo5767.152S.E.ofregression730.6306criterionSchwarz16.17670Sumsquaredresid8007316.criterionHannan-Quinn16.32510Loglikelihood-142.5903criter.Durbin-Watson16.19717F-statistic522.0976stat1.173432Prob(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F检验，F=522.0976>F(2,15)=4.77,回归方程显著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.LNX21.5642210.08898817.577890.0000LNX31.7606950.6821152.5812290.0209C-20.520485.432487-3.7773630.0018MeandependentR-squared0.986295varS.D.dependent8.400112AdjustedR-squared0.984467varAkaikeinfo0.941530S.E.ofregression0.117343criterionSchwarz-1.296424Sumsquaredresid0.206540criterionHannan-Quinn-1.148029Loglikelihood14.66782criter.-1.275962Durbin-WatsonF-statistic539.7364stat0.686656Prob(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由Eviews分析结果如(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DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:09:03Sample:118Includedobservations:18

CoefficienStd.Errort-StatisticProb.VariabletX0.0864500.0293632.9441860.0101T52.370315.20216710.067020.0000C-50.0163849.46026-1.0112440.3279MeandependentR-squared0.951235varS.D.dependent755.1222AdjustedR-squared0.944732varAkaikeinfo258.7206S.E.ofregression60.82273criterionSchwarz11.20482Sumsquaredresid55491.07criterionHannan-Quinn11.35321Loglikelihood-97.84334criter.Durbin-Watson11.22528F-statistic146.2974stat2.605783Prob(F-statistic)0.000000①模型为：Y=0.086450X+52.37031T-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。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:18VariabletStd.Errort-StatisticProb.T63.016764.54858113.854160.0000C-11.5817158.02290-0.1996060.8443

MeandependentR-squared0.923054varS.D.dependent755.1222AdjustedR-squared0.918245varAkaikeinfo258.7206S.E.ofregression73.97565criterionSchwarz11.54979Sumsquaredresid87558.36criterionHannan-Quinn11.64872Loglikelihood-101.9481criter.Durbin-Watson11.56343F-statisticProb(F-statistic)191.9377stat0.0000002.134043DependentVariable:XMethod:LeastSquaresDate:12/24/15Time:09:34Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.T123.151631.841503.8676440.0014C444.5888406.17861.0945650.2899MeandependentR-squared0.483182varS.D.dependent1942.933AdjustedR-squared0.450881varAkaikeinfo698.8325S.E.ofregression517.8529criterionSchwarz15.44170Sumsquaredresid4290746.criterionHannan-Quinn15.54063Loglikelihood-136.9753criter.Durbin-Watson15.45534F-statistic14.95867stat1.052251Prob(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:E1Method:LeastSquaresDate:12/24/15Time:09:39Sample:118Includedobservations:18CoefficienStd.Errort-StatisticProb.VariabletE20.0864500.0284313.0407420.0078C3.96E-1413.880832.85E-151.0000MeandependentR-squared0.366239varS.D.dependent2.30E-14AdjustedR-squared0.326629varAkaikeinfo71.76693S.E.ofregression58.89136criterionSchwarz11.09370Sumsquaredresid55491.07criterionHannan-Quinn11.19264Loglikelihood-97.84334criter.Durbin-Watson11.10735F-statisticProb(F-statistic)9.246111stat0.0077882.605783模型为：Ei=0.086450E2+3.96e-14参数：斜率系数a为0.086450,截距为3.96e-14样的,(3)由上可知，32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样的,3.6(1)预期的符号是Xi,X2,X3,X4,X5的符号为正，线的符号为负(2)根据Eviews分析得到数据如下：DependentVariable:丫Method:LeastSquaresDate:12/24/15Time:10:13Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X20.0013820.0011021.2543300.2336X30.0019420.0039600.4905010.6326X4-3.5790903.559949-1.0053770.3346X50.0047910.0050340.9516710.3600X60.0455420.0955520.4766210.6422C-13.7773215.73366-0.8756590.3984MeandependentR-squared0.994869varS.D.dependent12.76667AdjustedR-squared0.992731var9.746631S.E.ofregression0.830963Akaikeinfo2.728738

SumsquaredresidLoglikelihoodF-statisticProb(F-statistic)criterionSchwarzSumsquaredresidLoglikelihoodF-statisticProb(F-statistic)Hannan-Quinn-18.55865criter.2.769662Durbin-Watson465.3617stat1.5532940.000000①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。F检验，F=465.3617>F(5.12)=3,89,回归方程显著T检验，X,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:18VariableCoefficientProb.Std.Errort-StatisticX50.0010322.20E-0546.799460.0000X6-0.0549650.031184-1.7625810.0983C4.2054813.3356021.2607860.2266R-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。F检验，F=1164.567>F(5.12)=3,89,回归方程显著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:27CoefficienStd.Errort-StatisticProb.VariabletLNGDP1.3385330.08861015.105820.0000LNCPI-0.4217910.233295-1.8079750.0832C-3.1114860.463010-6.7201260.0000MeandependentR-squared0.988051var9.484710

S.D.dependentAdjustedR-squared0.987055varAkaikeinfo1.425517S.E.ofregression0.162189criterionSchwarz-0.695670Sumsquaredresid0.631326criterionHannan-Quinn-0.551689Loglikelihood12.39155criter.Durbin-Watson-0.652857F-statistic992.2582stat0.522613Prob(F-statistic)0.000000得到的模型方程为：LNY=1.338533LNGDP-0.421791LNCPIt-3.111486⑵①该模型的可决系数为0.988051,可决系数很高，F检验彳1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：LNYLNGDPLNCPILNY1.0000000.9931890.935116LNGDP0.9931891.0000000.953740LNCPI0.9351160.9537401.000000LNGDPLNCPI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.LNGDP1.1857390.02782242.619330.0000

C-3.7506700.312255-12.011560.0000MeandependentR-squared0.986423varS.D.dependent9.484710AdjustedR-squared0.985880varAkaikeinfo1.425517S.E.ofregression0.169389criterionSchwarz-0.642056Sumsquaredresid0.717312criterionHannan-Quinn-0.546068Loglikelihood10.66776criter.Durbin-Watson-0.613514F-statistic1816.407stat0.471111Prob(F-statistic)0.000000DependentVariable:LNYMethod:LeastSquaresDate:12/24/15Time:10:55Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNCPI2.9392950.22275613.195110.0000C-6.8545351.242243-5.5178710.0000MeandependentR-squared0.874442varS.D.dependent9.484710AdjustedR-squared0.869419varAkaikeinfo1.425517S.E.ofregression0.515124criterionSchwarz1.582368Sumsquaredresid6.633810criterionHannan-Quinn1.678356Loglikelihood-19.36196criter.Durbin-Watson1.610910F-statistic174.1108stat0.137042Prob(F-statistic)0.000000DependentVariable:LNGDPMethod:LeastSquares

Date:12/24/15Time:11:07Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNCPI2.5110220.15830215.862270.0000C-2.7963810.882798-3.1676340.0040MeandependentR-squared0.909621varS.D.dependent11.16214AdjustedR-squared0.906005varAkaikeinfo1.194029S.E.ofregression0.366072criterionSchwarz0.899213Sumsquaredresid3.350216criterionHannan-Quinn0.995201Loglikelihood-10.13938criter.Durbin-Watson0.927755F-statistic251.6117stat0.099623Prob(F-statistic)0.000000①得到的回归方程分别为LNY=1.185739LNGDR-3.750670LNY=2.939295LNCPIt-6.854535LNGDP2.511022LNCPIt-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，GD林口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.CZZC0.0901140.0443672.0311290.0540GDP-0.0253340.005069-4.9980360.0000SSZE1.1768940.06216218.932710.0000C-221.8540130.6532-1.6980380.1030MeandependentR-squared0.999857varS.D.dependent22572.56AdjustedR-squared0.999838varAkaikeinfo27739.49S.E.ofregression353.0540criterionSchwarz14.70707Sumsquaredresid2866884.criterionHannan-Quinn14.89905Loglikelihood-194.5455criter.14.76416Durbin-WatsonF-statistic53493.93stat1.458128Prob(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,模型拟合白很好。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：CZSRCZZCGDPSSZECZSR1.0000000.9987290.9928380.999832CZZC0.9987291.0000000.9925360.998575GDP0.9928380.9925361.0000000.994370SSZE0.9998320.9985750.9943701.000000由上表可知，CZZdGDPCZZCWSSZEGD*SSZ此间的相关系数都非常高，说明确实存在多重共线性。(3)做辅助回归被解释变量可决系数方差扩大因子CZZC0.997168353GDP0.98883390SSZE0.997862468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。1,000 1,5001,000 1,500 2,000 2,500 3,000 3,500 4,000X5.2(1)①用图形法检验绘制e2的散点图，用Eviews分析如下：30,00025,000_20,0002E15,00010,0005,0000-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:7CoefficienVariabletStd.Errort-StatisticProb.Variable35.206644.9014927.1828430.0020

XC0.10994977.125880.0619651.77438082.328440.9368070.15070.4019MeandependentR-squared0.943099varS.D.dependent565.6857AdjustedR-squared0.914649varAkaikeinfo108.2755S.E.ofregression31.63265criterionSchwarz10.04378Sumsquaredresid4002.499criterionHannan-Quinn10.02060Loglikelihood-32.15324criter.Durbin-Watson9.757267F-statistic33.14880stat1.426262Prob(F-statistic)0.003238得汇eii2=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:7CoefficienVariabletStd.Errort-StatisticProb.T52.405886.9233787.5694090.0016X0.0686890.0537631.2776350.2705C-8.78926579.92542-0.1099680.9177MeandependentR-squared0.984688varS.D.dependent887.6143AdjustedR-squared0.977032varAkaikeinfo274.4148S.E.ofregression41.58810criterionSchwarz10.59103Sumsquaredresid6918.280criterionHannan-Quinn10.56785Loglikelihood-34.06861criter.Durbin-Watson10.30451F-statistic128.6166stat2.390329Prob(F-statistic)0.000234得汇ez2=6918.2803)根据Goldfeld-Quanadt检验，F统计量为：F=Ee//三e/=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。5.3(1)由Eviews软件分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:16:00Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.X1.2442810.07903215.744110.0000C242.4488291.19400.8326020.4119MeandependentR-squared0.895260var4443.526S.D.dependentAdjustedR-squared0.891649var1972.072S.E.ofregression649.1426Akaikeinfo15.85152SumsquaredresidLoglikelihoodF-statisticProb(F-statistic)criterionSchwarz12220196criterionHannan-Quinn-243.6986criter.Durbin-Watson247.8769stat0.00000015.9440415.881681.078581由上表可知，2007年我国农村居民家庭人均消费支出（丫=1.244281X+242.4488x）对人均纯收入（v）的模型为:⑵①由图形法检验6,000,0005,000,0004,000,000一E3,000,0002,000,0001,000,000_002,0004,0006,0008,00010,000X由上图可知，模型可能存在异方差。②Goldfeld-Quanadt检验1)定义区间为1-12时，由软件分析得:DependentVariable:Y1Method:LeastSquaresDate:12/24/15Time:16:05Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.X11.4852960.5003862.9682970.0141C-550.54921220.063-0.4512470.6614MeandependentR-squared0.468390varS.D.dependent3052.950AdjustedR-squared0.415229varAkaikeinfo550.5148S.E.ofregression420.9803criterionSchwarz15.07406Sumsquaredresid1772245.criterionHannan-Quinn15.15488Loglikelihood-88.44437criter.Durbin-Watson15.04414F-statisticProb(F-statistic)8.810789stat0.0140872.354167得三而2=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:12CoefficienStd.Errort-StatisticProb.VariabletX11.0869400.1488637.3016230.0000C1173.307733.25201.6001410.1407MeandependentR-squared0.842056varS.D.dependent6188.329AdjustedR-squared0.826262varAkaikeinfo2133.692S.E.ofregression889.3633criterionSchwarz16.56990Sumsquaredresid7909670.criterionHannan-Quinn16.65072Loglikelihood-97.41940criter.Durbin-Watson16.53998F-statistic53.31370stat2.339767Prob(F-statistic)0.000026得汇ez2=7909670.3）根据Goldfeld-Quanadt检验，F统计量为:F=Ee2i2/三eii2=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Fo.o5(10,10)=2.98,因为F=4.4631>Fo.o5(10,10)=2.98,所以拒绝原假设，此检验表明模型存在异方差。1)采用WLSt估计过程中，①用权数w1=1/X,建立回归得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:16:29Sample:131Includedobservations:31Weightingseries:W1VariableCoefficientStd.Errort-StatisticProb.X1.4258590.11910411.971570.0000C-334.8131344.3523-0.9722980.3389WeightedStatisticsMeandependentR-squared0.831707varS.D.dependent3946.082AdjustedR-squared0.825904varAkaikeinfo536.1907S.E.ofregression536.6796criterionSchwarz15.47102Sumsquaredresid8352726.criterionHannan-Quinn15.56354Loglikelihood-237.8008criter.Durbin-Watson15.50118F-statistic143.3184stat1.369081Prob(F-statistic)0.000000UnweightedStatisticsMeandependentR-squared0.875855varS.D.dependent4443.526AdjustedR-squared0.871574varSumsquared1972.072S.E.ofregression706.7236resid14484289Durbin-Watsonstat1.532908对此模型进行White检验得:HeteroskedasticityTest:WhiteF-statistic0.299395Prob.F(2,28)Prob.0.7436Obs*R-squared0.649065Chi-Square(2)Prob.0.7229ScaledexplainedSS1.798067Chi-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*WGTA2282.4407747.97800.3776060.7086MeandependentR-squared0.020938var269442.8S.D.dependentAdjustedR-squared-0.048995var689166.5AkaikeinfoS.E.ofregression705847.6criterion29.86395Sumsquaredresid1.40E+13Schwarz30.00273

criterionHannan-QuinnLoglikelihoodF-statisticProb(F-statistic)-459.8913LoglikelihoodF-statisticProb(F-statistic)Durbin-Watson0.299395stat1.9223360.743610从上可知，nR2=0.649065,比较计算的*‘统计量的临界值，因为nR2=0.649065<f0.05(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=1/x2,用回归分析得:DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:16:40Sample:131Includedobservations:31Weightingseries:W2Coefficient-StatisticProb.VariabletStd.ErrorX1.5570400.14539210.709220.0000C-693.1946376.4760-1.8412720.0758WeightedStatisticsMeandependentR-squared0.798173varS.D.dependent3635.028AdjustedR-squared0.791214varAkaikeinfo1029.830S.E.ofregression466.8513criterion15.19224Sumsquaredresid6320554.Schwarz15.28475

LoglikelihoodF-statisticProb(F-statistic)-233.4797114.68750.000000criterioncriter.statHannan-QuinnDurbin-Watson15.222401.562975UnweightedStatisticsMeandependentR-squared0.834850varS.D.dependent4443.526AdjustedR-squared0.829156varSumsquared1972.072S.E.ofregression815.1229resid19268334Durbin-Watsonstat1.678365对此模型进行White检验得:HeteroskedasticityTest:WhiteF-statistic0.299790Prob.F(3,27)Prob.0.8252Obs*R-squared0.999322Chi-Square(3)Prob.0.8014ScaledexplainedSS1.789507Chi-Square(3)0.6172TestEquation:DependentVariable:WGT_RESIDA2Method:LeastSquares

Date: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*WGTA2-583.21512082.820-0.2800120.7816MeandependentR-squared0.032236varS.D.dependent203888.8AdjustedR-squared-0.075293varAkaikeinfo419282.0S.E.ofregression434780.1criterionSchwarz28.92298Sumsquaredresid5.10E+12criterion29.10801Hannan-QuinnLoglikelihood-444.3062criter.Durbin-Watson28.98330F-statistic0.299790stat1.835854Prob(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)2R=0.798173F=114.6875DW=1.562975③用权数w3=1/sqr(x)，用回归分析得:DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:16:49Sample:131

Includedobservations:31Weightingseries:W3VariableCoefficientStd.Errort-StatisticProb.X1.3301300.09834513.525070.0000C-47.40242313.1154-0.1513900.8807WeightedStatisticsMeandependentR-squared0.863161varS.D.dependent4164.118AdjustedR-squared0.858442varAkaikeinfo991.2079S.E.ofregression586.9555criterionSchwarz15.65012Sumsquaredresid9990985.criterionHannan-Quinn15.74263Loglikelihood-240.5768criter.Durbin-Watson15.68027F-statistic182.9276stat1.237664Prob(F-statistic)0.000000UnweightedStatisticsMeandependentR-squared0.890999varS.D.dependent4443.526AdjustedR-squared0.887240varSumsquared1972.072S.E.ofregression662.2171resid12717412Durbin-Watsonstat1.314859对此模型进行White检验得:HeteroskedasticityTest:WhiteF-statistic0.423886Prob.F(2,28)Prob.0.6586Obs*R-squared0.911022Chi-Square(2)Prob.0.6341ScaledexplainedSS2.768332Chi-Square(2)0.2505TestEquation:DependentVariable:WGT_RESIDA2Method:LeastSquaresDate:12/24/15Time:16:57Sample:131Includedobservations:31CollineartestregressorsdroppedfromspecificationVariableCoefficienProb.tStd.Errort-StatisticC1212308.2141958.0.5659810.5759WGTA2-715673.01301839.-0.5497400.5869XA2*WGTA2-0.0151940.082276-0.1846770.8548R-squaredMeandependent0.029388var322289.8AdjustedR-squaredS.D.dependent-0.039942var863356.7S.E.ofregressionAkaikeinfo880429.8criterion30.30597SumsquaredresidSchwarz2.17E+13criterion30.44475LoglikelihoodHannan-Quinn-466.7426criter.30.35121F-statisticDurbin-Watson0.423886stat1.887426Prob(F-statistic)0.65862822从上可知，nR2=0.911022,比较计算的*统计量的临界值，因为nR2=0.911022〈反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=1.330130X-47.40242t=(13.52507)(-0.151390)R2=0.863161F=182.9276DW=1.237664经过检验发现，用权数w1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=1.3690815.6⑴a)用Eviews模型分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:19:16Sample:19782011Includedobservations:34CoefficienStd.Errort-StatisticProb.VariabletX0.7462410.01912039.030270.0000C92.5542242.805292.1622150.0382MeandependentR-squared0.979426varS.D.dependent1295.802AdjustedR-squared0.978783varAkaikeinfo1188.791S.E.ofregression173.1597criterionSchwarz13.20333Sumsquaredresid959497.2criterionHannan-Quinn13.29311Loglikelihood-222.4566criter.Durbin-Watson13.23395F-statisticProb(F-statistic)1523.362stat0.0000001.534491得回归模型为：Y=0.746241X+92.55422b）检验是否存在异方差：

①用Goldfeld-Quanadt检验如下：1)当定义区间为1-13时，由软件分析得:DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:19:27Sample:113Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.X0.9678390.02687936.007710.0000C-18.868618.963780-2.1049840.0591Mean