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:Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.

C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001R-squared0.526082

Meandependentvar62.50000AdjustedR-squared0.502386

S.D.dependentvar10.08889S.E.ofregression7.116881

Akaikeinfocriterion6.849324Sumsquaredresid1013.000

Schwarzcriterion6.948510Loglikelihood-73.34257

Hannan-Quinncriter.6.872689F-statistic22.20138

Durbin-Watsonstat0.629074Prob(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:LeastSquaresProb(F-statistic)0.000103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（β1）=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（β2）=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（β3）=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/Sample(adjusted):133Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.

X0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004R-squared0.983702

Meandependentvar902.5148AdjustedR-squared0.983177

S.D.dependentvar1351.009S.E.ofregression175.2325

Akaikeinfocriterion13.22880Sumsquaredresid951899.7

Schwarzcriterion13.31949Loglikelihood-216.2751

Hannan-Quinncriter.13.25931F-statistic1871.115

Durbin-Watsonstat0.100021Prob(F-statistic)0.000000②由上可知，模型的参数：斜率系数0.176124，截距为—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（β2）=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：XY

Mean

6000.441

902.5148

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

Probability

0.001755

0.000087

Sum

198014.5

29782.99

SumSq.Dev.

1.85E+09

58407195

Observations

33

33由上表可知，∑x2=∑（Xi—X）2=δ2x(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≤Yf≤5481.6617+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:12/23/1Sample(adjusted):133Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.

LNX0.9802750.03429628.582680.0000C-1.9182890.268213-7.1521210.0000R-squared0.963442

Meandependentvar5.573120AdjustedR-squared0.962263

S.D.dependentvar1.684189S.E.ofregression0.327172

Akaikeinfocriterion0.662028Sumsquaredresid3.318281

Schwarzcriterion0.752726Loglikelihood-8.923468

Hannan-Quinncriter.0.692545F-statistic816.9699

Durbin-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（β2）=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:Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.

X-64.184004.809828-13.344340.0000C1845.47519.2644695.796880.0000R-squared0.946829

Meandependentvar1619.333AdjustedR-squared0.941512

S.D.dependentvar131.2252S.E.ofregression31.73600

Akaikeinfocriterion9.903792Sumsquaredresid10071.74

Schwarzcriterion9.984610Loglikelihood-57.42275

Hannan-Quinncriter.9.873871F-statistic178.0715

Durbin-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：用Eviews分析：YX

Mean

1619.333

3.523333

Median

1630.000

3.715000

Maximum

1860.000

6.230000

Minimum

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

SumSq.Dev.

189420.7

43.53567

Observations

12

12由上表可知，∑x2=∑（Xi—X）2=δ2x(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≤Yf≤1556.647+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）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:12/23/1Sample:131Includedobservations: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

Meandependentvar16.77355AdjustedR-squared0.628957

S.D.dependentvar8.252535S.E.ofregression5.026889

Akaikeinfocriterion6.187394Sumsquaredresid682.2795

Schwarzcriterion6.372424Loglikelihood-91.90460

Hannan-Quinncriter.6.247709F-statistic17.95108

Durbin-Watsonstat1.147253Prob(F-statistic)0.000001

②得到模型得：Y=246.8540+5.996865X2-0.524027X3-2.265680X4③对模型进行检验：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。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：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:Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.

X25.1356701.0102705.0834650.0000LNX3-22.810056.771820-3.3683780.0023LNX4-230.848149.46791-4.6666240.0001C1148.758228.29175.0319740.0000R-squared0.691952

Meandependentvar16.77355AdjustedR-squared0.657725

S.D.dependentvar8.252535S.E.ofregression4.828088

Akaikeinfocriterion6.106692Sumsquaredresid629.3818

Schwarzcriterion6.291723Loglikelihood-90.65373

Hannan-Quinncriter.6.167008F-statistic20.21624

Durbin-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:Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

X20.1354740.01279910.584540.0000X318.853489.7761811.9285120.0729C-18231.588638.216-2.1105730.0520R-squared0.985838

Meandependentvar6619.191AdjustedR-squared0.983950

S.D.dependentvar5767.152S.E.ofregression730.6306

Akaikeinfocriterion16.17670Sumsquaredresid8007316.

Schwarzcriterion16.32510Loglikelihood-142.5903

Hannan-Quinncriter.16.19717F-statistic522.0976

Durbin-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:12/24/15Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

LNX21.5642210.08898817.577890.0000LNX31.7606950.6821152.5812290.0209C-20.520485.432487-3.7773630.0018R-squared0.986295

Meandependentvar8.400112AdjustedR-squared0.984467

S.D.dependentvar0.941530S.E.ofregression0.117343

Akaikeinfocriterion-1.296424Sumsquaredresid0.206540

Schwarzcriterion-1.148029Loglikelihood14.66782

Hannan-Quinncriter.-1.275962F-statistic539.7364

Durbin-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。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（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:Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

X0.0864500.0293632.9441860.0101T52.370315.20216710.067020.0000C-50.0163849.46026-1.0112440.3279R-squared0.951235

Meandependentvar755.1222AdjustedR-squared0.944732

S.D.dependentvar258.7206S.E.ofregression60.82273

Akaikeinfocriterion11.20482Sumsquaredresid55491.07

Schwarzcriterion11.35321Loglikelihood-97.84334

Hannan-Quinncriter.11.22528F-statistic146.2974

Durbin-Watsonstat2.605783Prob(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。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:Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

T63.016764.54858113.854160.0000C-11.5817158.02290-0.1996060.8443R-squared0.923054

Meandependentvar755.1222AdjustedR-squared0.918245

S.D.dependentvar258.7206S.E.ofregression73.97565

Akaikeinfocriterion11.54979Sumsquaredresid87558.36

Schwarzcriterion11.64872Loglikelihood-101.9481

Hannan-Quinncriter.11.56343F-statistic191.9377

Durbin-Watsonstat2.134043Prob(F-statistic)0.000000②DependentVariable:XMethod:LeastSquaresDate:12/24/15Time:Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

T123.151631.841503.8676440.0014C444.5888406.17861.0945650.2899R-squared0.483182

Meandependentvar1942.933AdjustedR-squared0.450881

S.D.dependentvar698.8325S.E.ofregression517.8529

Akaikeinfocriterion15.44170Sumsquaredresid4290746.

Schwarzcriterion15.54063Loglikelihood-136.9753

Hannan-Quinncriter.15.45534F-statistic14.95867

Durbin-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:E1Method:LeastSquaresDate:12/24/15Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

E20.0864500.0284313.0407420.0078C3.96E-1413.880832.85E-151.0000R-squared0.366239

Meandependentvar2.30E-14AdjustedR-squared0.326629

S.D.dependentvar71.76693S.E.ofregression58.89136

Akaikeinfocriterion11.09370Sumsquaredresid55491.07

Schwarzcriterion11.19264Loglikelihood-97.84334

Hannan-Quinncriter.11.10735F-statistic9.246111

Durbin-Watsonstat2.605783Prob(F-statistic)0.007788模型为：E1=0.086450E2+3.96e-14参数：斜率系数α为0.086450，截距为3.96e-14（3）由上可知，β2与α2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：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:Sample: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-13.7773215.73366-0.8756590.3984R-squared0.994869

Meandependentvar12.76667AdjustedR-squared0.992731

S.D.dependentvar9.746631S.E.ofregression0.830963

Akaikeinfocriterion2.728738Sumsquaredresid8.285993

Schwarzcriterion3.025529Loglikelihood-18.55865

Hannan-Quinncriter.2.769662F-statistic465.3617

Durbin-Watsonstat1.553294Prob(F-statistic)0.000000①与预期不相符。②评价：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，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：DependentVariable:YMethod:LeastSquaresDate:12/24/15Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

X50.0010322.20E-0546.799460.0000X6-0.0549650.031184-1.7625810.0983C4.2054813.3356021.2607860.2266R-squared0.993601

Meandependentvar12.76667AdjustedR-squared0.992748

S.D.dependentvar9.746631S.E.ofregression0.830018

Akaikeinfocriterion2.616274Sumsquaredresid10.33396

Schwarzcriterion2.764669Loglikelihood-20.54646

Hannan-Quinncriter.2.636736F-statistic1164.567

Durbin-Watsonstat1.341880Prob(F-statistic)0.000000①得到模型的方程为：Y=0.001032X5-0.054965X6+4.205481②评价：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:12/24/1Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.

LNGDP1.3385330.08861015.105820.0000LNCPI-0.4217910.233295-1.8079750.0832C-3.1114860.463010-6.7201260.0000R-squared0.988051

Meandependentvar9.484710AdjustedR-squared0.987055

S.D.dependentvar1.425517S.E.ofregression0.162189

Akaikeinfocriterion-0.695670Sumsquaredresid0.631326

Schwarzcriterion-0.551689Loglikelihood12.39155

Hannan-Quinncriter.-0.652857F-statistic992.2582

Durbin-Watsonstat0.522613Prob(F-statistic)0.000000得到的模型方程为：LNY=1.338533LNGDPt-0.421791LNCPIt-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α=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：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）DependentVariable:LNYMethod:LeastSquaresDate:12/24/15Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.

LNGDP1.1857390.02782242.619330.0000C-3.7506700.312255-12.011560.0000R-squared0.986423

Meandependentvar9.484710AdjustedR-squared0.985880

S.D.dependentvar1.425517S.E.ofregression0.169389

Akaikeinfocriterion-0.642056Sumsquaredresid0.717312

Schwarzcriterion-0.546068Loglikelihood10.66776

Hannan-Quinncriter.-0.613514F-statistic1816.407

Durbin-Watsonstat0.471111Prob(F-statistic)0.000000b)DependentVariable:LNYMethod:LeastSquaresDate:12/24/15Time:1Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.

LNCPI2.9392950.22275613.195110.0000C-6.8545351.242243-5.5178710.0000R-squared0.874442

Meandependentvar9.484710AdjustedR-squared0.869419

S.D.dependentvar1.425517S.E.ofregression0.515124

Akaikeinfocriterion1.582368Sumsquaredresid6.633810

Schwarzcriterion1.678356Loglikelihood-19.36196

Hannan-Quinncriter.1.610910F-statistic174.1108

Durbin-Watsonstat0.137042Prob(F-statistic)0.000000c)DependentVariable:LNGDPMethod:LeastSquaresDate:12/24/1Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.

LNCPI2.5110220.15830215.862270.0000C-2.7963810.882798-3.1676340.0040R-squared0.909621

Meandependentvar11.16214AdjustedR-squared0.906005

S.D.dependentvar1.194029S.E.ofregression0.366072

Akaikeinfocriterion0.899213Sumsquaredresid3.350216

Schwarzcriterion0.995201Loglikelihood-10.13938

Hannan-Quinncriter.0.927755F-statistic251.6117

Durbin-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:12/24/1Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.

CZZC0.0901140.0443672.0311290.0540GDP-0.0253340.005069-4.9980360.0000SSZE1.1768940.06216218.932710.0000C-221.8540130.6532-1.6980380.1030R-squared0.999857

Meandependentvar22572.56AdjustedR-squared0.999838

S.D.dependentvar27739.49S.E.ofregression353.0540

Akaikeinfocriterion14.70707Sumsquaredresid2866884.

Schwarzcriterion14.89905Loglikelihood-194.5455

Hannan-Quinncriter.14.76416F-statistic53493.93

Durbin-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α=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：CZSRCZZCGDPSSZECZSR

1.000000

0.998729

0.992838

0.999832CZZC

0.998729

1.000000

0.992536

0.998575GDP

0.992838

0.992536

1.000000

0.994370SSZE

0.999832

0.998575

0.994370

1.000000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。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，Goldfeld-Quanadt检验1）定义区间为1-7时，由软件分析得：DependentVariable:YMethod:LeastSquaresDate:12/24Sample:17Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.

T35.206644.9014927.1828430.0020X0.1099490.0619651.7743800.1507C77.1258882.328440.9368070.4019R-squared0.943099

Meandependentvar565.6857AdjustedR-squared0.914649

S.D.dependentvar108.2755S.E.ofregression31.63265

Akaikeinfocriterion10.04378Sumsquaredresid4002.499

Schwarzcriterion10.02060Loglikelihood-32.15324

Hannan-Quinncriter.9.757267F-statistic33.14880

Durbin-Watsonstat1.426262Prob(F-statistic)0.003238得∑e1i2=4002.4992）定义区间为12-18时，由软件分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:1Sample:1218Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.

T52.405886.9233787.5694090.0016X0.0686890.0537631.2776350.2705C-8.78926579.92542-0.1099680.9177R-squared0.984688

Meandependentvar887.6143AdjustedR-squared0.977032

S.D.dependentvar274.4148S.E.ofregression41.58810

Akaikeinfocriterion10.59103Sumsquaredresid6918.280

Schwarzcriterion10.56785Loglikelihood-34.06861

Hannan-Quinncriter.10.30451F-statistic128.6166

Durbin-Watsonstat2.390329Prob(F-statistic)0.000234得∑e2i2=6918.2803）根据Goldfeld-Quanadt检验，F统计量为：F=∑e2i2/∑e1i2=6918.280/4002.499=1.7285在α=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:12/24Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.

X1.2442810.07903215.744110.0000C242.4488291.19400.8326020.4119R-squared0.895260

Meandependentvar4443.526AdjustedR-squared0.891649

S.D.dependentvar1972.072S.E.ofregression649.1426

Akaikeinfocriterion15.85152Sumsquaredresid12220196

Schwarzcriterion15.94404Loglikelihood-243.6986

Hannan-Quinncriter.15.88168F-statistic247.8769

Durbin-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。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:Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.

X11.4852960.5003862.9682970.0141C-550.54921220.063-0.4512470.6614R-squared0.468390

Meandependentvar3052.950AdjustedR-squared0.415229

S.D.dependentvar550.5148S.E.ofregression420.9803

Akaikeinfocriterion15.07406Sumsquaredresid1772245.

Schwarzcriterion15.15488Loglikelihood-88.44437

Hannan-Quinncriter.15.04414F-statistic8.810789

Durbin-Watsonstat2.354167Prob(F-statistic)0.014087得∑e1i2=1772245.2）定义区间为20-31时，由软件分析得：DependentVariable:Y1Method:LeastSquaresDate:12/24/15Sample:2031Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.

X11.0869400.1488637.3016230.0000C1173.307733.25201.6001410.1407R-squared0.842056

Meandependentvar6188.329AdjustedR-squared0.826262

S.D.dependentvar2133.692S.E.ofregression889.3633

Akaikeinfocriterion16.56990Sumsquaredresid7909670.

Schwarzcriterion16.65072Loglikelihood-97.41940

Hannan-Quinncriter.16.53998F-statistic53.31370

Durbin-Watsonstat2.339767Prob(F-statistic)0.000026得∑e2i2=7909670.3）根据Goldfeld-Quanadt检验，F统计量为：F=∑e2i2/∑e1i2=7909670./1772245=4.4631在α=0.05水平下，分子分母的自由度均为10，查分布表得临界值F0.05（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w1=1/X,建立回归得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:1Sample:131Includedobservations:31Weightingseries:W1VariableCoefficientStd.Errort-StatisticProb.

X1.4258590.11910411.971570.0000C-334.8131344.3523-0.9722980.3389WeightedStatisticsR-squared0.831707

Meandependentvar3946.082AdjustedR-squared0.825904

S.D.dependentvar536.1907S.E.ofregression536.6796

Akaikeinfocriterion15.47102Sumsquaredresid8352726.

Schwarzcriterion15.56354Loglikelihood-237.8008

Hannan-Quinncriter.15.50118F-statistic143.3184

Durbin-Watsonstat1.369081Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.875855

Meandependentvar4443.526AdjustedR-squared0.871574

S.D.dependentvar1972.072S.E.ofregression706.7236

Sumsquaredresid14484289Durbin-Watsonstat1.532908

对此模型进行White检验得：HeteroskedasticityTest:WhiteF-statistic0.299395

Prob.F(2,28)0.7436Obs*R-squared0.649065

Prob.Chi-Square(2)0.7229ScaledexplainedSS1.798067

Prob.Chi-Square(2)0.4070TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:12/24/15Time:Sample:131Includedobservations:31CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticProb.

C61927.891045682.0.0592220.9532WGT^2-593927.91173622.-0.5060640.6168X*WGT^2282.4407747.97800.3776060.7086R-squared0.020938

Meandependentvar269442.8AdjustedR-squared-0.048995

S.D.dependentvar689166.5S.E.ofregression705847.6

Akaikeinfocriterion29.86395Sumsquaredresid1.40E+13

Schwarzcriterion30.00273Loglikelihood-459.8913

Hannan-Quinncriter.29.90919F-statistic0.299395

Durbin-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=1/x2,用回归分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:Sample:131Includedobservations:31Weightingseries:W2VariableCoefficientStd.Errort-StatisticProb.

X1.5570400.14539210.709220.0000C-693.1946376.4760-1.8412720.0758WeightedStatisticsR-squared0.798173

Meandependentvar3635.028AdjustedR-squared0.791214

S.D.dependentvar1029.830S.E.ofregression466.8513

Akaikeinfocriterion15.19224Sumsquaredresid6320554.

Schwarzcriterion15.28475Loglikelihood-233.4797

Hannan-Quinncriter.15.22240F-statistic114.6875

Durbin-Watsonstat1.562975Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.834850

Meandependentvar4443.526AdjustedR-squared0.829156

S.D.dependentvar1972.072S.E.ofregression815.1229

Sumsquaredresid19268334Durbin-Watsonstat1.678365

对此模型进行White检验得：HeteroskedasticityTest:WhiteF-statistic0.299790

Prob.F(3,27)0.8252Obs*R-squared0.999322

Prob.Chi-Square(3)0.8014ScaledexplainedSS1.789507

Prob.Chi-Square(3)0.6172TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:12/24/15Time:Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.

C-111661.8549855.7-0.2030750.8406WGT^2426220.22240181.0.1902620.8505X^2*WGT^20.1948880.5163950.3774020.7088X*WGT^2-583.21512082.820-0.2800120.7816R-squared0.032236

Meandependentvar203888.8AdjustedR-squared-0.075293

S.D.dependentvar419282.0S.E.ofregression434780.1

Akaikeinfocriterion28.92298Sumsquaredresid5.10E+12

Schwarzcriterion29.10801Loglikelihood-444.3062

Hannan-Quinncriter.28.98330F-statistic0.299790

Durbin-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=1/sqr（x）,用回归分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Time:Sample:131Includedobservations:31Weightingseries:W3VariableCoefficientStd.Errort-StatisticProb.

X1.3301300.09834513.525070.0000C-47.40242313.1154-0.1513900.8807WeightedStatisticsR-squared0.863161

Meandependentvar4164.118AdjustedR-squared0.858442

S.D.dependentvar991.2079S.E.ofregression586.9555

Akaikeinfocriterion15.65012Sumsquaredresid9990985.

Schwarzcriterion15.74263Loglikelihood-240.5768

Hannan-Quinncriter.15.68027F-statistic182.9276

Durbin-Watsonstat1.237664Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.890999

Meandependentvar4443.526AdjustedR-squared0.887240

S.D.dependentvar1972.072S.E.ofregression662.2171

Sumsquaredresid12717412Durbin-Watsonstat1.314859

对此模型进行White检验得：HeteroskedasticityTest:WhiteF-statistic0.423886

Prob.F(2,28)0.6586Obs*R-squared0.911022

Prob.Chi-Square(2)0.6341ScaledexplainedSS2.768332

Prob.Chi-Square(2)0.2505TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:12/24/15Time:Sample:131Includedobservations:31CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticProb.

C1212308.2141958.0.5659810.5759WGT^2-715673.01301839.-0.5497400.5869X^2*WGT^2-0.0151940.082276-0.1846770.8548R-squared0.029388

Meandependentvar322289.8AdjustedR-squared-0.039942

S.D.dependentvar863356.7S.E.ofregression880429.8

Akaikeinfocriterion30.30597Sumsquaredresid2.17E+13

Schwarzcriterion30.44475Loglikelihood-466.7426

Hannan-Quinncriter.30.35121F-statistic0.423886

Durbin-Watsonstat1.887426Prob(F-statistic)0.658628从上可知，nR2=0.911022，比较计算的统计量的临界值，因为nR2=0.911022<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=1.3690815.6(1)a)用Eviews模型分析得：DependentVariable:YMethod:LeastSquaresDate:12/24/15Sample:19782011Includedobservations:34VariableCoefficientStd.Errort-StatisticProb.

X0.7462410.01912039.030270.0000C92.5542242.805292.1622150.0382R-squared0.979426

Meandependentvar1295.802AdjustedR-squared0.978783

S.