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1、第二章简单线性回归模型2.1Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001R-squared0.526082Meandependentvar62.50000AdjustedR-squared0.502386S.D.dependentvar10.08889S.E.ofregression7.116881Akaikeinfocriterion6.849324Sumsquaredresid
2、1013.000Schwarzcriterion6.948510Loglikelihood-73.34257Hannan-Quinncriter.6.872689F-statistic22.20138Durbin-Watsonstat0.629074Prob(F-statistic)0.000134有上可知,关系式为y=56.64794+0.128360 x1关于人均寿命与成人识字率的关系,用Eviews分析如下:DependentVariable:YMethod:LeastSquaresDate:11/26/14Time:21:10Sample:122Includedobservations
3、:22VariableCoefficientStd.Errort-StatisticProb.C38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825Meandependentvar62.50000AdjustedR-squared0.702666S.D.dependentvar10.08889S.E.ofregression5.501306Akaikeinfocriterion6.334356Sumsquaredresid605.2873Schwarzcriterion6.433542Lo
4、glikelihood-67.67792Hannan-Quinncriter.6.357721F-statistic50.62761Durbin-Watsonstat1.846406Prob(F-statistic)0.000001由上可知,关系式为y=38.79424+0.331971x2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:DependentVariable:YMethod:LeastSquaresDate:11/26/14Time:21:14Sample:122Includedobservations:22VariableCoefficientStd.Error
5、t-StatisticProb.C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001R-squared0.537929Meandependentvar62.50000AdjustedR-squared0.514825S.D.dependentvar10.08889S.E.ofregression7.027364Akaikeinfocriterion6.824009Sumsquaredresid987.6770Schwarzcriterion6.923194Loglikelihood-73.06409Hannan-Quin
6、ncriter.6.847374F-statistic23.28338Durbin-Watsonstat0.952555Prob(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(B丿=4.711834t0025(20)=2.086,对斜率系数的显著性检验表明,人均GDP对人均寿命有显著影响。关于人均寿命与成人识字率模型,由上可知,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
7、的t检验:t(B2)=7.115308t0025(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(B3)=4.825285t0025(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。对于浙江省预算收入与全省生产总值的模型,用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:12/03/1
8、4Time:17:00Sample(adjusted):1332.2(1)Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.X0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004R-squared0.983702Meandependentvar902.5148AdjustedR-squared0.983177S.D.dependentvar1351.009S.E.ofregression175.2325Ak
9、aikeinfocriterion13.22880Sumsquaredresid951899.7Schwarzcriterion13.31949Loglikelihood-216.2751Hannan-Quinncriter.13.25931F-statistic1871.115Durbin-Watsonstat0.100021Prob(F-statistic)0.000000由上可知,模型的参数:斜率系数0.176124,截距为一154.3063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
10、的t检验:t(B2)=43.25639t002(31)=2.0395,对斜率系数的显著性检验表明,全省生产总值对财政预算总收入有显著影响。用规范形式写出检验结果如下:Y=0.176124X154.3063(0.004072)(39.08196)t=(43.25639)(-3.948274)R2=0.983702F=1871.115n=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:
11、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,5x2=5(X
12、X)2=62x(n-1)=7608.0212x(33-1)=1852223.473(XfX)2=(320006000.441)2=675977068.2当Xf=32000时,将相关数据代入计算得到:5481.6617-2.0395x175.2325xV1/33+1852223.473/675977068.2WYfW5481.6617+2.0395x175.2325xV1/33+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:
13、DependentVariable:LNYMethod:LeastSquaresDate:12/03/14Time:18:00Sample(adjusted):133Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.LNX0.9802750.03429628.582680.0000C-1.9182890.268213-7.1521210.0000R-squared0.963442Meandependentvar5.573120AdjustedR-squared0.962263S.
14、D.dependentvar1.684189S.E.ofregression0.327172Akaikeinfocriterion0.662028Sumsquaredresid3.318281Schwarzcriterion0.752726Loglikelihood-8.923468Hannan-Quinncriter.0.692545F-statistic816.9699Durbin-Watsonstat0.096208Prob(F-statistic)0.000000模型方程为:lnY=0.980275lnX-1.918289由上可知,模型的参数:斜率系数为0.980275,截距为-1.9
15、18289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(码)=28.58268t0025(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%(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:12/01/14Time:12:40Sample:1122.4Includedobser
16、vations:12VariableCoefficientStd.Errort-StatisticProb.X-64.184004.809828-13.344340.0000C1845.47519.2644695.796880.0000R-squared0.946829Meandependentvar1619.333AdjustedR-squared0.941512S.D.dependentvar131.2252S.E.ofregression31.73600Akaikeinfocriterion9.903792Sumsquaredresid10071.74Schwarzcriterion9.
17、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)首先进行点预测,由Y=1845.475-64.18400X得,当x=4.5,y=1556.647再进行区间估计用Eviews分析:YXMean1619.3333.523333Med
18、ian1630.0003.715000Maximum1860.0006.230000Minimum1419.0000.600000Std.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,5x2=5(XX)2=62x(n-1)=1.9894192x(12-1)=43.5
19、357(XfX)2=(4.53.523333)2=0.95387843当Xf=4.5时,将相关数据代入计算得到:1556.647-2.228x31.73600 xV1/12+43.5357/0.95387843WYfG556.647+2.228x31.73600 xV1/12+43.5357/0.95387843即Yf的置信区间为(1556.647-478.1231,1556.647+478.1231)对百户拥有家用汽车量计量经济模型,用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:11/25
20、/14Time:12:38Sample:1313.1(1)Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.X25.9968651.4060584.2650200.0002X3-0.5240270.179280-2.9229500.0069X4-2.2656800.518837-4.3668420.0002C246.854051.975004.7494760.0001R-squared0.666062Meandependentvar16.77355AdjustedR-squared0.628957S.D.dep
21、endentvar8.252535S.E.ofregression5.026889Akaikeinfocriterion6.187394Sumsquaredresid682.2795Schwarzcriterion6.372424Loglikelihood-91.90460Hannan-Quinncriter.6.247709F-statistic17.95108Durbin-Watsonstat1.147253Prob(F-statistic)0.000001得到模型得:Y=246.8540+5.996865X2-0.524027X3-2.265680X4对模型进行检验:可决系数是0.666
22、062,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=17.95108F(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。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5.9
23、96865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:12/08/14Time:17:28Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.X25.1356701.0102705.0834650.0000LNX3-22.810056.771820-3.3683780.0023LNX4
24、-230.848149.46791-4.6666240.0001C1148.758228.29175.0319740.0000R-squared0.691952Meandependentvar16.77355AdjustedR-squared0.657725S.D.dependentvar8.252535S.E.ofregression4.828088Akaikeinfocriterion6.106692Sumsquaredresid629.3818Schwarzcriterion6.291723Loglikelihood-90.65373Hannan-Quinncriter.6.167008
25、F-statistic20.21624Durbin-Watsonstat1.150090Prob(F-statistic)0.000000模型方程为:Y=5.135670X-22.81005LNX-230.8481LNX+1148.758234此分析得出的可决系数为0.6919520.666062,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::DependentVariable:YMethod:LeastSquaresDate:12/01/14Time:20:25Sample:19942011Includedobservations:18Var
26、iableCoefficientStd.Errort-StatisticProb.X20.1354740.01279910.584540.0000X318.853489.7761811.9285120.0729C-18231.588638.216-2.1105730.0520R-squared0.985838Meandependentvar6619.191AdjustedR-squared0.983950S.D.dependentvar5767.152S.E.ofregression730.6306Akaikeinfocriterion16.17670Sumsquaredresid800731
27、6.Schwarzcriterion16.32510Loglikelihood-142.5903Hannan-Quinncriter.16.19717F-statistic522.0976Durbin-Watsonstat1.173432Prob(F-statistic)0.000000由上可知,模型为:Y=0.135474X2+18.85348X3-18231.5823对模型进行检验:1)可决系数是0.985838,修正的可决系数为0.983950,说明模型对样本拟合较好2)F检验,F=522.0976F(2,15)=4.77,回归方程显著3)t检验,t统计量分别为X2的系数对应t值为10.
28、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。对于对数模型,用Eviews分析结果如下DependentVariable:LNYMethod:LeastSquaresDate:12/01/14Time:20:25Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.LNX21.5642210.08898817.577890.0000LNX31.7606950.6821152.5812290.
29、0209C-20.520485.432487-3.7773630.0018R-squared0.986295Meandependentvar8.400112AdjustedR-squared0.984467S.D.dependentvar0.941530S.E.ofregression0.117343S.E.ofregression0.117343Sumsquaredresid0.206540Loglikelihood14.66782F-statistic539.7364Prob(F-statistic)0.000000Akaikeinfocriterion-1.296424Schwarzcr
30、iterion-1.148029Hannan-Quinncriter.-1.275962Durbin-Watsonstat0.686656由上可知,模型为:LNY=-20.52048+1.564221LNX2+1.760695LNX323对模型进行检验: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=539.7364F(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。(3)(1)式中的经济意义:工业增加1亿元,出口货物总额增加
31、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:12/01/14Time:20:30Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X0.0864
32、500.0293632.9441860.0101T52.370315.20216710.067020.0000C-50.0163849.46026-1.0112440.3279R-squared0.951235Meandependentvar755.1222AdjustedR-squared0.944732S.D.dependentvar258.7206S.E.ofregression60.82273Akaikeinfocriterion11.20482Sumsquaredresid55491.07Schwarzcriterion11.35321Loglikelihood-97.84334Ha
33、nnan-Quinncriter.11.22528F-statistic146.2974Durbin-Watsonstat2.605783Prob(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0.944732,说明模型对样本拟合较好。2)F检验,F=539.7364F(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
34、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:DependentVariable:YMethod:LeastSquaresDate:12/01/14Time:22:30Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.T63.016764.54858113.854160.0000C-11.5817158.02290-0.1996060.8443R-squared0.923054Meandependentvar755.12
35、22AdjustedR-squared0.918245S.D.dependentvar258.7206S.E.ofregression73.97565Akaikeinfocriterion11.54979Sumsquaredresid87558.36Schwarzcriterion11.64872Loglikelihood-101.9481Hannan-Quinncriter.11.56343F-statistic191.9377Durbin-Watsonstat2.134043Prob(F-statistic)0.000000DependentVariable:XMethod:LeastSq
36、uaresDate:12/01/14Time:22:34Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.T123.151631.841503.8676440.0014C444.5888406.17861.0945650.2899R-squared0.483182Meandependentvar1942.933AdjustedR-squared0.450881S.D.dependentvar698.8325S.E.ofregression517.8529Akaikeinfocriterion
37、15.44170Sumsquaredresid4290746.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对残差进行模型分析,用Eviews分析结果如下:DependentVariable:E1Method:LeastSquaresD
38、ate:12/03/14Time:20:39Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.E20.0864500.0284313.0407420.0078C3.96E-1413.880832.85E-151.0000R-squared0.366239Meandependentvar2.30E-14AdjustedR-squared0.326629S.D.dependentvar71.76693S.E.ofregression58.89136Akaikeinfocriterion11.09
39、370Sumsquaredresid55491.07Schwarzcriterion11.19264Loglikelihood-97.84334Hannan-Quinncriter.11.10735F-statistic9.246111Durbin-Watsonstat2.605783Prob(F-statistic)0.007788模型为:E1=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X,X2,X3,X4,X
40、5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:12/04/14Time:13:24Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X20.0013820.0011021.2543300.2336X30.0019420.0039600.4905010.6326X4-3.5790903.559949-1.0053770.3346X50.0047910.0050340.95167
41、10.3600X60.0455420.0955520.4766210.6422C-13.7773215.73366-0.8756590.3984R-squared0.994869Meandependentvar12.76667AdjustedR-squared0.992731S.D.dependentvar9.746631S.E.ofregression0.830963Akaikeinfocriterion2.728738Sumsquaredresid8.285993Schwarzcriterion3.025529Loglikelihood-18.55865Hannan-Quinncriter
42、.2.769662F-statistic465.3617Durbin-Watsonstat1.553294Prob(F-statistic)0.000000与预期不相符。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=465.3617F(5.12)=3,89,回归方程显著3)T检验,X,X,X,X,XXc系数对应的t值分别为:1.254330,0.490501,-1.005377,12345,60.951671,0.476621,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:Y
43、Method:LeastSquaresDate:12/03/14Time:11:12Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X50.0010322.20E-0546.799460.0000X6-0.0549650.031184-1.7625810.0983C4.2054813.3356021.2607860.226666R-squared0.993601Meandependentvar12.76667AdjustedR-squared0.992748S.D.depende
44、ntvar9.746631S.E.ofregression0.830018Akaikeinfocriterion2.616274Sumsquaredresid10.33396Schwarzcriterion2.764669Loglikelihood-20.54646Hannan-Quinncriter.2.636736F-statistic1164.567Durbin-Watsonstat1.341880Prob(F-statistic)0.000000得到模型的方程为:Y=0.001032X5-0.054965X6+4.20548156评价:1)可决系数为0.993601,数据相当大,可以认
45、为拟合程度很好。F检验,F=1164.567F(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。X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。VariableCoefficientStd.Errort-StatisticProb.VariableCoefficientStd.Errort-StatisticProb.4.3(1)根据Eviews分析得到数据如下DependentVariable:LNYMethod:LeastSquaresD
46、ate:12/05/14Time:11:39Sample: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
47、.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)该模型的可决系数为0.988051,可决系数很高,F检验值
48、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。得到相关系数矩阵如下:LNYLNGDPLNCPILNY1.0000000.9931890.935116LNGDP0.9931891.0000000.953740LNCPI0.9351160.9537401.000000LNGDP,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:12/03/14Time:14:41Sample:19852011Include
49、dobservations:27LNGDP1.1857390.02782242.619330.0000C-3.7506700.312255-12.011560.0000R-squared0.986423Meandependentvar9.484710AdjustedR-squared0.985880S.D.dependentvar1.425517S.E.ofregression0.169389Akaikeinfocriterion-0.642056Sumsquaredresid0.717312Schwarzcriterion-0.546068Loglikelihood10.66776Hanna
50、n-Quinncriter.-0.613514F-statistic1816.407Durbin-Watsonstat0.471111Prob(F-statistic)0.000000b)DependentVariable:LNYMethod:LeastSquaresDate:12/03/14Time:14:41Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNCPI2.9392950.22275613.195110.0000C-6.8545351.242243-5.51787
51、10.0000R-squared0.874442Meandependentvar9.484710AdjustedR-squared0.869419S.D.dependentvar1.425517S.E.ofregression0.515124Akaikeinfocriterion1.582368Sumsquaredresid6.633810Schwarzcriterion1.678356Loglikelihood-19.36196Hannan-Quinncriter.1.610910F-statistic174.1108Durbin-Watsonstat0.137042Prob(F-stati
52、stic)0.000000c)DependentVariable:LNGDPMethod:LeastSquaresDate:12/05/14Time:11:11Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNCPI2.5110220.15830215.862270.0000C-2.7963810.882798-3.1676340.0040R-squared0.909621Meandependentvar11.16214AdjustedR-squared0.906005S.D.
53、dependentvar1.194029S.E.ofregression0.366072Akaikeinfocriterion0.899213Sumsquaredresid3.350216Schwarzcriterion0.995201Loglikelihood-10.13938Hannan-Quinncriter.0.927755F-statistic251.6117Durbin-Watsonstat0.099623Prob(F-statistic)0.000000得到的回归方程分别为LNY=1.185739LNGDPt-3.750670LNY=2.939295LNCPIt-6.854535
54、LNGDP2.511022LNCPI-2.796381t=t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:12/03/14Time:11:40Sample:19852011Includedobservations:2
55、7VariableCoefficientStd.Errort-StatisticProb.CZZC0.0901140.0443672.0311290.0540GDP-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.ofregression353.0540Akaik
56、einfocriterion14.70707Sumsquaredresid2866884.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
57、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,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CZZC0.9
58、97168353GDP0.98883390SSZE0.997862468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)用图形法检验绘制e2的散点图,用Eviews分析如下:30,000-25,000-20,000-15,000-10,000-5,000-1,0001,5002,0002,5003,0003,5004,000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DependentVariabl
59、e:YMethod:LeastSquaresDate:12/10/14Time:14:52Sample:17Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.T35.206644.9014927.1828430.0020X0.1099490.0619651.7743800.1507C77.1258882.328440.9368070.4019R-squared0.943099Meandependentvar565.6857AdjustedR-squared0.914649S.D.dependentvar108.2
60、755S.E.ofregression31.63265Akaikeinfocriterion10.04378Sumsquaredresid4002.499Schwarzcriterion10.02060Loglikelihood-32.15324Hannan-Quinncriter.9.757267F-statistic33.14880Durbin-Watsonstat1.426262Prob(F-statistic)0.003238得工e=4002.4992)定义区间为12-18时,由软件分析得:DependentVariable:YMethod:LeastSquaresDate:12/10
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