第二章 简单线性回归模型[1]

1、 第二章 简单线性回归模型2.1（1） 首先分析人均寿命与人均GDP的数量关系，用Eviews分析：Dependent Variable: YMethod: Least SquaresDate: 12/27/14 Time: 21:00Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001R-squared0.526082Mean dependent var62

2、.50000Adjusted R-squared0.502386S.D. dependent var10.08889S.E. of regression7.116881Akaike info criterion6.849324Sum squared resid1013.000Schwarz criterion6.948510Log likelihood-73.34257Hannan-Quinn criter.6.872689F-statistic22.20138Durbin-Watson stat0.629074Prob(F-statistic)0.000134有上可知，关系式为y=56.64

3、794+0.128360 x1关于人均寿命与成人识字率的关系，用Eviews分析如下：Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 21:10Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.C38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825Mean dependent var62.50000A

4、djusted R-squared0.702666S.D. dependent var10.08889S.E. of regression5.501306Akaike info criterion6.334356Sum squared resid605.2873Schwarz criterion6.433542Log likelihood-67.67792Hannan-Quinn criter.6.357721F-statistic50.62761Durbin-Watson stat1.846406Prob(F-statistic)0.000001由上可知，关系式为y=38.79424+0.3

5、31971x2关于人均寿命与一岁儿童疫苗接种率的关系，用Eviews分析如下：Dependent Variable: YMethod: Least SquaresDate: 11/26/14 Time: 21:14Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001R-squared0.537929Mean dependent var62.50000Adjus

6、ted R-squared0.514825S.D. dependent var10.08889S.E. of regression7.027364Akaike info criterion6.824009Sum squared resid987.6770Schwarz criterion6.923194Log likelihood-73.06409Hannan-Quinn criter.6.847374F-statistic23.28338Durbin-Watson stat0.952555Prob(F-statistic)0.000103由上可知，关系式为y=31.79956+0.38727

7、6x3（2）关于人均寿命与人均GDP模型，由上可知，可决系数为0.526082，说明所建模型整体上对样本数据拟合较好。 对于回归系数的t检验：t（1）=4.711834t0.025(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。关于人均寿命与成人识字率模型，由上可知，可决系数为0.716825，说明所建模型整体上对样本数据拟合较好。对于回归系数的t检验：t（2）=7.115308t0.025(20)=2.086，对斜率系数的显著性检验表明，成人识字率对人均寿命有显著影响。关于人均寿命与一岁儿童疫苗的模型，由上可知，可决系数为0.537929，说明所建模型整体上

8、对样本数据拟合较好。 对于回归系数的t检验：t（3）=4.825285t0.025(20)=2.086，对斜率系数的显著性检验表明，一岁儿童疫苗接种率对人均寿命有显著影响。2.2（1）对于浙江省预算收入与全省生产总值的模型，用Eviews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/03/14 Time: 17:00Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariableCoefficientStd. Errort-Statistic

9、Prob.X0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004R-squared0.983702Mean dependent var902.5148Adjusted R-squared0.983177S.D. dependent var1351.009S.E. of regression175.2325Akaike info criterion13.22880Sum squared resid951899.7Schwarz criterion13.31949Log likelihood-216.2751Hannan-Q

10、uinn criter.13.25931F-statistic1871.115Durbin-Watson stat0.100021Prob(F-statistic)0.000000由上可知，模型的参数：斜率系数0.176124，截距为154.3063关于浙江省财政预算收入与全省生产总值的模型，检验模型的显著性：1）可决系数为0.983702，说明所建模型整体上对样本数据拟合较好。2）对于回归系数的t检验：t（2）=43.25639t0.025(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。用规范形式写出检验结果如下：Y=0.176124X154.30

11、63 (0.004072) (39.08196)t= (43.25639) （-3.948274）R2=0.983702 F=1871.115 n=33经济意义是：全省生产总值每增加1亿元，财政预算总收入增加0.176124亿元。（2）当x=32000时，进行点预测，由上可知Y=0.176124X154.3063，代入可得：Y= Y=0.176124*32000154.3063=5481.6617进行区间预测：先由Eviews分析：XYMean6000.441902.5148Median2689.280209.3900Maximum27722.314895.410Minimum123.7200

12、25.87000Std. Dev.7608.0211351.009Skewness1.4325191.663108Kurtosis4.0105154.590432Jarque-Bera12.6906818.69063Probability0.0017550.000087Sum198014.529782.99Sum Sq. Dev.1.85E+0958407195Observations3333由上表可知，x2=（XiX）2=2x(n1)= 7608.0212 x (331)=1852223.473(XfX)2=(320006000.441)2=675977068.2当Xf=32000时，将相关

13、数据代入计算得到：5481.66172.0395x175.2325x1/33+1852223.473/675977068.2Yf5481.6617+2.0395x175.2325x1/33+1852223.473/675977068.2即Yf的置信区间为（5481.661764.9649, 5481.6617+64.9649）(3) 对于浙江省预算收入对数与全省生产总值对数的模型，由Eviews分析结果如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/03/14 Time: 18:00Sample (adjusted): 1 33I

14、ncluded observations: 33 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.LNX0.9802750.03429628.582680.0000C-1.9182890.268213-7.1521210.0000R-squared0.963442Mean dependent var5.573120Adjusted R-squared0.962263S.D. dependent var1.684189S.E. of regression0.327172Akaike info criterion0.662

15、028Sum squared resid3.318281Schwarz criterion0.752726Log likelihood-8.923468Hannan-Quinn criter.0.692545F-statistic816.9699Durbin-Watson stat0.096208Prob(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-1.918289关于浙江省财政预算收入与全省生产总值的模型，检验其显著性：1）可决系数为0.963442，说明所建模型整体上对样本数据

16、拟合较好。2）对于回归系数的t检验：t（2）=28.58268t0.025(31)=2.0395，对斜率系数的显著性检验表明，全省生产总值对财政预算总收入有显著影响。经济意义：全省生产总值每增长1%，财政预算总收入增长0.980275%2.4（1）对建筑面积与建造单位成本模型，用Eviews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 12:40Sample: 1 12Included observations: 12VariableCoefficientStd. Errort-StatisticPr

17、ob.X-64.184004.809828-13.344340.0000C1845.47519.2644695.796880.0000R-squared0.946829Mean dependent var1619.333Adjusted R-squared0.941512S.D. dependent var131.2252S.E. of regression31.73600Akaike info criterion9.903792Sum squared resid10071.74Schwarz criterion9.984610Log likelihood-57.42275Hannan-Qui

18、nn criter.9.873871F-statistic178.0715Durbin-Watson stat1.172407Prob(F-statistic)0.000000由上可得：建筑面积与建造成本的回归方程为：Y=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：YXMean1619.3333.523333Median1630.0003.715000Maximum1860.000

19、6.230000Minimum1419.0000.600000Std. Dev.131.22521.989419Skewness0.003403-0.060130Kurtosis2.3465111.664917Jarque-Bera0.2135470.898454Probability0.8987290.638121Sum19432.0042.28000Sum Sq. Dev.189420.743.53567Observations1212由上表可知，x2=（XiX）2=2x(n1)= 1.9894192 x (121)=43.5357(XfX)2=(4.53.523333)2=0.95387

20、843当Xf=4.5时，将相关数据代入计算得到：1556.6472.228x31.73600 x1/12+43.5357/0.95387843Yf1556.647+2.228x31.73600 x1/12+43.5357/0.95387843即Yf的置信区间为（1556.647478.1231, 1556.647+478.1231）3.1（1）对百户拥有家用汽车量计量经济模型，用Eviews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 11/25/14 Time: 12:38Sample: 1 31Included observa

21、tions: 31VariableCoefficientStd. Errort-StatisticProb.X25.9968651.4060584.2650200.0002X3-0.5240270.179280-2.9229500.0069X4-2.2656800.518837-4.3668420.0002C246.854051.975004.7494760.0001R-squared0.666062Mean dependent var16.77355Adjusted R-squared0.628957S.D. dependent var8.252535S.E. of regression5.

22、026889Akaike info criterion6.187394Sum squared resid682.2795Schwarz criterion6.372424Log likelihood-91.90460Hannan-Quinn criter.6.247709F-statistic17.95108Durbin-Watson stat1.147253Prob(F-statistic)0.000001得到模型得：Y=246.8540+5.996865X2-0.524027 X3-2.265680 X4对模型进行检验：可决系数是0.666062，修正的可决系数为0.628957，说明模型

23、对样本拟合较好F检验，F=17.95108F（3,27）=3.65，回归方程显著。3）t检验，t统计量分别为4.749476，4.265020，-2.922950，-4.366842，均大于t（27）=2.0518，所以这些系数都是显著的。依据：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：人均增加万元，百户拥有家用汽车增加5.996865辆，城镇人口比重增加个百分点，百户拥有家用汽

24、车减少0.524027辆，交通工具消费价格指数每上升，百户拥有家用汽车减少2.265680辆。（3）用EViews分析得：Dependent Variable: YMethod: Least SquaresDate: 12/08/14 Time: 17:28Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.X25.1356701.0102705.0834650.0000LNX3-22.810056.771820-3.3683780.0023LNX4-230.848149.46791

25、-4.6666240.0001C1148.758228.29175.0319740.0000R-squared0.691952Mean dependent var16.77355Adjusted R-squared0.657725S.D. dependent var8.252535S.E. of regression4.828088Akaike info criterion6.106692Sum squared resid629.3818Schwarz criterion6.291723Log likelihood-90.65373Hannan-Quinn criter.6.167008F-s

26、tatistic20.21624Durbin-Watson stat1.150090Prob(F-statistic)0.000000模型方程为：Y=5.135670 X2-22.81005 LNX3-230.8481 LNX4+1148.758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：Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 20:25Sample: 1994 2011Included observ

27、ations: 18VariableCoefficientStd. Errort-StatisticProb.X20.1354740.01279910.584540.0000X318.853489.7761811.9285120.0729C-18231.588638.216-2.1105730.0520R-squared0.985838Mean dependent var6619.191Adjusted R-squared0.983950S.D. dependent var5767.152S.E. of regression730.6306Akaike info criterion16.176

28、70Sum squared resid8007316.Schwarz criterion16.32510Log likelihood-142.5903Hannan-Quinn criter.16.19717F-statistic522.0976Durbin-Watson stat1.173432Prob(F-statistic)0.000000由上可知，模型为：Y = 0.135474X2 + 18.85348X3 - 18231.58对模型进行检验：1）可决系数是0.985838，修正的可决系数为0.983950，说明模型对样本拟合较好2）F检验，F=522.0976F（2,15）=4.77

29、，回归方程显著3）t检验，t统计量分别为X2的系数对应t值为10.58454，大于t（15）=2.131，系数是显著的，X3的系数对应t值为1.928512，小于t（15）=2.131，说明此系数是不显著的。 （2）对于对数模型，用Eviews分析结果如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/01/14 Time: 20:25Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-StatisticProb.LNX21.5642210.

30、08898817.577890.0000LNX31.7606950.6821152.5812290.0209C-20.520485.432487-3.7773630.0018R-squared0.986295Mean dependent var8.400112Adjusted R-squared0.984467S.D. dependent var0.941530S.E. of regression0.117343Akaike info criterion-1.296424Sum squared resid0.206540Schwarz criterion-1.148029Log likelih

31、ood14.66782Hannan-Quinn criter.-1.275962F-statistic539.7364Durbin-Watson stat0.686656Prob(F-statistic)0.000000由上可知，模型为：LNY=-20.52048+1.564221 LNX2+1.760695 LNX3对模型进行检验：1）可决系数是0.986295，修正的可决系数为0.984467，说明模型对样本拟合较好。2）F检验，F=539.7364 F（2,15）=4.77，回归方程显著。3）t检验，t统计量分别为-3.777363，17.57789，2.581229，均大于t（15）=

32、2.131，所以这些系数都是显著的。（3）（1）式中的经济意义：工业增加1亿元，出口货物总额增加0.135474亿元，人民币汇率增加1，出口货物总额增加18.85348亿元。（2）式中的经济意义：工业增加额每增加1%，出口货物总额增加1.564221%，人民币汇率每增加1%，出口货物总额增加1.760695%3.3（1）对家庭书刊消费对家庭月平均收入和户主受教育年数计量模型，由Eviews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 20:30Sample: 1 18Included observat

33、ions: 18VariableCoefficientStd. Errort-StatisticProb.X0.0864500.0293632.9441860.0101T52.370315.20216710.067020.0000C-50.0163849.46026-1.0112440.3279R-squared0.951235Mean dependent var755.1222Adjusted R-squared0.944732S.D. dependent var258.7206S.E. of regression60.82273Akaike info criterion11.20482Su

34、m squared resid55491.07Schwarz criterion11.35321Log likelihood-97.84334Hannan-Quinn criter.11.22528F-statistic146.2974Durbin-Watson stat2.605783Prob(F-statistic)0.000000模型为：Y = 0.086450X + 52.37031T-50.01638对模型进行检验：1）可决系数是0.951235，修正的可决系数为0.944732，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

35、检验，t统计量分别为2.944186，10.06702，均大于t（15）=2.131，所以这些系数都是显著的。经济意义：家庭月平均收入增加1元，家庭书刊年消费支出增加0.086450元，户主受教育年数增加1年，家庭书刊年消费支出增加52.37031元。（2）用Eviews分析：Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 22:30Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.T63.016764.

36、54858113.854160.0000C-11.5817158.02290-0.1996060.8443R-squared0.923054Mean dependent var755.1222Adjusted R-squared0.918245S.D. dependent var258.7206S.E. of regression73.97565Akaike info criterion11.54979Sum squared resid87558.36Schwarz criterion11.64872Log likelihood-101.9481Hannan-Quinn criter.11.5

37、6343F-statistic191.9377Durbin-Watson stat2.134043Prob(F-statistic)0.000000Dependent Variable: XMethod: Least SquaresDate: 12/01/14 Time: 22:34Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.T123.151631.841503.8676440.0014C444.5888406.17861.0945650.2899R-squared0.483

38、182Mean dependent var1942.933Adjusted R-squared0.450881S.D. dependent var698.8325S.E. of regression517.8529Akaike info criterion15.44170Sum squared resid4290746.Schwarz criterion15.54063Log likelihood-136.9753Hannan-Quinn criter.15.45534F-statistic14.95867Durbin-Watson stat1.052251Prob(F-statistic)0

39、.001364以上分别是y与T，X与T的一元回归模型分别是：Y = 63.01676T - 11.58171X = 123.1516T + 444.5888（3）对残差进行模型分析，用Eviews分析结果如下：Dependent Variable: E1Method: Least SquaresDate: 12/03/14 Time: 20:39Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.E20.0864500.0284313.0407420.0078C3.96E-1413.

40、880832.85E-151.0000R-squared0.366239Mean dependent var2.30E-14Adjusted R-squared0.326629S.D. dependent var71.76693S.E. of regression58.89136Akaike info criterion11.09370Sum squared resid55491.07Schwarz criterion11.19264Log likelihood-97.84334Hannan-Quinn criter.11.10735F-statistic9.246111Durbin-Wats

41、on stat2.605783Prob(F-statistic)0.007788模型为：E1 = 0.086450E2 + 3.96e-14参数：斜率系数为0.086450，截距为3.96e-14（3）由上可知，2与2的系数是一样的。回归系数与被解释变量的残差系数是一样的，它们的变化规律是一致的。3.6（1）预期的符号是X1，X2,X3,X4,X5的符号为正，X6的符号为负（2）根据Eviews分析得到数据如下：Dependent Variable: YMethod: Least SquaresDate: 12/04/14 Time: 13:24Sample: 1994 2011Include

42、d observations: 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-squared0.994869Mean dependent var12.7666

43、7Adjusted R-squared0.992731S.D. dependent var9.746631S.E. of regression0.830963Akaike info criterion2.728738Sum squared resid8.285993Schwarz criterion3.025529Log likelihood-18.55865Hannan-Quinn criter.2.769662F-statistic465.3617Durbin-Watson stat1.553294Prob(F-statistic)0.000000与预期不相符。评价：可决系数为0.9948

44、69，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T检验，X1，X2,X3,X4,X5，X6 系数对应的t值分别为：1.254330，0.490501，-1.005377，0.951671，0.476621，均小于t（12）=2.179，所以所得系数都是不显著的。（3）根据Eviews分析得到数据如下：Dependent Variable: YMethod: Least SquaresDate: 12/03/14 Time: 11:12Sample: 1994 2011Included observations: 18VariableCo

45、efficientStd. Errort-StatisticProb.X50.0010322.20E-0546.799460.0000X6-0.0549650.031184-1.7625810.0983C4.2054813.3356021.2607860.2266R-squared0.993601Mean dependent var12.76667Adjusted R-squared0.992748S.D. dependent var9.746631S.E. of regression0.830018Akaike info criterion2.616274Sum squared resid1

46、0.33396Schwarz criterion2.764669Log likelihood-20.54646Hannan-Quinn criter.2.636736F-statistic1164.567Durbin-Watson stat1.341880Prob(F-statistic)0.000000得到模型的方程为：Y=0.001032 X5-0.054965 X6+4.205481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=1164.567F（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

47、，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：Dependent Variable: LNYMethod: Least SquaresDate: 12/05/14 Time: 11:39Sample: 1985 2011Included observations: 27VariableCoefficientStd. Errort-StatisticProb.LNGDP1.3385330.08861015.105820.0000LNCPI-0.42

48、17910.233295-1.8079750.0832C-3.1114860.463010-6.7201260.0000R-squared0.988051Mean dependent var9.484710Adjusted R-squared0.987055S.D. dependent var1.425517S.E. of regression0.162189Akaike info criterion-0.695670Sum squared resid0.631326Schwarz criterion-0.551689Log likelihood12.39155Hannan-Quinn cri

49、ter.-0.652857F-statistic992.2582Durbin-Watson stat0.522613Prob(F-statistic)0.000000得到的模型方程为：LNY=1.338533 LNGDPt-0.421791 LNCPIt-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=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.

50、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）Dependent Variable: LNYMethod: Least SquaresDate: 12/03/14 Time: 14:41Sample: 1985 2011Included observations: 27VariableCoefficientStd. Errort-StatisticProb.LNGDP1.1857390.02782242.619330.0000C-3.7506700.312255-12.011

51、560.0000R-squared0.986423Mean dependent var9.484710Adjusted R-squared0.985880S.D. dependent var1.425517S.E. of regression0.169389Akaike info criterion-0.642056Sum squared resid0.717312Schwarz criterion-0.546068Log likelihood10.66776Hannan-Quinn criter.-0.613514F-statistic1816.407Durbin-Watson stat0.

52、471111Prob(F-statistic)0.000000b)Dependent Variable: LNYMethod: Least SquaresDate: 12/03/14 Time: 14:41Sample: 1985 2011Included observations: 27VariableCoefficientStd. Errort-StatisticProb.LNCPI2.9392950.22275613.195110.0000C-6.8545351.242243-5.5178710.0000R-squared0.874442Mean dependent var9.48471

53、0Adjusted R-squared0.869419S.D. dependent var1.425517S.E. of regression0.515124Akaike info criterion1.582368Sum squared resid6.633810Schwarz criterion1.678356Log likelihood-19.36196Hannan-Quinn criter.1.610910F-statistic174.1108Durbin-Watson stat0.137042Prob(F-statistic)0.000000c)Dependent Variable:

54、 LNGDPMethod: Least SquaresDate: 12/05/14 Time: 11:11Sample: 1985 2011Included observations: 27VariableCoefficientStd. Errort-StatisticProb.LNCPI2.5110220.15830215.862270.0000C-2.7963810.882798-3.1676340.0040R-squared0.909621Mean dependent var11.16214Adjusted R-squared0.906005S.D. dependent var1.194

55、029S.E. of regression0.366072Akaike info criterion0.899213Sum squared resid3.350216Schwarz criterion0.995201Log likelihood-10.13938Hannan-Quinn criter.0.927755F-statistic251.6117Durbin-Watson stat0.099623Prob(F-statistic)0.000000得到的回归方程分别为1）LNY=1.185739 LNGDPt-3.7506702）LNY=2.939295 LNCPIt-6.8545353

56、）LNGDPt=2.511022 LNCPIt-2.796381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：Dependent Variable: CZSRMethod: Least SquaresDate: 12/03/14 Time: 11:40Sample: 1985 2011Included o

57、bservations: 27VariableCoefficientStd. Errort-StatisticProb.CZZC0.0901140.0443672.0311290.0540GDP-0.0253340.005069-4.9980360.0000SSZE1.1768940.06216218.932710.0000C-221.8540130.6532-1.6980380.1030R-squared0.999857Mean dependent var22572.56Adjusted R-squared0.999838S.D. dependent var27739.49S.E. of r

58、egression353.0540Akaike info criterion14.70707Sum squared resid2866884.Schwarz criterion14.89905Log likelihood-194.5455Hannan-Quinn criter.14.76416F-statistic53493.93Durbin-Watson stat1.458128Prob(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=0.05,水平下，回归方程回归方程

59、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，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

60、。（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）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：Dependent Variable: YMethod: Least SquaresDate: 12/10/14 Ti