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1、第二章简单线性回归模型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: 12/27/14Time: 21:00Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001R-squared0.526082 Mean depen
2、dent var62.50000Adjusted R-squared0.502386 S.D. dependent var10.08889S.E. of regression7.116881 Akaike info criterion6.849324Sum squared resid1013.000 Schwarz criterion6.948510Log likelihood-73.34257 Hannan-Quinn criter.6.872689F-statistic22.20138 Durbin-Watson stat0.629074Prob(F-statistic)0.000134有
3、上可知，关系式为 y=56.64794+0.128360x1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: 11/26/14Time: 21:10Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.C38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825 Mean depende
4、nt var62.50000Adjusted R-squared0.702666 S.D. dependent var10.08889S.E. of regression5.501306 Akaike info criterion6.334356Sum squared resid605.2873 Schwarz criterion6.433542Log likelihood-67.67792 Hannan-Quinn criter.6.357721F-statistic50.62761 Durbin-Watson stat1.846406Prob(F-statistic)0.000001由上可
5、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：Dependent Variable: YMethod: Least SquaresDate: 11/26/14Time: 21:14Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001R-squared0.537929 Mean depe
6、ndent var62.50000Adjusted R-squared0.514825 S.D. dependent var10.08889S.E. of regression7.027364 Akaike info criterion6.824009Sum squared resid987.6770 Schwarz criterion6.923194Log likelihood-73.06409 Hannan-Quinn criter.6.847374F-statistic23.28338 Durbin-Watson stat0.952555Prob(F-statistic)0.000103
7、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（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
8、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（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: 12/03/14Time: 17:00Sample (adjusted): 1 33Included observations: 33 after adjustmentsV
9、ariableCoefficientStd. Errort-StatisticProb.X0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004R-squared0.983702 Mean dependent var902.5148Adjusted R-squared0.983177 S.D. dependent var1351.009S.E. of regression175.2325 Akaike info criterion13.22880Sum squared resid951899.7 Schwarz crite
10、rion13.31949Log likelihood-216.2751 Hannan-Quinn criter.13.25931F-statistic1871.115 Durbin-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
11、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：=0.176124X154.3063(0.004072)(39.08196)= (43.25639)（-3.948274）2=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：先由 Eviews 分析： Mean Median Maximum Minimum Std. Dev
12、. Skewness Kurtosis Jarque-Bera Probability Sum Sum Sq. Dev. ObservationsX 6000.441 2689.280 27722.31 123.7200 7608.021 1.432519 4.010515 12.69068 0.001755 198014.5 1.85E+09 33Y 902.5148 209.3900 4895.410 25.87000 1351.009 1.663108 4.590432 18.69063 0.000087 29782.99 58407195 33由上表可知，x2=（XiX）2=2x(n1
13、)= 7608.0212 x (331)=1852223.473(XfX)2=(32000 6000.441)2=675977068.2当 Xf=32000 时，将相关数据代入计算得到：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：Depende
14、nt Variable: LNYMethod: Least SquaresDate: 12/03/14Time: 18:00Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.LNX0.9802750.03429628.582680.0000C-1.9182890.268213-7.1521210.0000R-squared0.963442 Mean dependent var5.573120Adjusted R-square
15、d0.962263 S.D. dependent var1.684189S.E. of regression0.327172 Akaike info criterion0.662028Sum squared resid3.318281 Schwarz criterion0.752726Log likelihood-8.923468 Hannan-Quinn criter.0.692545F-statistic816.9699 Durbin-Watson stat0.096208Prob(F-statistic)0.000000模型方程为：lnY=0.980275lnX-1.918289由上可知
16、，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: 12/0
17、1/14Time: 12:40Sample: 1 12Included observations: 12VariableCoefficientStd. Errort-StatisticProb.X-64.184004.809828-13.344340.0000C1845.47519.2644695.796880.0000R-squared0.946829 Mean dependent var1619.333Adjusted R-squared0.941512 S.D. dependent var131.2252S.E. of regression31.73600 Akaike info cri
18、terion9.903792Sum squared resid10071.74 Schwarz criterion9.984610Log likelihood-57.42275 Hannan-Quinn criter.9.873871F-statistic178.0715 Durbin-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
19、.18400X 得，当 x=4.5，y=1556.647再进行区间估计：用 Eviews 分析： Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis Jarque-Bera ProbabilityY 1619.333 1630.000 1860.000 1419.000 131.2252 0.003403 2.346511 0.213547 0.898729X 3.523333 3.715000 6.230000 0.600000 1.989419-0.060130 1.664917 0.898454 0.638121 Sum Sum
20、 Sq. Dev. Observations 19432.00 189420.7 12 42.28000 43.53567 12由上表可知，x2=（XiX）2=2x(n1)= 1.9894192 x (121)=43.5357(XfX)2=(4.5 3.523333)2=0.95387843当 Xf=4.5 时，将相关数据代入计算得到：1556.6472.228x31.73600x1/12+43.5357/0.95387843Yf1556.647+2.228x31.73600x1/12+43.5357/0.95387843即 Yf 的置信区间为（1556.647478.1231, 1556.6
21、47+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: 11/25/14Time: 12:38Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.X25.9968651.4060584.2650200.0002X3-0.5240270.179280-2.9229500.0069X4-2.2656800.518837-4.3668420.0002C
22、246.854051.975004.7494760.0001R-squared0.666062 Mean dependent var16.77355Adjusted R-squared0.628957 S.D. dependent var8.252535S.E. of regression5.026889 Akaike info criterion6.187394Sum squared resid682.2795 Schwarz criterion6.372424Log likelihood-91.90460 Hannan-Quinn criter.6.247709F-statistic17.
23、95108 Durbin-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：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=17.95108F（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：1）可决系数越大，说明拟合程度越好
24、2）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。3）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: 12/08/14Time: 17:
25、28Sample: 1 31Included observations: 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 Mean dependent var16.77355Adjusted R-squared0.657725 S.D. depen
26、dent var8.252535S.E. of regression4.828088 Akaike info criterion6.106692Sum squared resid629.3818 Schwarz criterion6.291723Log likelihood-90.65373 Hannan-Quinn criter.6.167008F-statistic20.21624 Durbin-Watson stat1.150090Prob(F-statistic)0.000000模型方程为：Y=5.135670 X2-22.81005 LNX3-230.8481 LNX4+1148.7
27、58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: 12/01/14Time: 20:25Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-StatisticProb.X20.1354740.01279910.584540.0000X318.853489.7761811.9285120.0729
28、C-18231.588638.216-2.1105730.0520R-squared0.985838 Mean dependent var6619.191Adjusted R-squared0.983950 S.D. dependent var5767.152S.E. of regression730.6306 Akaike info criterion16.17670Sum squared resid8007316. Schwarz criterion16.32510Log likelihood-142.5903 Hannan-Quinn criter.16.19717F-statistic
29、522.0976 Durbin-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，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
30、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: 12/01/14Time: 20:25Sample: 1994 2011Included observations: 18VariableCoefficientStd. Errort-StatisticProb.LNX21.5642210.08898817.577890.0000LNX31.7606950.6821152.5812290.0209C-20.520485.432487-3.7773630.0018R-squared0.9
31、86295 Mean dependent var8.400112Adjusted R-squared0.984467 S.D. dependent var0.941530S.E. of regression0.117343 Akaike info criterion-1.296424Sum squared resid0.206540 Schwarz criterion-1.148029Log likelihood14.66782 Hannan-Quinn criter.-1.275962F-statistic539.7364 Durbin-Watson stat0.686656Prob(F-s
32、tatistic)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）=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 18.853
33、48 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: 12/01/14Time: 20:30Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.X0.0864500.0293632.9441860.01
34、01T52.370315.20216710.067020.0000C-50.0163849.46026-1.0112440.3279R-squared0.951235 Mean dependent var755.1222Adjusted R-squared0.944732 S.D. dependent var258.7206S.E. of regression60.82273 Akaike info criterion11.20482Sum squared resid55491.07 Schwarz criterion11.35321Log likelihood-97.84334 Hannan
35、-Quinn criter.11.22528F-statistic146.2974 Durbin-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 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
36、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: 12/01/14Time: 22:30Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.T63.016764.54858113.85416C-11.5817158.02290-0.199606R-squared0.923054 Mean
37、 dependent varAdjusted R-squared0.918245 S.D. dependent varS.E. of regression73.97565 Akaike info criterionSum squared resid87558.36 Schwarz criterionLog likelihood-101.9481 Hannan-Quinn criter.F-statistic191.9377 Durbin-Watson statProb(F-statistic)0.000000Dependent Variable: XMethod: Least SquaresD
38、ate: 12/01/14Time: 22:34Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticT123.151631.841503.867644C444.5888406.17861.094565R-squared0.483182 Mean dependent varAdjusted R-squared0.450881 S.D. dependent varS.E. of regression517.8529 Akaike info criterionSum squared resid429
39、0746. Schwarz criterionLog likelihood-136.9753 Hannan-Quinn criter.F-statistic14.95867 Durbin-Watson statProb(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：Dependent Variable: E1Method: Least SquaresDate: 12/03/14Time: 20:
40、39Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticE20.0864500.0284313.0407420.00000.8443755.1222258.720611.5497911.6487211.563432.134043Prob.0.00140.28991942.933698.832515.4417015.5406315.455341.052251Prob.0.0078C3.96E-1413.880832.85E-151.0000R-squared0.366239 Mean depen
41、dent var2.30E-14Adjusted R-squared0.326629 S.D. dependent var71.76693S.E. of regression58.89136 Akaike info criterion11.09370Sum squared resid55491.07 Schwarz criterion11.19264Log likelihood-97.84334 Hannan-Quinn criter.11.10735F-statistic9.246111 Durbin-Watson stat2.605783Prob(F-statistic)0.007788模
42、型为：E1 = 0.086450E2 + 3.96e-14参数：斜率系数为 0.086450，截距为 3.96e-14（4）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: 12/04/14Time: 13:24Sample: 1994 2011Included observations: 18VariableCoefficien
43、tStd. 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 Mean dependent var12.76667Adjusted R-squared0.992731 S.D. de
44、pendent var9.746631S.E. of regression0.830963 Akaike info criterion2.728738Sum squared resid8.285993 Schwarz criterion3.025529Log likelihood-18.55865 Hannan-Quinn criter.2.769662F-statistic465.3617 Durbin-Watson stat1.553294Prob(F-statistic)0.000000与预期不相符。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，
45、F=465.3617F（5.12）=3,89，回归方程显著3）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: 12/03/14Time: 11:12Sample: 1994 2011Included observations: 18VariableCoefficientStd. Error
46、t-StatisticProb.X50.0010322.20E-0546.799460.0000X6-0.0549650.031184-1.7625810.0983C4.2054813.3356021.2607860.2266R-squared0.993601 Mean dependent var12.76667Adjusted R-squared0.992748 S.D. dependent var9.746631S.E. of regression0.830018 Akaike info criterion2.616274Sum squared resid10.33396 Schwarz
47、criterion2.764669Log likelihood-20.54646 Hannan-Quinn criter.2.636736F-statistic1164.567 Durbin-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：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=1164.567F（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
48、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: 12/05/14Time: 11:39Sample: 1985 2011Included observations: 27VariableCoefficientStd. Errort-StatisticProb.LNGDP1.3385330.08861015.105820.0000LNCPI-0.4
49、217910.233295-1.8079750.0832C-3.1114860.463010-6.7201260.0000R-squared0.988051 Mean dependent var9.484710Adjusted R-squared0.987055 S.D. dependent var1.425517S.E. of regression0.162189 Akaike info criterion-0.695670Sum squared resid0.631326 Schwarz criterion-0.551689Log likelihood12.39155 Hannan-Qui
50、nn criter.-0.652857F-statistic992.2582 Durbin-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：LNYLNGDPLNCPILNY 1.000000 0.993189 0.935116LNGDP 0
51、.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）Dependent Variable: LNYMethod: Least SquaresDate: 12/03/14Time: 14:41Sample: 1985 2011Included observations: 27VariableCoefficientStd. Errort-StatisticProb.LNGDP1.1857390.02782242.619330.0000C
52、-3.7506700.312255-12.011560.0000R-squared0.986423 Mean dependent var9.484710Adjusted R-squared0.985880 S.D. dependent var1.425517S.E. of regression0.169389 Akaike info criterion-0.642056Sum squared resid0.717312 Schwarz criterion-0.546068Log likelihood10.66776 Hannan-Quinn criter.-0.613514F-statisti
53、c1816.407 Durbin-Watson stat0.471111Prob(F-statistic)0.000000b)Dependent Variable: LNYMethod: Least SquaresDate: 12/03/14Time: 14:41Sample: 1985 2011Included observations: 27VariableCoefficientStd. Errort-StatisticLNCPI2.9392950.22275613.19511C-6.8545351.242243-5.517871R-squared0.874442 Mean depende
54、nt varAdjusted R-squared0.869419 S.D. dependent varS.E. of regression0.515124 Akaike info criterionSum squared resid6.633810 Schwarz criterionLog likelihood-19.36196 Hannan-Quinn criter.F-statistic174.1108 Durbin-Watson statProb(F-statistic)0.000000c)Dependent Variable: LNGDPMethod: Least SquaresDat
55、e: 12/05/14Time: 11:11Sample: 1985 2011Included observations: 27VariableCoefficientStd. Errort-StatisticLNCPI2.5110220.15830215.86227C-2.7963810.882798-3.167634Prob.0.00000.00009.4847101.4255171.5823681.6783561.6109100.137042Prob.0.00000.0040R-squared0.909621 Mean dependent var11.16214Adjusted R-squ
56、ared0.906005 S.D. dependent var1.194029S.E. of regression0.366072 Akaike info criterion0.899213Sum squared resid3.350216 Schwarz criterion0.995201Log likelihood-10.13938 Hannan-Quinn criter.0.927755F-statistic251.6117 Durbin-Watson stat0.099623Prob(F-statistic)0.000000得到的回归方程分别为1）LNY=1.185739 LNGDPt
57、-3.7506702）LNY=2.939295 LNCPIt-6.8545353）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: 1
58、2/03/14Time: 11:40Sample: 1985 2011Included observations: 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 Mean dependent var22572.56Adjusted R-squa
59、red0.999838 S.D. dependent var27739.49S.E. of regression353.0540 Akaike info criterion14.70707Sum squared resid2866884. Schwarz criterion14.89905Log likelihood-194.5455 Hannan-Quinn criter.14.76416F-statistic53493.93 Durbin-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
60、.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
61、.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CZZC可决系数0.997168方差扩大因子353GDPSSZE0.9888330.99786290468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：30,00025,00020,000E215,00010,0
62、005,00001,0001,5002,0002,500X3,0003,5004,000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：Dependent Variable: YMethod: Least SquaresDate: 12/10/14Time: 14:52Sample: 1 7Included observations: 7VariableCoefficientStd. Errort-StatisticT35.206644.9014927.182843X0.1099490.0619651.774380C77.1258
63、882.328440.936807R-squared0.943099 Mean dependent varAdjusted R-squared0.914649 S.D. dependent varS.E. of regression31.63265 Akaike info criterionSum squared resid4002.499 Schwarz criterionLog likelihood-32.15324 Hannan-Quinn criter.F-statistic33.14880 Durbin-Watson statProb(F-statistic)0.0032382得e1
64、i=4002.499Prob.0.00200.15070.4019565.6857108.275510.0437810.020609.7572671.4262622）定义区间为 12-18 时，由软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/10/14Time: 13:50Sample: 12 18Included observations: 7VariableCoefficientStd. Errort-StatisticProb.T52.405886.9233787.5694090.0016X0.0686890.05376
65、31.2776350.2705C-8.78926579.92542-0.1099680.9177R-squared0.984688 Mean dependent var887.6143Adjusted R-squared0.977032 S.D. dependent var274.4148S.E. of regression41.58810 Akaike info criterion10.59103Sum squared resid6918.280 Schwarz criterion10.56785Log likelihood-34.06861 Hannan-Quinn criter.10.3
66、0451F-statistic128.6166 Durbin-Watson stat2.390329Prob(F-statistic)0.0002342得e2i=6918.2803）根据 Goldfeld-Quanadt检验，F 统计量为：F=e2i2/e1i2=6918.280/4002.499=1.7285在=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（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，用权数 w1=1/X,建立回归得：Dependent V
67、ariable: YMethod: Least SquaresDate: 12/09/14Time: 11:13Sample: 1 31Included observations: 31Weighting series: W1VariableCoefficientStd. Errort-StatisticProb.X1.4258590.11910411.971570.0000C-334.8131344.3523-0.9722980.3389Weighted StatisticsR-squared0.831707 Mean dependent var3946.082Adjusted R-squa
68、red0.825904 S.D. dependent var536.1907S.E. of regression536.6796 Akaike info criterion15.47102Sum squared resid8352726. Schwarz criterion15.56354Log likelihood-237.8008 Hannan-Quinn criter.15.50118F-statistic143.3184 Durbin-Watson stat1.369081Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.
69、875855 Mean dependent var4443.526Adjusted R-squared0.871574 S.D. dependent var1972.072S.E. of regression706.7236 Sum squared resid14484289Durbin-Watson stat1.532908对此模型进行 White 检验得：Heteroskedasticity Test: WhiteF-statistic0.299395 Prob. F(2,28)0.7436Obs*R-squared0.649065 Prob. Chi-Square(2)0.7229Sca
70、led explained SS1.798067 Prob. Chi-Square(2)0.4070Test Equation:Dependent Variable: WGT_RESID2Method: Least SquaresDate: 12/10/14Time: 21:13Sample: 1 31Included observations: 31Collinear test regressors dropped from specificationVariableCoefficientStd. Errort-StatisticProb.C61927.891045682.0.0592220
71、.9532WGT2-593927.91173622.-0.5060640.6168X*WGT2282.4407747.97800.3776060.7086R-squared0.020938 Mean dependent var269442.8Adjusted R-squared-0.048995 S.D. dependent var689166.5S.E. of regression705847.6 Akaike info criterion29.86395Sum squared resid1.40E+13 Schwarz criterion30.00273Log likelihood-459
72、.8913 Hannan-Quinn criter.29.90919F-statistic0.299395 Durbin-Watson stat1.922336Prob(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（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=1.369081用权数 w2=1/x2,用回归分析得：Dependent Variable:
73、YMethod: Least SquaresDate: 12/09/14Time: 21:08Sample: 1 31Included observations: 31Weighting series: W2VariableCoefficientStd. Errort-StatisticX1.5570400.14539210.70922C-693.1946376.4760-1.841272Weighted StatisticsR-squared0.798173 Mean dependent varAdjusted R-squared0.791214 S.D. dependent varS.E.
74、 of regression466.8513 Akaike info criterionSum squared resid6320554. Schwarz criterionLog likelihood-233.4797 Hannan-Quinn criter.0.05Prob.0.00000.07583635.0281029.83015.1922415.2847515.22240F-statistic114.6875 Durbin-Watson stat1.562975Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.83485
75、0 Mean dependent var4443.526Adjusted R-squared0.829156 S.D. dependent var1972.072S.E. of regression815.1229 Sum squared resid19268334Durbin-Watson stat1.678365对此模型进行 White 检验得：Heteroskedasticity Test: WhiteF-statistic0.299790 Prob. F(3,27)0.8252Obs*R-squared0.999322 Prob. Chi-Square(3)0.8014Scaled e
76、xplained SS1.789507 Prob. Chi-Square(3)0.6172Test Equation:Dependent Variable: WGT_RESID2Method: Least SquaresDate: 12/10/14Time: 21:29Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.C-111661.8549855.7-0.2030750.8406WGT2426220.22240181.0.1902620.8505X2*WGT20.1948880
77、.5163950.3774020.7088X*WGT2-583.21512082.820-0.2800120.7816R-squared0.032236 Mean dependent var203888.8Adjusted R-squared-0.075293 S.D. dependent var419282.0S.E. of regression434780.1 Akaike info criterion28.92298Sum squared resid5.10E+12 Schwarz criterion29.10801Log likelihood-444.3062 Hannan-Quinn
78、 criter.28.98330F-statistic0.299790 Durbin-Watson stat1.835854Prob(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（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=0.798173 F=114.6875DW=1.5629750.05用权数 w3=1/sqr（x）,用回归分析得：Dependent Variable: YMethod:
79、Least SquaresDate: 12/09/14Time: 21:35Sample: 1 31Included observations: 31Weighting series: W3VariableCoefficientStd. Errort-StatisticProb.X1.3301300.09834513.525070.0000C-47.40242313.1154-0.1513900.8807Weighted StatisticsR-squared0.863161 Mean dependent var4164.118Adjusted R-squared0.858442 S.D. d
80、ependent var991.2079S.E. of regression586.9555 Akaike info criterion15.65012Sum squared resid9990985. Schwarz criterion15.74263Log likelihood-240.5768 Hannan-Quinn criter.15.68027F-statistic182.9276 Durbin-Watson stat1.237664Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.890999 Mean depend
81、ent var4443.526Adjusted R-squared0.887240 S.D. dependent var1972.072S.E. of regression662.2171 Sum squared resid12717412Durbin-Watson stat1.314859对此模型进行 White 检验得：Heteroskedasticity Test: WhiteF-statistic0.423886 Prob. F(2,28)0.6586Obs*R-squared0.911022 Prob. Chi-Square(2)0.6341Scaled explained SS2.
82、768332 Prob. Chi-Square(2)0.2505Test Equation:Dependent Variable: WGT_RESID2Method: Least SquaresDate: 12/09/14Time: 20:36Sample: 1 31Included observations: 31Collinear test regressors dropped from specificationVariableCoefficientStd. Errort-StatisticProb.CWGT2X2*WGT2R-squaredAdjusted R-squaredS.E.
83、of regressionSum squared residLog likelihoodF-statisticProb(F-statistic)1212308.2141958.0.565981-715673.01301839.-0.549740-0.0151940.082276-0.1846770.029388 Mean dependent var-0.039942 S.D. dependent var880429.8 Akaike info criterion2.17E+13 Schwarz criterion-466.7426 Hannan-Quinn criter.0.423886 Du
84、rbin-Watson stat0.6586280.57590.58690.8548322289.8863356.730.3059730.4447530.351211.8874260.05从上可知，nR2=0.911022，比较计算的统计量的临界值，因为 nR2=0.911022 F0.05（11,11）=4.47，所以拒绝原假设，此检验表明模型存在异方差。White 检验用 EViews 软件分析得：Heteroskedasticity Test: WhiteF-statistic10.36759 Prob. F(2,31)0.0004Obs*R-squared13.62701 Prob.
85、Chi-Square(2)0.0011Scaled explained SS76.13635 Prob. Chi-Square(2)0.0000Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/11/14Time: 12:56Sample: 1 34Included observations: 34VariableCoefficientStd. Errort-StatisticProb.C11581.1126117.110.443430X-27.6990127.86540-0.994029X20.0122
86、300.0051562.371861R-squared0.400795 Mean dependent varAdjusted R-squared0.362136 S.D. dependent varS.E. of regression81255.15 Akaike info criterionSum squared resid2.05E+11 Schwarz criterionLog likelihood-431.0554 Hannan-Quinn criter.F-statistic10.36759 Durbin-Watson statProb(F-statistic)0.000357从上图
87、中可以看出，nR2=13.62701，比较计算的nR2=13.62701异方差。用以上两种方法，可以检验模型是存在异方差的。c)修正模型1）用加权二乘法修正异方差现象步骤如下：当权数 w1=1/x 时，用软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/11/14Time: 13:22Sample: 1 34Included observations: 34Weighting series: W1VariableCoefficientStd. Errort-StatisticX0.8210130.01686648.67993C17
88、.693186.2832562.815926Weighted StatisticsR-squared0.986676 Mean dependent varAdjusted R-squared0.986260 S.D. dependent varS.E. of regression37.91285 Akaike info criterionSum squared resid45996.29 Schwarz criterionLog likelihood-170.8132 Hannan-Quinn criter.F-statistic2369.735 Durbin-Watson statProb(
89、F-statistic)0.0000000.66050.32790.024128220.51101738.925.5326725.6673525.578603.021651统计量的临界值，因为0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在Prob.0.00000.0083457.850541.7038410.1654810.2552710.196100.605852Unweighted StatisticsR-squared0.968070 Mean dependent var1295.802Adjusted R-squared0.967072 S.D. depen
90、dent var1188.791S.E. of regression215.7175 Sum squared resid1489089.Durbin-Watson stat1.079107得方程模型为：Y=0.821013X-17.69318t=（48.67993）（2.815926）R2=0.986676 F=2369.735DW=0.605852对此模型进行 White 检验如下：Heteroskedasticity Test: WhiteF-statistic1.348072 Prob. F(2,31)0.2745Obs*R-squared2.720457 Prob. Chi-Squar
91、e(2)0.2566Scaled explained SS1.221901 Prob. Chi-Square(2)0.5428Test Equation:Dependent Variable: WGT_RESID2Method: Least SquaresDate: 12/11/14Time: 11:20Sample: 1 34Included observations: 34Collinear test regressors dropped from specificationVariableCoefficientStd. Errort-StatisticProb.C1678.870416.
92、54174.0304980.0003WGT2-32.13071187.6175-0.1712570.8651X*WGT2-0.4840401.279449-0.3783190.7078R-squared0.080013 Mean dependent var1352.832Adjusted R-squared0.020659 S.D. dependent var1382.825S.E. of regression1368.467 Akaike info criterion17.36487Sum squared resid58053732 Schwarz criterion17.49955Log
93、likelihood-292.2027 Hannan-Quinn criter.17.41080F-statistic1.348072 Durbin-Watson stat1.199640Prob(F-statistic)0.274545从上图中可以看出，nR2=2.720457，比较计算的统计量的临界值，因为 nR2=2.720457Prob.0.92920.50930.07590.2923247.0857435.479114.6387614.8183314.700001.586012统计量的临界值，因为0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。此模型
94、并未消除异方差。当权数 w3=1/sqr(x)时，用软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/11/14Time: 13:21Sample: 1 34Included observations: 34Weighting series: W3VariableCoefficientStd. Errort-StatisticX0.7785510.01567749.66347C40.4577014.575282.775775Weighted StatisticsR-squared0.987192 Mean dependent va
95、rAdjusted R-squared0.986792 S.D. dependent varS.E. of regression79.19828 Akaike info criterionSum squared resid200715.8 Schwarz criterionLog likelihood-195.8597 Hannan-Quinn criter.F-statistic2466.460 Durbin-Watson statProb.0.00000.0091776.3266367.315211.6388111.7285911.669431.178340Prob(F-statistic
96、)0.000000Unweighted StatisticsR-squared0.977590 Mean dependent varAdjusted R-squared0.976890 S.D. dependent varS.E. of regression180.7210 Sum squared residDurbin-Watson stat1.460832得方程模型为：Y=0.778551X+40.45770t=（49.66347）（2.775775）R2=0.986792 F=2466.460 DW=1.178340对所得模型进行White 检验：Heteroskedasticity T
97、est: WhiteF-statistic8.158958 Prob. F(2,31)Obs*R-squared11.72514 Prob. Chi-Square(2)Scaled explained SS28.08353 Prob. Chi-Square(2)Test Equation:Dependent Variable: WGT_RESID2Method: Least SquaresDate: 12/10/14Time: 13:23Sample: 1 34Included observations: 34Collinear test regressors dropped from spe
98、cificationVariableCoefficientStd. Errort-StatisticC-7585.1865311.263-1.428132WGT22468.3691996.0411.236632X2*WGT20.0091390.0024813.684177R-squared0.344857 Mean dependent varAdjusted R-squared0.302590 S.D. dependent varS.E. of regression11636.97 Akaike info criterionSum squared resid4.20E+09 Schwarz c
99、riterionLog likelihood-364.9796 Hannan-Quinn criter.F-statistic8.158958 Durbin-Watson statProb(F-statistic)0.001423从 上 图 中 可 以 看 出 ， nR2=11.72514 ， 比 较 计 算 的nR2=11.725141295.8021188.7911045123.0.00140.00280.0000Prob.0.16330.22550.00095903.40513934.6421.6458621.7805421.691792.344068统 计 量 的 临 界 值 ， 因
100、为0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。此模型并未消除异方差。综上所述，用加权二乘法w1 的效果最好，所以模型为：得方程模型为：Y=0.821013X-17.69318t=（48.67993）（2.815926）R2=0.986676 F=2369.735DW=0.6058522）用对数模型法用软件分析得：Dependent Variable: LNYMethod: Least SquaresDate: 12/11/14Time: 09:54Sample: 1 34Included observations: 34VariableCoefficien
101、tStd. Errort-StatisticProb.LNX0.9468870.01122884.335490.0000C0.2018610.0779052.5911000.0143R-squared0.995521 Mean dependent var6.687779Adjusted R-squared0.995381 S.D. dependent var1.067124S.E. of regression0.072525 Akaike info criterion-2.352753Sum squared resid0.168315 Schwarz criterion-2.262967Log
102、 likelihood41.99680 Hannan-Quinn criter.-2.322134F-statistic7112.475 Durbin-Watson stat0.812150Prob(F-statistic)0.000000得到模型为：LnY=0.946887 LNX+0.201861对此模型进行 White 检验得：Heteroskedasticity Test: WhiteF-statistic1.003964 Prob. F(2,31)0.3780Obs*R-squared2.068278 Prob. Chi-Square(2)0.3555Scaled explained
103、 SS1.469638 Prob. Chi-Square(2)0.4796Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/11/14Time: 09:55Sample: 1 34Included observations: 34VariableCoefficientStd. Errort-StatisticProb.C0.0395470.0467590.8457530.4042LNX-0.0116010.014012-0.8279690.4140LNX20.0009320.0010280.9067740
104、.3715R-squared0.060832 Mean dependent var0.004950Adjusted R-squared0.000240 S.D. dependent var0.006365S.E. of regression0.006364 Akaike info criterion-7.192271Sum squared resid0.001255 Schwarz criterion-7.057592Log likelihood125.2686 Hannan-Quinn criter.-7.146342F-statistic1.003964 Durbin-Watson sta
105、t2.022904Prob(F-statistic)0.378027从 上 图 中 可 以 看 出 ， nR2=2.068278 ， 比 较 计 算 的统 计 量 的 临 界 值 ，nR2=2.068278 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。2）用 White 检验，软件分析结果为：Heteroskedasticity Test: WhiteF-statistic7.312529 Prob. F(5,28)0.0002Obs*R-squared19.25463 Prob. Chi-Square(5)0.0017Scaled explained SS1
106、19.3072 Prob. Chi-Square(5)0.0000Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/12/14Time: 19:31Sample: 1 34Included observations: 34VariableCoefficientStd. Errort-StatisticProb.C79541.08112647.30.7061070.4860X209.496463.904003.2782980.0028X2-0.0241330.010712-2.2528410.0323X*P
107、-0.2351370.106647-2.2048220.0358P-1175.3261156.253-1.0164950.3181P21.6373662.6000200.6297510.5340R-squared0.566313 Mean dependent var27555.40Adjusted R-squared0.488869 S.D. dependent var107990.9S.E. of regression77206.44 Akaike info criterion25.50514Sum squared resid1.67E+11 Schwarz criterion25.7745
108、0Log likelihood-427.5874 Hannan-Quinn criter.25.59700F-statistic7.312529 Durbin-Watson stat2.787044Prob(F-statistic)0.000171从 上 图 中 可 以 看 出 ， nR2=19.25463 ， 比 较 计 算 的统 计 量 的 临 界 值 ， 因 为nR2=19.254630.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。2）修正建立对数模型，用软件分析如下：Dependent Variable: LNYMethod: Least Squar
109、esDate: 12/12/14Time: 19:24Sample: 1 34Included observations: 34VariableCoefficientStd. Errort-StatisticProb.LNX0.9396050.01364568.860880.0000LNP0.0268210.0284540.9426090.3532C0.1082300.1263220.8567840.3981R-squared0.995646 Mean dependent var6.687779Adjusted R-squared0.995365 S.D. dependent var1.067
110、124S.E. of regression0.072652 Akaike info criterion-2.322188Sum squared resid0.163625 Schwarz criterion-2.187509Log likelihood42.47720 Hannan-Quinn criter.-2.276259F-statistic3544.292 Durbin-Watson stat0.930109Prob(F-statistic)0.000000对此模型进行 White 检验：Heteroskedasticity Test: WhiteF-statistic3.523832
111、 Prob. F(5,28)0.0135Obs*R-squared13.13158 Prob. Chi-Square(5)0.0222Scaled explained SS12.14373 Prob. Chi-Square(5)0.0329Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/12/14Time: 19:24Sample: 1 34Included observations: 34VariableCoefficientStd. Errort-StatisticProb.C0.4228720.2
112、737461.5447590.1336LNX0.0807120.0318332.5355020.0171LNX2-0.0039170.003037-1.2895640.2078LNX*LNP-0.0049550.005136-0.9647650.3429LNP-0.2549920.129858-1.9636310.0596LNP20.0264700.0126752.0883900.0460R-squared0.386223 Mean dependent var0.004813Adjusted R-squared0.276620 S.D. dependent var0.007286S.E. of
113、 regression0.006197 Akaike info criterionSum squared resid0.001075 Schwarz criterionLog likelihood127.9017 Hannan-Quinn criter.F-statistic3.523832 Durbin-Watson statProb(F-statistic)0.013502从 上 图 中 可 以 看 出 ， nR2=13.13158 ， 比 较 计 算 的nR2=13.13158-7.170690-6.901332-7.0788312.264261统 计 量 的 临 界 值 ， 因 为0.
114、05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。当 w1=1/x 时，用软件分析如下：Dependent Variable: YMethod: Least SquaresDate: 12/13/14Time: 18:49Sample: 1 34Included observations: 34Weighting series: W1VariableCoefficientStd. Errort-StatisticX0.7232180.02296531.49212P0.7195060.1410855.099795C-44.7208413.1
115、1268-3.410502Weighted StatisticsR-squared0.992755 Mean dependent varAdjusted R-squared0.992287 S.D. dependent varS.E. of regression28.40494 Akaike info criterionSum squared resid25012.05 Schwarz criterionLog likelihood-160.4567 Hannan-Quinn criter.F-statistic2123.843 Durbin-Watson statProb(F-statist
116、ic)0.000000Unweighted StatisticsR-squared0.977704 Mean dependent varAdjusted R-squared0.976266 S.D. dependent varS.E. of regression183.1446 Sum squared residDurbin-Watson stat1.740795所得模型为：Y=0.723218X+0.719506p-44.72084Prob.0.00000.00000.0018457.850541.703849.6151009.7497799.6610301.2983891295.80211
117、88.7911039800.对此模型进行White检验得：Heteroskedasticity Test: WhiteF-statistic2.088840 Prob. F(5,28)0.0966Obs*R-squared9.236835 Prob. Chi-Square(5)0.1000Scaled explained SS25.50696 Prob. Chi-Square(5)0.0001Test Equation:Dependent Variable: WGT_RESID2Method: Least SquaresDate: 12/14/14Time: 19:57Sample: 1 34
118、Included observations: 34Collinear test regressors dropped from specificationVariableCoefficientStd. Errort-StatisticProb.C3861.7931068.8063.6131830.0012WGT23260.1994309.9880.7564290.4557X*WGT213.722418.4534731.6232870.1157X*P*WGT2-0.1517250.061588-2.4635670.0202P2*WGT20.4311620.2783151.5491860.1326
119、P*WGT2-76.1322173.40636-1.0371340.3085R-squared0.271672 Mean dependent var735.6486Adjusted R-squared0.141613 S.D. dependent var1924.655S.E. of regression1783.177 Akaike info criterion17.96897Sum squared resid89032169 Schwarz criterion18.23832Log likelihood-299.4724 Hannan-Quinn criter.18.06082F-stat
120、istic2.088840 Durbin-Watson stat2.336495Prob(F-statistic)0.096616因为 nR2=9.2368350.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。当 w3=1/sqr(x)时，用软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/14/14Time: 19:06Sample: 1 34Included observations: 34Weighting series: W3VariableCoefficient
121、Std. Errort-StatisticX0.7446610.01982537.56252P0.4518610.1799712.510739C-13.4964325.37768-0.531823Weighted StatisticsR-squared0.989356 Mean dependent varAdjusted R-squared0.988670 S.D. dependent varS.E. of regression73.35237 Akaike info criterionSum squared resid166797.7 Schwarz criterionLog likelih
122、ood-192.7129 Hannan-Quinn criter.F-statistic1440.783 Durbin-Watson statProb(F-statistic)0.000000Unweighted StatisticsR-squared0.979407 Mean dependent varAdjusted R-squared0.978079 S.D. dependent varS.E. of regression176.0098 Sum squared residDurbin-Watson stat1.761225Prob.0.00000.01750.5986776.32663
123、67.315211.5125211.6472011.558451.5995901295.8021188.791960362.6所得模型为：Y=0.744661X+0.451861p-13.49643对所得模型进行White 检验得：Heteroskedasticity Test: WhiteF-statistic4.459272 Prob. F(5,28)0.0041Obs*R-squared15.07219 Prob. Chi-Square(5)0.0101Scaled explained SS72.39077 Prob. Chi-Square(5)0.0000Test Equation:D
124、ependent Variable: WGT_RESID2Method: Least SquaresDate: 12/14/14Time: 19:08Sample: 1 34Included observations: 34Collinear test regressors dropped from specificationVariableCoefficientStd. Errort-StatisticProb.C61163.2227531.932.2215380.0346WGT228251.9817350.391.6283200.1147X2*WGT2-0.0010930.006624-0
125、.1649500.8702X*P*WGT2-0.2358360.077110-3.0584470.0049P2*WGT21.2368840.6448721.9180300.0654P*WGT2-503.3080262.5884-1.9167180.0655R-squared0.443300 Mean dependent var4905.814Adjusted R-squared0.343889 S.D. dependent var16926.97S.E. of regression13710.96 Akaike info criterion22.04856Sum squared resid5.
126、26E+09 Schwarz criterion22.31792Log likelihood-368.8256 Hannan-Quinn criter.22.14042F-statistic4.459272 Durbin-Watson stat2.450171Prob(F-statistic)0.004103因为 nR2=15.072190.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。综上所述，修改后的模型为：Y= Y=0.723218X+0.719506p-44.72084t=(31.49212)(5.099705) (-3.41
127、0502)R2=0.992755 F=2123.843DW=1.298389(3)体会：对于不同的模型，可采取对数模型法或者加权二乘法对具有异方差性的模型进行改进，从而消除异方差。但对于不同的模型，自由度的不同，可能导致改进的方法不同，所以要对改进的模型进行进一步的检验才行。6.1(1)建立居民收入-消费模型，用 Eviews 分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/20/14Time: 14:22Sample: 1 19Included observations: 19VariableCoefficientStd.
128、Errort-StatisticX0.6904880.01287753.62068C79.9300412.399196.446390R-squared0.994122 Mean dependent varAdjusted R-squared0.993776 S.D. dependent varS.E. of regression19.44245 Akaike info criterionSum squared resid6426.149 Schwarz criterionLog likelihood-82.28490 Hannan-Quinn criter.F-statistic2875.17
129、8 Durbin-Watson statProb(F-statistic)0.000000所得模型为：=0.690488X+79.93004Se=(0.012877)(12.39919)t=(53.62068)(6.446390)R2=0.994122 F=2875.178 DW=0.574663（2）1）检验模型中存在的问题做出残差图如下：50403020100-10-20-30-4024681012141618Prob.0.00000.0000700.2747246.44918.8720958.9715108.8889200.574663Y Residuals残差的变动有系统模式，连续为正
130、和连续为负，表明残差项存在一阶自相关。该回归方程可决系数较高，回归系数均显著。对样本量为19，一个解释变量的模型，5%的显著水平，查 DW 统计表可知，dL=1.180，dU=1.401，模型中 DW=0.574663, dL,显然模型中有自相关。对模型进行 BG 检验，用 Eviews 分析结果如下：Breusch-Godfrey Serial Correlation LM Test:F-statistic4.811108 Prob. F(2,15)0.0243Obs*R-squared7.425088 Prob. Chi-Square(2)0.0244Test Equation:Depen
131、dent Variable: RESIDMethod: Least SquaresDate: 12/20/14Time: 15:03Sample: 1 19Included observations: 19Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.X-0.0032750.010787-0.3035860.7656C1.92954610.355930.1863230.8547RESID(-1)0.6088860.2927072.0801890.
132、0551RESID(-2)0.0899880.2911200.3091100.7615R-squared0.390794 Mean dependent var-1.65E-13Adjusted R-squared0.268953 S.D. dependent var18.89466S.E. of regression16.15518 Akaike info criterion8.587023Sum squared resid3914.848 Schwarz criterion8.785852Log likelihood-77.57671 Hannan-Quinn criter.8.620672
133、F-statistic3.207406 Durbin-Watson stat1.570723Prob(F-statistic)0.053468如上表显示，LM=TR2=7.425088，其 p 值为 0.0244，表明存在自相关。2）对模型进行处理：采取广义差分法a)为估计自相关系数。对et进行滞后一期的自回归，用EViews 分析结果如下：Dependent Variable: EMethod: Least SquaresDate: 12/20/14Time: 15:04Sample (adjusted): 2 19Included observations: 18 after adjust
134、mentsVariableCoefficientStd. Errort-StatisticProb.E(-1)0.6573520.1776263.7007590.0018R-squared0.440747 Mean dependent var1.717433Adjusted R-squared0.440747 S.D. dependent var17.85134S.E. of regression13.34980 Akaike info criterion8.074833Sum squared resid3029.692 Schwarz criterion8.124298Log likelih
135、ood-71.67349 Hannan-Quinn criter.8.081653Durbin-Watson stat1.634573由上可知，=0.657352b)对原模型进行广义差分回归，用Eviews 进行分析所得结果如下：Dependent Variable: Y-0.657352*Y(-1)Method: Least SquaresDate: 12/20/14Time: 15:04Sample (adjusted): 2 19Included observations: 18 after adjustmentsVariableCoefficientStd. Errort-Statis
136、ticProb.C35.977618.1035464.4397370.0004X-0.657352*X(-1)0.6686950.02064232.395120.0000R-squared0.984983 Mean dependent var278.1002Adjusted R-squared0.984044 S.D. dependent var105.1781S.E. of regression13.28570 Akaike info criterion8.115693Sum squared resid2824.158 Schwarz criterion8.214623Log likelih
137、ood-71.04124 Hannan-Quinn criter.8.129334F-statistic1049.444 Durbin-Watson stat1.830746Prob(F-statistic)0.000000由上图可知回归方程为：Yt*=35.97761+0.668695Xt*Se=(8.103546)(0.020642)t=(4.439737)(32.39512)R2=0.984983 F=1049.444 DW=1.830746式中，Yt*=Yt-0.657352Yt-1, Xt*=Xt-0.657352Xt-1由于使用了广义差分数据，样本容量减少了1 个，为 18 个。查
138、 5%显著水平的 DW 统计表可知，dL=1.158,dU=1.391 模型中 DW=1,830746，duDW4- dU，说明在 5%的显著水平下广义差分模型中已无自相关。可决系数R2，t，F 统计量也均达到理想水平。由差分方程，1=35.97761/(1-0.657352)=104.9987由此最终的消费模型为：Yt=104.9987+0.668695Xt用科克伦-奥克特迭代法，用 EVIews 分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/20/14Time: 15:15Sample (adjusted): 2 19I
139、ncluded observations: 18 after adjustmentsConvergence achieved after 5 iterationsVariableCoefficientStd. Errort-StatisticProb.C104.044923.876184.357687X0.6692620.02083132.12757AR(1)0.6300150.1642183.836462R-squared0.997097 Mean dependent varAdjusted R-squared0.996710 S.D. dependent varS.E. of regres
140、sion13.70843 Akaike info criterionSum squared resid2818.814 Schwarz criterionLog likelihood-71.02419 Hannan-Quinn criter.F-statistic2575.896 Durbin-Watson statProb(F-statistic)0.000000Inverted AR Roots .63所得方程为：Yt=104.0449+0.669262Xt0.00060.00000.0016719.1867238.98668.2249108.3733068.2453721.787878（
141、3）经济意义：人均实际收入每增加 1 元，平均说来人均时间消费支出将增加 0.669262元。6.4（1）1）针对对数模型，用Eviews 分析结果如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/27/14Time: 16:13Sample: 1980 2000Included observations: 21VariableCoefficientStd. Errort-StatisticProb.LNXCR-squaredAdjusted R-squaredS.E. of regressionSum squared residL
142、og likelihoodF-statisticProb(F-statistic)所得模型为：0.9510900.03889724.451230.00002.1710410.2410259.0075290.00000.969199 Mean dependent var8.0393070.967578 S.D. dependent var0.5654860.101822 Akaike info criterion-1.6407850.196987 Schwarz criterion-1.54130719.22825 Hannan-Quinn criter.-1.619196597.8626 Du
143、rbin-Watson stat1.1597880.000000lnY=0,951090lnX+2.171041se=(0.038897)(0.241025)=(24.45123)(9.007529)2=0.969199 F=597.8626 DW=1.159788）检验模型的自相关性回归方程可决系数较高，回归系数均显著。对样本量为21，一个解释变量的模型，5%的显著水平，查DW 统计表可知，dL=1.221，dU=1.420，模型中DW=1.159788 dL,显然模型中有自相关。2)用广义差分法处理模型：1）为估计自相关系数。对et进行滞后一期的自回归，用EViews 分析结果如下：Dep
144、endent Variable: EMethod: Least SquaresDate: 12/27/14Time: 16:18Sample (adjusted): 1982 2000Included observations: 19 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.E(-1)-0.0128720.280581-0.0458780.9639R-squared0.000073 Mean dependent var-2.556737Adjusted R-squared0.000073 S.D. depend
145、ent var397.7924S.E. of regression397.7778 Akaike info criterion14.86086Sum squared resid2848090. Schwarz criterion14.91057Log likelihood-140.1782 Hannan-Quinn criter.14.86927Durbin-Watson stat1.700254由上可知，=-0.0128722）对原模型进行广义差分回归，用Eviews 进行分析所得结果如下：Dependent Variable: Y+0.012872*Y(-1)Method: Least S
146、quaresDate: 12/27/14Time: 21:06Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-104.9645197.7928-0.5306790.6021X+0.012872*X(-1)6.6537570.30415721.876050.0000R-squared0.963751 Mean dependent var3753.934Adjusted R-squared0.961737 S.D
147、. dependent var2045.606S.E. of regression400.1404 Akaike info criterion14.91615Sum squared resid2882022. Schwarz criterion15.01572Log likelihood-147.1615 Hannan-Quinn criter.14.93559F-statistic478.5614 Durbin-Watson stat1.822259Prob(F-statistic)0.000000由上图可知回归方程为：Yt*=-104.9645+6.653757Xt*Se=(197.792
148、8)( 0.304157)t=(-0.530679)( 21.87605)R2=0.963751 F=478.5614DW=1.8222596式中，Yt*=Yt+0.012872Yt-1, Xt*=Xt+0.012872Xt-1由于使用了广义差分数据，样本容量减少了1 个，为 20 个。查 5%显著水平的 DW 统计表可知，dL=1.201,dU=1.411 模型中 DW=1.8222596，duDW4- dU，说明在 5%的显著水平下广义差分模型中已无自相关。可决系数R2，t，F 统计量也均达到理想水平。由差分方程，1=-104.9645/(1+0.012872)=-103.6306由此最终
149、的模型为：Yt=-103.6306+6.653757Xt（3）对于此模型，用Eviews 分析结果如下：Dependent Variable: LNY1Method: Least SquaresDate: 12/27/14Time: 22:16Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsVariableCoefficientStd. ErrorLNX10.4422240.066024t-Statistic6.697901Prob.0.0000C0.0540470.0133224.0568960.0
150、007R-squared0.713658 Mean dependent var0.091592Adjusted R-squared0.697750 S.D. dependent var0.098311S.E. of regression0.054049 Akaike info criterion-2.903219Sum squared resid0.052583 Schwarz criterion-2.803646Log likelihood31.03219 Hannan-Quinn criter.-2.883781F-statistic44.86188 Durbin-Watson stat1.590363Prob(F-statistic)0.000003由题目可知， 此模型样本容量为 20， 查 5%显著水平的 DW 统计表可知， dL=1.201,dU=1.411模型中 DW=1.590363，duDW4- dU，说明在 5%的显著水平此模型中无自相关。 可决系数R2，t，F 统计量也均达到理想水平
