计量经济学庞皓第三版课后答案2.pdf

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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:22有上可知，关系式为y=56.64794+0.128360 x1VariableCoefficientStd.Error t-StatisticProb.c56.647941.960820 28.889920.0000X10.1283600.027242 4.7118340.0001R-squared0.5

2、26082Mean dependent var62.50000Adjusted 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

3、.000134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.Error t-StatisticProb.c38.794243.532079 10.983400.0000X20.3319710.046656 7.1153080.0000R-squared0.716825Mean dependent var62.50000Adjusted R-s

4、quared0.702666S.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+0.331971X2关于人均寿命

5、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.Error t-StatisticProb.C31.799566.536434 4.8649710.0001X30.3872760.080260 4.8252850.0001R-squared0.537929Mean dependent var62.50000Adjusted R-squared0.5

6、14825S.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+0.387276x3（2）关于人均寿命与人均GDP

7、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 i）=4.711834to.o25（2O）=2.O86,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（j）=7.115308to.o25（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

8、数的t 检验：t(B3)=4.825285to.o25(2O)=2.O86,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 adjustmentsVariable Coefficient Std.Error t-Statistic Prob.X0.176124 0.

9、004072 43.25639 0.0000c-154.3063 39.08196-3.948274 0.0004R-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-Quinn criter.13

10、.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)对于回归系数的t 检验：t(B2)=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=0.176124X154.3063(0.004072

11、)(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，由上可知丫=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:由上表可知,XYMean6000.441902.5148Median2689.280209.3900Maximum27722.314895.410Minimum123.720025.8700

12、0Std.Dev.7608.0211351.009Skewness1.4325191.663108Kurtosis4.0105154.590432Jarque-Bera12.6906818.69063Probability0.0017550.000087Sum198014.529782.99Sum Sq.Dev.1.85E+0958407195Observations3333口2=(Xj-X)2=82x(n-l)=7608.0212 x(33-1)=1852223.473(Xf-X)2=(32000-6000.441产=675977068.2当 Xf=32000时，将相关数据代入计算得到：54

13、81.66172.0395xl75.2325xVl/33+1852223.473/675977068.2Yft0.025（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.E

14、rror t-StatisticProb.X-64.184004.809828-13.344340.0000c1845.47519.26446 95.796880.0000R-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-5

15、7.42275Hannan-Quinn 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 丫=1845.475 64.18400X 得，当 x=4.5,y=1556.647再进行区间估计:用 Eviews分析：由上表可知，YXMean1619.3333.523333Median163

16、0.0003.715000Maximum1860.0006.230000Minimum1419.0000.600000Std.Dev.131.22521.989419Skewness0.003403-0.060130Kurtosis2.3465111.664917Jarque-Bera0.2135470.898454Probability0.8987290.638121Sum19432.0042.28000Sum Sq.Dev.189420.743.53567Observations12122=(Xi-X)2=82x(n-l)=1.98 941 92 x(12-1)=43.5357(Xf-X)

17、2=(4.5-3.523333)2=0.95387843当 Xf=4.5时，将相关数据代入计算得到：1556.647-2.228x31.73600 xVl/12+43.5357/0.95387843YfF(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

18、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G D P 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：Dependent Variable:YMethod:Least SquaresDate:12/08/14 Time:17:28Sample:1 31Included observations:31VariableCoefficientStd.Errort-Stati

19、sticProb.X25.1356701.0102705.0834650.0000LNX3-22.810056.771820-3.3683780.0023LNX4-230.848149.46791-4.6666240.0001c1148.758228.29175.0319740.0000R-squared0.691952Mean dependent var16.77355Adjusted R-squared0.657725S.D.dependent var8.252535S.E.of regression4.828088Akaike info criterion6.106692Sum squa

20、red resid629.3818Schwarz criterion6.291723Log likelihood-90.65373Hannan-Quinn criter.6.167008F-statistic20.21624Durbin-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(1 )对出口货物总额计量经济模型，用Eviews分析结果如下：:D

21、ependent Variable:YMethod:Least SquaresDate:12/01/14 Time:20:25Sample:1994 2011Included observations:18Y=0.135474X2+18.85348X3-18231.58VariableCoefficientStd.Error t-StatisticProb.X20.1354740.012799 10.584540.0000X318.853489.776181 1.9285120.0729c-18231.588638.216-2.1105730.0520R-squared0.985838Mean

22、 dependent var6619.191Adjusted R-squared0.983950S.D.dependent var5767.152S.E.of regression730.6306Akaike info criterion16.17670Sum squared resid8007316.Schwarz criterion16.32510Log likelihood-142.5903Hannan-Quinn criter.16.19717F-statistic522.0976Durbin-Watson stat1.173432Prob(F-statistic)0.000000由上

23、可知，模型为：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:

24、1994 2011Included observations:18由上可知，模型为:VariableCoefficientStd.Error t-StatisticProb.LNX21.5642210.088988 17.577890.0000LNX31.7606950.682115 2.5812290.0209c-20.520485.432487-3.7773630.0018R-squared0.986295Mean dependent var8.400112Adjusted R-squared0.984467S.D.dependent var0.941530S.E.of regressio

25、n0.117343Akaike info criterion-1.296424Sum squared resid0.206540Schwarz criterion-1.148029Log likelihood14.66782Hannan-Quinn criter.-1.275962F-statistic539.7364Durbin-Watson stat0.686656Prob(F-statistic)0.000000LNY=-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

26、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18.85348亿元。(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

27、下：Dependent Variable:YMethod:Least SquaresDate:12/01/14 Time:20:30Sample:1 18Included observations:18Variable Coefficient Std.Error t-Statistic Prob.X0.086450 0.029363 2.944186 0.0101模型为：Y=0.086450X+52.37031 T-50.01638T52.370315.202167 10.067020.0000c-50.0163849.46026-1.0112440.3279R-squared0.951235

28、Mean dependent var755.1222Adjusted R-squared0.944732S.D.dependent var258.7206S.E.of regression60.82273Akaike info criterion11,20482Sum squared resid55491.07Schwarz criterion11.35321Log likelihood-97.84334Hannan-Quinn criter.11.22528F-statistic146.2974Durbin-Watson stat2.605783Prob(F-statistic)0.0000

29、00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:

30、22:30Sample:1 18Included observations:18TVariableCoefficientStd.Error t-StatisticProb.T63.016764.548581 13.854160.0000c-11.5817158.02290-0.1996060.8443R-squared0.923054Mean dependent var755.1222Adjusted R-squared0.918245S.D.dependent var258.7206S.E.of regression73.97565Akaike info criterion11.54979S

31、um squared resid87558.36Schwarz criterion11.64872Log likelihood-101.9481Hannan-Quinn criter.11.56343F-statistic191.9377Durbin-Watson stat2.134043Prob(F-statistic)0.000000Dependent Variable:XMethod:Least SquaresDate:12/01/14 Time:22:34Sample:1 18Included observations:18VariableCoefficientStd.Error t-

32、StatisticProb.123.1516 31.84150 3.867644 0.0014c444.5888 406.1786 1.094565 0.2899R-squared0.483182Mean dependent var1942.933Adjusted R-squared0.450881S.D.dependent var698.8325S.E.of regression517.8529Akaike info criterion15.44170Sum squared resid4290746.Schwarz criterion15.54063Log likelihood-136.97

33、53Hannan-Quinn criter.15.45534F-statistic14.95867Durbin-Watson stat1.052251Prob(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:Dependent Variable:E1Method:Least SquaresDate:12/03/14 Time:20:39Sample:1 18Included observations:18VariableCo

34、efficientStd.Errort-StatisticProb.E20.0864500.0284313.0407420.0078C3.96E-1413.880832.85E-151.0000R-squared0.366239 Mean dependent var 2.30E-14Adjusted R-squared0.326629S.D.dependent var71.76693S.E.of regression58.89136Akaike info criterion11.09370Sum squared resid55491.07Schwarz criterion11.19264Log

35、 likelihood-97.84334Hannan-Quinn criter.11.10735F-statistic9.246111Durbin-Watson stat2.605783Prob(F-statistic)0.007788模型为：E1=0.086450E2+3.96e-14参数:斜率系数a 为 0.086450,截距为斜96e-14（3）由上可知，B 2与 a 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,Xs的符号为正，X6的符号为负（2）根据Eviews分析得到数据如下:Dependent

36、Variable:YMethod:Least SquaresDate:12/04/14 Time:13:24Sample:1994 2011Included observations:18与预期不相符。VariableCoefficientStd.Errort-StatisticProb.X20.0013820.0011021.2543300.2336X30.0019420.0039600.4905010.6326X4-3.5790903.559949-1.0053770.3346X50.0047910.0050340.9516710.3600X60.0455420.0955520.47662

37、10.6422c-13.7773215.73366-0.8756590.3984R-squared0.994869Mean dependent var12.76667Adjusted 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-statistic

38、465.3617Durbin-Watson stat1.553294Prob(F-statistic)0.000000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,F=465.3617F(5.12)=3,89,回归方程显著3)T检验，X i，X 2,X X 4,X 5,X 6 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Ev i e w s分析得到数据如下：Dependent Variable:YMethod:Lea

39、st SquaresDate:12/03/14 Time:11:12Sample:1994 2011得到模型的方程为:Included observations:18VariableCoefficientStd.Error t-StatisticProb.X50.0010322.20E-05 46.799460.0000X6-0.0549650.031184-1.7625810.0983c4.2054813.335602 1.2607860.2266R-squared0.993601Mean dependent var12.76667Adjusted R-squared0.992748S.D.

40、dependent var9.746631S.E.of regression0.830018Akaike info criterion2.616274Sum squared resid10.33396Schwarz criterion2.764669Log likelihood-20.54646Hannan-Quinn criter.2.636736F-statistic1164.567Durbin-Watson stat1.341880Prob(F-statistic)0.000000Y=0.001032 X5-0.054965 X6+4.205481评价：1)可决系数为0.993601,数

41、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，Xs系数对应的t 值为46.79946,大于t(1 2)=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:Dependent Variable:LNYMethod:Least SquaresDate:12/05/14 Time:11:39Sample:1985 2011Included observations:27R-sq

42、uaredVariableCoefficientStd.Errort-StatisticProb.LNGDP1.3385330.08861015.105820.0000LNCPI-0.4217910.233295-1.8079750.0832c-3.1114860.463010-6.7201260.00000.988051 Mean dependent var 9.484710Adjusted R-squared0.987055S.D.dependent var1.425517S.E.of regression0.162189Akaike info criterion-0.695670Sum

43、squared resid0.631326Schwarz criterion-0.551689Log likelihood12.39155Hannan-Quinn criter.-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a=0.05时，t(24)=2.064,LNCPI的系数不

44、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)Dependent Variable:LNYMethod:Least SquaresDate:12/03/14 Time:14:41Sample:1985 2011Included observations:27VariableCoefficientStd.

45、Error t-StatisticProb.LNGDP1.1857390.027822 42.619330.0000c-3.7506700.312255-12.011560.0000R-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 likel

46、ihood10.66776Hannan-Quinn criter.-0.613514F-statistic1816.407Durbin-Watson stat0.471111Prob(F-statistic)0.000000b)Dependent Variable:LNYMethod:Least SquaresDate:12/03/14 Time:14:41Sample:1985 2011Included observations:27Variable Coefficient Std.Error t-Statistic Prob.LNCPI2.939295 0.222756 13.19511

47、0.0000c-6.8545351.242243-5.5178710.0000R-squared0.874442Mean dependent var9.484710Adjusted 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-statistic1

48、74.1108Durbin-Watson stat0.137042Prob(F-statistic)0.000000c)Dependent Variable: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-squared0.909621Mea

49、n dependent var11.16214Adjusted R-squared0.906005S.D.dependent var1.194029S.E.of regression0.366072Akaike info criterion0.899213Sum squared resid3.350216Schwarz criterion0.995201Log likelihood-10.13938 Hannan-Quinn criter.0.927755F-statistic 251.6117 Durbin-Watson stat 0.099623Prob(F-statistic)0.000

50、000得到的回归方程分别为1)LNY=1.185739 LNGDPt-3.7506702)LNY=2.939295 LNCPIt-6.8545353)LNGDPt=2.511022 LNCPIr2.796381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，G D P 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:C