计量经济学第三版课后习题答案

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: 12/23/15 time: 14:37sample: 1 22included observations: 22variablecoefficientstd. errort-statisticprob.  c56.647941.96082028.889920.0000x10.1283600.0272424.7118340.0001r-squared0.526082 &#

2、160;  mean dependent 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 

3、   hannan-quinn criter.6.872689f-statistic22.20138    durbin-watson stat0.629074prob(f-statistic)0.000134有上可知，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: 12/23/15 time: 15:01sample: 1 22included observations:

4、 22variablecoefficientstd. errort-statisticprob.  c38.794243.53207910.983400.0000x20.3319710.0466567.1153080.0000r-squared0.716825    mean dependent var62.50000adjusted r-squared0.702666    s.d. dependent var10.08889s.e. of regression5.501306 &#

5、160;  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由上可知，关系式为y=3

6、8.79424+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: 12/23/14 time: 15:20sample: 1 22included observations: 22variablecoefficientstd. errort-statisticprob.  c31.799566.5364344.8649710.0001x30.3872760.0802604.8252850.0001r-squared0.537929 &#

7、160;  mean dependent 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 

8、   hannan-quinn criter.6.847374f-statistic23.28338    durbin-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）=4.711834>t0.025(20)=2.086，对斜率系数的显著性检验表明，人均gdp对人均寿命有显著影

9、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）=7.115308>t0.025(20)=2.086，对斜率系数的显著性检验表明，成人识字率对人均寿命有显著影响。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（3）=4.825285>t0.025(20)=2.086，对斜率系数的显著性检验表明，一岁儿童疫苗接种率对人均寿命有显著影响。2.2（1）对于浙江省预算收入与全省生产总值的模型，用eviews分析

10、结果如下：dependent variable: ymethod: least squaresdate: 12/23/15 time: 17:46sample (adjusted): 1 33included observations: 33 after adjustmentsvariablecoefficientstd. errort-statisticprob.  x0.1761240.00407243.256390.0000c-154.306339.08196-3.9482740.0004r-squared0.983702    

11、;mean dependent var902.5148adjusted r-squared0.983177    s.d. dependent var1351.009s.e. of regression175.2325    akaike info criterion13.22880sum squared resid951899.7    schwarz criterion13.31949log likelihood-216.2751   

12、60;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）=43.25639>t0.025(31)=2.0395，对斜率系数的显著性检验表明，全省生产总值对财政预算总

13、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=0.983702 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：xy mean 6000.441 902.5148

14、60;median 2689.280 209.3900 maximum 27722.31 4895.410 minimum 123.7200 25.87000 std. dev. 7608.021 1351.009 skewness 1.432519 1.663108 kurtosis 4.010515 4.590432 jarque-bera 12.69068 18.69063 pro

15、bability 0.001755 0.000087 sum 198014.5 29782.99 sum sq. dev. 1.85e+09 58407195 observations 33 33由上表可知，x2=（xix）2=2x(n1)=  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：5481.66172.0395x175.2325

16、x1/33+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: 12/23/15 time: 18:04sample (adjusted): 1 33included observations: 33 after ad

17、justmentsvariablecoefficientstd. errort-statisticprob.  lnx0.9802750.03429628.582680.0000c-1.9182890.268213-7.1521210.0000r-squared0.963442    mean dependent var5.573120adjusted r-squared0.962263    s.d. dependent var1.684189s.e. of regression0.32717

18、2    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

19、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拟合较好。2）对于回归系数的t检验：t（2）=28.58268>t0.025(31)=2.0395，对斜率系数的显著性检验表明，全省生产总值对财政预算总收入有显著影响。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:

20、ymethod: least squaresdate: 12/23/15 time: 20:11sample: 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&

21、#160;   s.d. dependent var131.2252s.e. of regression31.73600    akaike info criterion9.903792sum squared resid10071.74    schwarz criterion9.984610log likelihood-57.42275    hannan-quinn criter.9.873871f-statistic178.0715

22、0;   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=1845.475-64.18400x得，当x=4.5，y=1556.647再进行区间估计：用eviews分析：yx mean 1619.333 3.523333 median 1630.000 3.71

23、5000 maximum 1860.000 6.230000 minimum 1419.000 0.600000 std. dev. 131.2252 1.989419 skewness 0.003403-0.060130 kurtosis 2.346511 1.664917 jarque-bera 0.213547 0.898454 probability 0.898729 0.638121&#

24、160;sum 19432.00 42.28000 sum sq. dev. 189420.7 43.53567 observations 12 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+2.228x31.73600

25、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: 12/23/15 time: 20:59sample: 1 31included observations: 31variablecoefficientstd. errort-statisticprob.  x25.9968651.4060584.2650200.000

26、2x3-0.5240270.179280-2.9229500.0069x4-2.2656800.518837-4.3668420.0002c246.854051.975004.7494760.0001r-squared0.666062    mean dependent var16.77355adjusted r-squared0.628957    s.d. dependent var8.252535s.e. of regression5.026889    akaike

27、info criterion6.187394sum squared resid682.2795    schwarz criterion6.372424log likelihood-91.90460    hannan-quinn criter.6.247709f-statistic17.95108    durbin-watson stat1.147253prob(f-statistic)0.000001得到模型得：y=246.8540+5.996865x2-0.52402

28、7 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=17.95108>f（3,27）=3.65，回归方程显著。3）t检验，t统计量分别为4.749476，4.265020，-2.922950，-4.366842，均大于t（27）=2.0518，所以这些系数都是显著的。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，若大于临界值，则否定原假设，系数都是显

29、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: 12/23/15 time: 21:09sample: 1 31included observations: 31variablecoefficientstd. errort-statisticprob.  

30、;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. dependent var8.252535s.e. of regression4.8

31、28088    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)0.00000

32、0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0.691952>0.666062，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: 12/24/15 time: 08:23sample: 1994 2011included observations: 18variablecoefficientstd. errort-statisticprob. &

33、#160;x20.1354740.01279910.584540.0000x318.853489.7761811.9285120.0729c-18231.588638.216-2.1105730.0520r-squared0.985838    mean dependent var6619.191adjusted r-squared0.983950    s.d. dependent var5767.152s.e. of regression730.6306    akaik

34、e info criterion16.17670sum squared resid8007316.    schwarz criterion16.32510log likelihood-142.5903    hannan-quinn criter.16.19717f-statistic522.0976    durbin-watson stat1.173432prob(f-statistic)0.000000由上可知，模型为：y = 0.135474x2 + 18.8534

35、8x3 - 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=522.0976>f（2,15）=4.77，回归方程显著3）t检验，t统计量分别为x2的系数对应t值为10.58454，大于t（15）=2.131，系数是显著的，x3的系数对应t值为1.928512，小于t（15）=2.131，说明此系数是不显著的。 （2）对于对数模型，用eviews分析结果如下：dependent variable: lnymethod: least squaresdate: 12/24/15 time: 08:47sam

36、ple: 1994 2011included observations: 18variablecoefficientstd. errort-statisticprob.  lnx21.5642210.08898817.577890.0000lnx31.7606950.6821152.5812290.0209c-20.520485.432487-3.7773630.0018r-squared0.986295    mean dependent var8.400112adjusted r-squared0.984467 

37、0;  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  

38、;  durbin-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）=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

39、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: 12/24/15 time: 09:03sample: 1 18included observations: 18variablecoefficientstd. errort-sta

40、tisticprob.  x0.0864500.0293632.9441860.0101t52.370315.20216710.067020.0000c-50.0163849.46026-1.0112440.3279r-squared0.951235    mean dependent var755.1222adjusted r-squared0.944732    s.d. dependent var258.7206s.e. of regression60.82273  &

41、#160; akaike info criterion11.20482sum squared resid55491.07    schwarz criterion11.35321log likelihood-97.84334    hannan-quinn criter.11.22528f-statistic146.2974    durbin-watson stat2.605783prob(f-statistic)0.000000模型为：y = 0.086450x

42、 + 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 squaresd

43、ate: 12/24/15 time: 09:18sample: 1 18included observations: 18variablecoefficientstd. errort-statisticprob.  t63.016764.54858113.854160.0000c-11.5817158.02290-0.1996060.8443r-squared0.923054    mean dependent var755.1222adjusted r-squared0.918245    

44、s.d. dependent var258.7206s.e. of regression73.97565    akaike info criterion11.54979sum squared resid87558.36    schwarz criterion11.64872log likelihood-101.9481    hannan-quinn criter.11.56343f-statistic191.9377    dur

45、bin-watson stat2.134043prob(f-statistic)0.000000dependent variable: xmethod: least squaresdate: 12/24/15 time: 09:34sample: 1 18included observations: 18variablecoefficientstd. errort-statisticprob.  t123.151631.841503.8676440.0014c444.5888406.17861.0945650.2899r-squared0.483182  

46、;  mean dependent var1942.933adjusted r-squared0.450881    s.d. dependent var698.8325s.e. of regression517.8529    akaike info criterion15.44170sum squared resid4290746.    schwarz criterion15.54063log likelihood-136.9753 

47、60;  hannan-quinn criter.15.45534f-statistic14.95867    durbin-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: 12/24/15 time: 0

48、9:39sample: 1 18included observations: 18variablecoefficientstd. errort-statisticprob.  e20.0864500.0284313.0407420.0078c3.96e-1413.880832.85e-151.0000r-squared0.366239    mean dependent var2.30e-14adjusted r-squared0.326629    s.d. dependent var71.7

49、6693s.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 stat2.60578

50、3prob(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: 12/24/15 time: 10:13sample: 1994 2011included observations

51、: 18variablecoefficientstd. errort-statisticprob.  x20.0013820.0011021.2543300.2336x30.0019420.0039600.4905010.6326x4-3.5790903.559949-1.0053770.3346x50.0047910.0050340.9516710.3600x60.0455420.0955520.4766210.6422c-13.7773215.73366-0.8756590.3984r-squared0.994869    mea

52、n dependent var12.76667adjusted r-squared0.992731    s.d. dependent var9.746631s.e. of regression0.830963    akaike info criterion2.728738sum squared resid8.285993    schwarz criterion3.025529log likelihood-18.55865    h

53、annan-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，f=465.3617>f（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）=2.17

54、9，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: 12/24/15 time: 10:20sample: 1994 2011included observations: 18variablecoefficientstd. errort-statisticprob.  x50.0010322.20e-0546.799460.0000x6-0.0549650.031184-1.7625810.0983c4.2054813.3356021.2607860.2266r-squared0.993601    mean dependent var12.76667adjuste