计量经济学庞皓第三版课后答案.pdf
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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 dependent va
2、r62.50000Adjusted 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有上可知,关系式为
3、y=56.64794+0.128360 x1关于人均寿命与成人识字率的关系,用Eviews分析如下: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 dependent var62.50000A
4、djusted 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由上可知,关系式为 y=38.79424
5、+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 dependent var62.50000Adjuste
6、d 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由上可知,关系式为 y=31.79956+0.387
7、276x3(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 0.5379
8、29,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 adjustmentsVariableCoefficientStd.Errort-Stat
9、isticProb.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 criterion13.31949Log likelihood-216.2751
10、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:=0.176
11、124X154.3063(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.Skewness Kurtosis Jarque-Bera Probabili
12、ty 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)=7608.0212 x(331)=1852223.473(XfX)2=(32000
13、 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:Dependent Variable:LNYMethod:Least SquaresDate:12/03/1
14、4Time: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-squared0.962263 S.D.dependent var1.684189S.E.of regression0.3
15、27172 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,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
16、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:12/01/14Time:12:40Sample:1 12Included observations:12VariableCoe
17、fficientStd.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 criterion9.903792Sum squared resid10071.74 Schwarz criterion9.984610L
18、og 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=1845.475-64.18400X 得,当 x=4.5,y=1556.647再进行区间估计:用 Eviews 分析:Mean Median Maximu
19、m 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 Sq.Dev.Observations 19432.00 189420.7 12 42.28000 43.53567 12由上表可知,x
20、2=(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:1556.6472.228x31.73600 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:YMe
21、thod:Least SquaresDate:11/25/14Time:12:38Sample:1 31Included observations:31VariableCoefficientStd.Errort-StatisticProb.X25.9968651.4060584.2650200.0002X3-0.5240270.179280-2.9229500.0069X4-2.2656800.518837-4.3668420.0002C246.854051.975004.7494760.0001R-squared0.666062 Mean dependent var16.77355Adjus
22、ted 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-statistic17.95108 Durbin-Watson stat1.147253Prob(F-statistic)0.000001得到模型得:Y=246.8540+5.99686
23、5X2-0.524027 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
24、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:17:28Sample:1 31Included observations:31VariableCoefficientStd.Errort-StatisticProb.X25.
25、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 regression4.828088 Akaike info criterion6.106692Sum squared resid6
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