计量经济学 庞皓 第三版课后答案解析.doc
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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: 22VariableCoefficientStd. Errort-StatisticProb.C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001R-squared0.526082Mean dependent var
2、62.50000Adjusted 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.
3、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: 11/26/14 Time: 21:10Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.C38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825Mean dependent var62.50000
4、Adjusted 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.
5、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: 11/26/14 Time: 21:14Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001R-squared0.537929Mean dependent var62.50000Adju
6、sted 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+0.3872
7、76x3(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
8、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: 12/03/14 Time: 17:00Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariableCoefficientStd. Errort-Statisti
9、cProb.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-
10、Quinn 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=0.176124X154.3
11、063 (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:XYMean6000.441902.5148Median2689.280209.3900Maximum27722.314895.410Minimum123.720
12、025.87000Std. 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
13、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: 12/03/14 Time: 18:00Sample (adjusted): 1 33
14、Included 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 criterion0.66
15、2028Sum 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
16、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: 12/01/14 Time: 12:40Sample: 1 12Included observations: 12VariableCoefficientStd. Errort-StatisticP
17、rob.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-Qu
18、inn 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:YXMean1619.3333.523333Median1630.0003.715000Maximum1860.00
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