1、计量经济学庞皓第三版课后答案 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 d
2、ependent 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)0.000134有上
3、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: 11/26/14 Time: 21:10Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.C38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825Mean dependent
4、 var62.50000Adjusted 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
5、=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: 11/26/14 Time: 21:14Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001R-squared0.537929Mean dependent var
6、62.50000Adjusted 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.
7、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。关于人均寿命与一岁儿童疫苗的模型,由上可知,可决系数为0.537
8、929,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: 12/03/14 Time: 17:00Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariableCoefficientStd. Err
9、ort-StatisticProb.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
10、.2751Hannan-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.
11、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:XYMean6000.441902.5148Median2689.280209.3900Maximum27722.314895.410Mi
12、nimum123.720025.87000Std. 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
13、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: 12/03/14 Time: 18:00Sample (adj
14、usted): 1 33Included 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 c
15、riterion0.662028Sum 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
16、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: 12/01/14 Time: 12:40Sample: 1 12Included observations: 12VariableCoefficientStd. Error
17、t-StatisticProb.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-57.42
18、275Hannan-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:YXMean1619.3333.523333Median1630.0003.715000Ma
19、ximum1860.0006.230000Minimum1419.0000.600000Std. Dev.131.22521.989419Skewness0.003403-0.060130Kurtosis2.3465111.664917Jarque-Bera0.2135470.898454Probability0.8987290.638121Sum19432.0042.28000Sum Sq. Dev.189420.743.53567Observations1212由上表可知,x2=(XiX)2=2x(n1)= 1.9894192 x (121)=43.5357(XfX)2=(4.53.523
20、333)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, 1556.647+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: 11/25/14 Time: 12:38Sample: 1 31Inclu
21、ded 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-squared0.666062Mean dependent var16.77355Adjusted R-squared0.628957S.D. dependent var8.252535S.E. of r
22、egression5.026889Akaike info criterion6.187394Sum squared resid682.2795Schwarz criterion6.372424Log likelihood-91.90460Hannan-Quinn criter.6.247709F-statistic17.95108Durbin-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
23、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
24、,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: 12/08/14 Time: 17:28Sample: 1 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.X25.1356701.0102705.0834650.0000LNX3-22.810056.771820-3.3683780.0023
25、LNX4-230.848149.46791-4.6666240.0001C1148.758228.29175.0319740.0000R-squared0.691952Mean dependent var16.77355Adjusted R-squared0.657725S.D. dependent var8.252535S.E. of regression4.828088Akaike info criterion6.106692Sum squared resid629.3818Schwarz criterion6.291723Log likelihood-90.65373Hannan-Quinn criter.6.167008F-
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