庞浩计量经济学第二章答案.docx

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: 22Variable Coefficient Std. Error t-Statistic Prob. C 56.64794 1.960820 28.88992 0.0000X1 0.128360 0.027242 4.711834 0.0001R-squared 0.526082 M

2、ean dependent var 62.50000Adjusted R-squared 0.502386 S.D. dependent var 10.08889S.E. of regression 7.116881 Akaike info criterion 6.849324Sum squared resid 1013.000 Schwarz criterion 6.948510Log likelihood -73.34257 Hannan-Quinn criter. 6.872689F-statistic 22.20138 Durbin-Watson stat 0.629074Prob(F

3、-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: 11/26/14 Time: 21:10Sample: 1 22Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. C 38.79424 3.532079 10.98340 0.0000X2 0.331971 0.046656 7.115308

4、 0.0000R-squared 0.716825 Mean dependent var 62.50000Adjusted R-squared 0.702666 S.D. dependent var 10.08889S.E. of regression 5.501306 Akaike info criterion 6.334356Sum squared resid 605.2873 Schwarz criterion 6.433542Log likelihood -67.67792 Hannan-Quinn criter. 6.357721F-statistic 50.62761 Durbin

5、-Watson stat 1.846406Prob(F-statistic) 0.000001由上可知，关系式为 y=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: 22Variable Coefficient Std. Error t-Statistic Prob. C 31.79956 6.536434 4.864971 0.00

6、01X3 0.387276 0.080260 4.825285 0.0001R-squared 0.537929 Mean dependent var 62.50000Adjusted R-squared 0.514825 S.D. dependent var 10.08889S.E. of regression 7.027364 Akaike info criterion 6.824009Sum squared resid 987.6770 Schwarz criterion 6.923194Log likelihood -73.06409 Hannan-Quinn criter. 6.84

7、7374F-statistic 23.28338 Durbin-Watson stat 0.952555Prob(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）=4.711834t 0.025(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

8、。对于回归系数的 t 检验：t（ 2）=7.115308t 0.025(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）=4.825285t 0.025(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:

9、 12/03/14 Time: 17:00Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob. X 0.176124 0.004072 43.25639 0.0000C -154.3063 39.08196 -3.948274 0.0004R-squared 0.983702 Mean dependent var 902.5148Adjusted R-squared 0.983177 S.D. dependent va

10、r 1351.009S.E. of regression 175.2325 Akaike info criterion 13.22880Sum squared resid 951899.7 Schwarz criterion 13.31949Log likelihood -216.2751 Hannan-Quinn criter. 13.25931F-statistic 1871.115 Durbin-Watson stat 0.100021Prob(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

11、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 ）=43.25639t 0.025(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) (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

12、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：X YMean 6000.441 902.5148Median 2689.280 209.3900Maximum 27722.31 4895.410Minimum 123.7200 25.87000Std. Dev. 7608.021 1351.009Skewness 1.432519 1.663108Kurtosis 4.010515 4.590432Jarque-Bera 12.69068 18.69063P

13、robability 0.001755 0.000087Sum 198014.5 29782.99Sum Sq. Dev. 1.85E+09 58407195Observations 33 33由上表可知，x2=（X iX） 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：5481.66172.0395x175.2325x1/33+1852223.473/675977068.2Yf5481.6617+2.0395x175.2325x1/33+1

14、852223.473/675977068.2即 Yf 的置信区间为（5481.6617 64.9649, 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 33Included observations: 33 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob.

15、 LNX 0.980275 0.034296 28.58268 0.0000C -1.918289 0.268213 -7.152121 0.0000R-squared 0.963442 Mean dependent var 5.573120Adjusted R-squared 0.962263 S.D. dependent var 1.684189S.E. of regression 0.327172 Akaike info criterion 0.662028Sum squared resid 3.318281 Schwarz criterion 0.752726Log likelihoo

16、d -8.923468 Hannan-Quinn criter. 0.692545F-statistic 816.9699 Durbin-Watson stat 0.096208Prob(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

17、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: 12Variable Coefficient Std. Error t-Statistic Prob. X -64.18400 4.809828 -13.34434 0.0000C

18、1845.475 19.26446 95.79688 0.0000R-squared 0.946829 Mean dependent var 1619.333Adjusted R-squared 0.941512 S.D. dependent var 131.2252S.E. of regression 31.73600 Akaike info criterion 9.903792Sum squared resid 10071.74 Schwarz criterion 9.984610Log likelihood -57.42275 Hannan-Quinn criter. 9.873871F

19、-statistic 178.0715 Durbin-Watson stat 1.172407Prob(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：Y XMean 1619.333 3.523333Median 1630.000 3.715000Maximum 1860.000

20、 6.230000Minimum 1419.000 0.600000Std. Dev. 131.2252 1.989419Skewness 0.003403 -0.060130Kurtosis 2.346511 1.664917Jarque-Bera 0.213547 0.898454Probability 0.898729 0.638121Sum 19432.00 42.28000Sum Sq. Dev. 189420.7 43.53567Observations 12 12由上表可知，x2=（X iX） 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+2.228x31.73600x1/12+43.5357/0.95387843即 Yf 的置信区间为（1556.647 478.1231, 1556.647+478.1231）