计量经济学第三版课后习题答案

第二章 简单线性回归模型 2.1

(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: Y Method: Least Squares Date: 12/23/15 Time: 14:37 Sample: 1 22 Included observations: 22

Variable Coefficient Std. Error t-Statistic Prob. C 56.64794 1.960820 28.88992 0.0000 X1 0.128360 0.027242 4.711834 0.0001 R-squared 0.526082 Mean dependent var 62.50000

Adjusted R-squared 0.502386 S.D. dependent var 10.08889 S.E. of regression 7.116881 Akaike info criterion 6.849324 Sum squared resid 1013.000 Schwarz criterion 6.948510 Log likelihood -73.34257 Hannan-Quinn criter. 6.872689 F-statistic 22.20138 Durbin-Watson stat 0.629074 Prob(F-statistic) 0.000134

有上可知,关系式为y=56.64794+0.128360x1

②关于人均寿命与成人识字率的关系,用Eviews分析如下: Dependent Variable: Y Method: Least Squares Date: 12/23/15 Time: 15:01 Sample: 1 22 Included observations: 22

Variable Coefficient Std. Error t-Statistic Prob. C 38.79424 3.532079 10.98340 0.0000 X2 0.331971 0.046656 7.115308 0.0000 R-squared 0.716825 Mean dependent var 62.50000

Adjusted R-squared 0.702666 S.D. dependent var 10.08889 S.E. of regression 5.501306 Akaike info criterion 6.334356 Sum squared resid 605.2873 Schwarz criterion 6.433542 Log likelihood -67.67792 Hannan-Quinn criter. 6.357721 F-statistic 50.62761 Durbin-Watson stat 1.846406 Prob(F-statistic) 0.000001

由上可知,关系式为y=38.79424+0.331971x2

③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: Y Method: Least Squares Date: 12/23/14 Time: 15:20 Sample: 1 22 Included observations: 22

Variable Coefficient Std. Error t-Statistic Prob. C 31.79956 6.536434 4.864971 0.0001 X3 0.387276 0.080260 4.825285 0.0001 R-squared 0.537929 Mean dependent var 62.50000

Adjusted R-squared 0.514825 S.D. dependent var 10.08889 S.E. of regression 7.027364 Akaike info criterion 6.824009 Sum squared resid 987.6770 Schwarz criterion 6.923194 Log likelihood -73.06409 Hannan-Quinn criter. 6.847374 F-statistic 23.28338 Durbin-Watson stat 0.952555 Prob(F-statistic) 0.000103

由上可知,关系式为y=31.79956+0.387276x3

(2)①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(β1)=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响。

②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(β2)=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。

③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(β3)=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)

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: Y Method: Least Squares Date: 12/23/15 Time: 17:46 Sample (adjusted): 1 33 Included observations: 33 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. X 0.176124 0.004072 43.25639 0.0000 C -154.3063 39.08196 -3.948274 0.0004 R-squared 0.983702 Mean dependent var 902.5148

Adjusted R-squared 0.983177 S.D. dependent var 1351.009 S.E. of regression 175.2325 Akaike info criterion 13.22880 Sum squared resid 951899.7 Schwarz criterion 13.31949 Log likelihood -216.2751 Hannan-Quinn criter. 13.25931 F-statistic 1871.115 Durbin-Watson stat 0.100021 Prob(F-statistic) 0.000000

②由上可知,模型的参数:斜率系数0.176124,截距为—154.3063

③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(β2)=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收入有显著影响。

④用规范形式写出检验结果如下:

Y=0.176124X—154.3063

(0.004072) (39.08196)

t= (43.25639) (-3.948274) R2=0.983702 F=1871.115 n=33

⑤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,

①进行点预测,由上可知Y=0.176124X—154.3063,代入可得: Y= Y=0.176124*32000—154.3063=5481.6617

②进行区间预测: 先由Eviews分析:

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis Jarque-Bera Probability Sum Sum Sq. Dev. Observations X 6000.441 2689.280 27722.31 123.7200 7608.021 1.432519 4.010515 12.69068 0.001755 198014.5 1.85E+09 33 Y 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=∑(Xi—X)2=δ2x(n—1)= 7608.0212 x (33—1)=1852223.473 (Xf—X)2=(32000— 6000.441)2=675977068.2 当Xf=32000时,将相关数据代入计算得到:

5481.6617—2.0395x175.2325x√1/33+1852223.473/675977068.2≤ Yf≤5481.6617+2.0395x175.2325x√1/33+1852223.473/675977068.2

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: LNY Method: Least Squares Date: 12/23/15 Time: 18:04 Sample (adjusted): 1 33 Included observations: 33 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. LNX 0.980275 0.034296 28.58268 0.0000 C -1.918289 0.268213 -7.152121 0.0000 R-squared 0.963442 Mean dependent var 5.573120

Adjusted R-squared 0.962263 S.D. dependent var 1.684189 S.E. of regression 0.327172 Akaike info criterion 0.662028 Sum squared resid 3.318281 Schwarz criterion 0.752726 Log likelihood -8.923468 Hannan-Quinn criter. 0.692545 F-statistic 816.9699 Durbin-Watson stat 0.096208 Prob(F-statistic) 0.000000

①模型方程为:lnY=0.980275lnX-1.918289

②由上可知,模型的参数:斜率系数为0.980275,截距为-1.918289

③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(β2)=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。

④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: Y Method: Least Squares Date: 12/23/15 Time: 20:11 Sample: 1 12 Included observations: 12

Variable Coefficient Std. Error t-Statistic Prob. X -64.18400 4.809828 -13.34434 0.0000 C 1845.475 19.26446 95.79688 0.0000 R-squared 0.946829 Mean dependent var 1619.333

Adjusted R-squared 0.941512 S.D. dependent var 131.2252 S.E. of regression 31.73600 Akaike info criterion 9.903792 Sum squared resid 10071.74 Schwarz criterion 9.984610 Log likelihood -57.42275 Hannan-Quinn criter. 9.873871 F-statistic 178.0715 Durbin-Watson stat 1.172407 Prob(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)

①首先进行点预测,由Y=1845.475--64.18400X得,当x=4.5,y=1556.647

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