第二章
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: 12/03/14 Time: 17:00 Sample (adjusted): 1 33
Included observations: 33 after adjustments
Variable
X C
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic
Coefficie
nt Std. Error t-Statistic Prob.?? 0.176124 0.004072 43.25639 0.0000 -154.306
3 39.08196 -3.948274 0.0004 ????Mean 902.514
0.983702 dependent var 8
????S.D. dependent 1351.00
0.983177 var 9
????Akaike info 13.2288
175.2325 criterion 0
????Schwarz 13.3194
951899.7 criterion 9 -216.275????Hannan-Quinn 13.2593
1 criter. 1 ????Durbin-Watson 0.10002
1871.115 stat 1
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,检验模型的显着性:
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,对斜率系数的显着性检验表明,全省生产总值对财政预算总收入有显着影响。 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 X Y ?6000.441 ?902.5148 ?2689.280 ?209.3900 ?27722.31 ?4895.410 ?123.7200 ?25.87000 ?7608.021 ?1351.009 ?1.432519 ?1.663108 ?4.010515 ?4.590432 ?Jarque-Bera ?12.69068 ?18.69063 ?Probability ?0.001755 ?0.000087 ?Sum ?Sum Sq. Dev. ?198014.5 ?29782.99 ?1.85E+09 ?Observations ?33 ?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
当Xf=32000时,将相关数据代入计算得到:
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: 12/03/14 Time: 18:00 Sample (adjusted): 1 33
Included observations: 33 after adjustments
Variable LNX C
R-squared Adjusted R-squared S.E. of regression Sum squared resid
Log likelihood
Coefficie
nt Std. Error t-Statistic Prob.?? 0.980275 0.034296 28.58268 0.0000 -1.91828
9 0.268213 -7.152121 0.0000 ????Mean 5.57312
0.963442 dependent var 0
????S.D. dependent 1.68418
0.962263 var 9
????Akaike info 0.66202
0.327172 criterion 8
????Schwarz 0.75272
3.318281 criterion 6 -8.92346????Hannan-Quinn 0.69254
F-statistic
8 criter. 5 ????Durbin-Watson 0.09620
816.9699 stat 8
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,检验其显着性: 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,对斜率系数的显着性检验表明,全省生产总值对财政预算总收入有显着影响。 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: 12/01/14 Time: 12:40 Sample: 1 12
Included observations: 12
Variable X C
R-squared Adjusted R-squared
Coefficie
nt Std. Error t-Statistic Prob.?? -64.1840
0 4.809828 -13.34434 0.0000
1845.475 19.26446 95.79688 0.0000 ????Mean 1619.33
0.946829 dependent var 3
????S.D. dependent 131.225
0.941512 var 2
S.E. of regression Sum squared resid Log likelihood F-statistic ????Akaike info 9.90379
31.73600 criterion 2
????Schwarz 9.98461
10071.74 criterion 0 -57.4227????Hannan-Quinn 9.87387
5 criter. 1 ????Durbin-Watson 1.17240
178.0715 stat 7
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 ②再进行区间估计: 用Eviews分析: ?Mean ?Median ?Maximum ?Minimum ?Std. Dev. ?Skewness ?Kurtosis
Y X ?1619.333 ?3.523333 ?1630.000 ?3.715000 ?1860.000 ?6.230000 ?1419.000 ?0.600000 ?131.2252 ?1.989419 ?0.003403 -0.060130 ?2.346511 ?1.664917 ?Jarque-Bera ?0.213547 ?0.898454 ?Probability ?0.898729 ?0.638121 ?Sum ?Sum Sq. ?19432.00 ?42.28000 ?189420.7 ?43.53567