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R2=0.984983 F=1049.444 DW=1.830746 式中，Yt*=Yt-0.657352Yt-1, Xt*=Xt-0.657352Xt-1

由于使用了广义差分数据，样本容量减少了1个，为18个。查5%显著水平的DW统计表可知，dL=1.158,dU=1.391模型中DW=1,830746，du

②用科克伦-奥克特迭代法，用EVIews分析结果如下： Dependent Variable: Y Method: Least Squares Date: 12/26/15 Time: 09:45 Sample (adjusted): 2 19 Included observations: 18 after adjustments Convergence achieved after 5 iterations

Variable Coefficient Std. Error t-Statistic C 104.0449 23.87618 4.357687 X 0.669262 0.020831 32.12757 AR(1) 0.630015 0.164218 3.836462 R-squared 0.997097 Mean dependent var

Adjusted R-squared 0.996710 S.D. dependent var S.E. of regression 13.70843 Akaike info criterion Sum squared resid 2818.814 Schwarz criterion Log likelihood -71.02419 Hannan-Quinn criter. F-statistic 2575.896 Durbin-Watson stat Prob(F-statistic) 0.000000

Inverted AR Roots .63

所得方程为：

Yt=104.0449+0.669262Xt

Prob. 0.0006 0.0000 0.0016 719.1867 238.9866 8.224910 8.373306 8.245372 1.787878

（3）经济意义：人均实际收入每增加1元，平均说来人均时间消费支出将增加0.669262元。

6.4 （1）

1）针对对数模型，用Eviews分析结果如下： Dependent Variable: LNY Method: Least Squares Date: 12/26/15 Time: 10:03 Sample: 1980 2000 Included observations: 21

Variable Coefficient Std. Error t-Statistic Prob. LNX 0.951090 0.038897 24.45123 0.0000 C 2.171041 0.241025 9.007529 0.0000 R-squared 0.969199 Mean dependent var 8.039307

Adjusted R-squared 0.967578 S.D. dependent var 0.565486 S.E. of regression 0.101822 Akaike info criterion -1.640785 Sum squared resid 0.196987 Schwarz criterion -1.541307 Log likelihood 19.22825 Hannan-Quinn criter. -1.619196 F-statistic 597.8626 Durbin-Watson stat 1.159788 Prob(F-statistic) 0.000000

所得模型为：

lnY=0,951090lnX+2.171041 se=(0.038897) (0.241025) t=(24.45123) (9.007529)

R2=0.969199 F=597.8626 DW=1.159788

2）检验模型的自相关性

该回归方程可决系数较高，回归系数均显著。对样本量为21，一个解释变量的模型，5%的显著水平，查DW统计表可知，dL=1.221，dU=1.420，模型中DW=1.159788< dL,显然模型中有自相关。

(2)用广义差分法处理模型：

1）为估计自相关系数ρ。对et进行滞后一期的自回归，用EViews分析结果如下： Dependent Variable: E Method: Least Squares Date: 12/26/15 Time: 10:18 Sample (adjusted): 1982 2000 Included observations: 19 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. E(-1) -0.012872 0.280581 -0.045878 0.9639 R-squared 0.000073 Mean dependent var -2.556737

Adjusted R-squared 0.000073 S.D. dependent var 397.7924 S.E. of regression 397.7778 Akaike info criterion 14.86086 Sum squared resid 2848090. Schwarz criterion 14.91057 Log likelihood -140.1782 Hannan-Quinn criter. 14.86927 Durbin-Watson stat 1.700254

由上可知，ρ=-0.012872

2）对原模型进行广义差分回归，用Eviews进行分析所得结果如下： Dependent Variable: Y+0.012872*Y(-1) Method: Least Squares Date: 12/26/15 Time: 10:25 Sample (adjusted): 1981 2000 Included observations: 20 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. C -104.9645 197.7928 -0.530679 0.6021

X+0.012872*X(-1) 6.653757 0.304157 21.87605 0.0000

R-squared 0.963751 Mean dependent var 3753.934

Adjusted R-squared 0.961737 S.D. dependent var 2045.606 S.E. of regression 400.1404 Akaike info criterion 14.91615 Sum squared resid 2882022. Schwarz criterion 15.01572 Log likelihood -147.1615 Hannan-Quinn criter. 14.93559 F-statistic 478.5614 Durbin-Watson stat 1.822259 Prob(F-statistic) 0.000000

由上图可知回归方程为： Yt*=-104.9645+6.653757Xt* Se=(197.7928)( 0.304157) t=(-0.530679)( 21.87605)

R2=0.963751 F=478.5614DW=1.8222596 式中，Yt*=Yt+0.012872Yt-1, Xt*=Xt+0.012872Xt-1

由于使用了广义差分数据，样本容量减少了1个，为20个。查5%显著水平的DW统计表可知，dL=1.201,dU=1.411模型中DW=1.8222596，du

（3）对于此模型，用Eviews分析结果如下： Dependent Variable: LNY1 Method: Least Squares Date: 12/26/15 Time: 10:32 Sample (adjusted): 1981 2000 Included observations: 20 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. LNX1 0.442224 0.066024 6.697901 0.0000 C 0.054047 0.013322 4.056896 0.0007 R-squared 0.713658 Mean dependent var 0.091592

Adjusted R-squared 0.697750 S.D. dependent var 0.098311 S.E. of regression 0.054049 Akaike info criterion -2.903219 Sum squared resid 0.052583 Schwarz criterion -2.803646 Log likelihood 31.03219 Hannan-Quinn criter. -2.883781 F-statistic 44.86188 Durbin-Watson stat 1.590363 Prob(F-statistic) 0.000003

由题目可知，此模型样本容量为20，查5%显著水平的DW统计表可知，dL=1.201,dU=1.411模型中DW=1.590363，du