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④当w3=1/sqr(x)时，用软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/26/15 Time: 07:34 Sample: 1 34 Included observations: 34 Weighting series: W3

Variable Coefficient Std. Error t-Statistic X 0.744661 0.019825 37.56252 P 0.451861 0.179971 2.510739 C -13.49643 25.37768 -0.531823 Weighted Statistics R-squared 0.989356 Mean dependent var

Adjusted R-squared 0.988670 S.D. dependent var S.E. of regression 73.35237 Akaike info criterion Sum squared resid 166797.7 Schwarz criterion Log likelihood -192.7129 Hannan-Quinn criter. F-statistic 1440.783 Durbin-Watson stat Prob(F-statistic) 0.000000

Unweighted Statistics R-squared 0.979407 Mean dependent var

Adjusted R-squared 0.978079 S.D. dependent var S.E. of regression 176.0098 Sum squared resid Durbin-Watson stat 1.761225

所得模型为：

Y=0.744661X+0.451861p-13.49643

Prob. 0.0000 0.0175 0.5986 776.3266 367.3152 11.51252 11.64720 11.55845 1.599590

1295.802 1188.791 960362.6

对所得模型进行White检验得： Heteroskedasticity Test: White

F-statistic 4.459272 Prob. F(5,28) 0.0041

Obs*R-squared 15.07219 Prob. Chi-Square(5) 0.0101 Scaled explained SS 72.39077 Prob. Chi-Square(5) 0.0000

Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/26/15 Time: 07:43 Sample: 1 34 Included observations: 34 Collinear test regressors dropped from specification

Variable Coefficient Std. Error t-Statistic Prob. C 61163.22 27531.93 2.221538 0.0346 WGT^2 28251.98 17350.39 1.628320 0.1147 X^2*WGT^2 -0.001093 0.006624 -0.164950 0.8702 X*P*WGT^2 -0.235836 0.077110 -3.058447 0.0049 P^2*WGT^2 1.236884 0.644872 1.918030 0.0654 P*WGT^2 -503.3080 262.5884 -1.916718 0.0655

R-squared 0.443300 Mean dependent var 4905.814

Adjusted R-squared 0.343889 S.D. dependent var 16926.97 S.E. of regression 13710.96 Akaike info criterion 22.04856 Sum squared resid 5.26E+09 Schwarz criterion 22.31792 Log likelihood -368.8256 Hannan-Quinn criter. 22.14042 F-statistic 4.459272 Durbin-Watson stat 2.450171 Prob(F-statistic) 0.004103

因为nR2=15.07219>0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。

综上所述，修改后的模型为：

Y= Y=0.723218X+0.719506p-44.72084 t=(31.49212) (5.099705) (-3.410502) R2=0.992755 F=2123.843 DW=1.298389

(3)体会：对于不同的模型，可采取对数模型法或者加权二乘法对具有异方差性的模型进行改进，从而消除异方差。但对于不同的模型，自由度的不同，可能导致改进的方法不同，所

以要对改进的模型进行进一步的检验才行。 6.1

(1)建立居民收入-消费模型，用Eviews分析结果如下： Dependent Variable: Y Method: Least Squares Date: 12/26/15 Time: 08:22 Sample: 1 19 Included observations: 19

Variable Coefficient Std. Error t-Statistic X 0.690488 0.012877 53.62068 C 79.93004 12.39919 6.446390 R-squared 0.994122 Mean dependent var

Adjusted R-squared 0.993776 S.D. dependent var S.E. of regression 19.44245 Akaike info criterion Sum squared resid 6426.149 Schwarz criterion Log likelihood -82.28490 Hannan-Quinn criter. F-statistic 2875.178 Durbin-Watson stat Prob(F-statistic) 0.000000

所得模型为： Y=0.690488X+79.93004 Se=(0.012877)(12.39919) t=(53.62068)(6.446390) R2=0.994122 F=2875.178 DW=0.574663 （2） 1）检验模型中存在的问题 ①做出残差图如下： 50403020100-10-20-30-4024681012141618 Prob. 0.0000 0.0000 700.2747 246.4491 8.872095 8.971510 8.888920 0.574663

Y Residuals 残差的变动有系统模式，连续为正和连续为负，表明残差项存在一阶自相关。

②该回归方程可决系数较高，回归系数均显著。对样本量为19，一个解释变量的模型，5%的显著水平，查DW统计表可知，dL=1.180，dU=1.401，模型中DW=0.574663,< dL,显然模型中有自相关。

③对模型进行BG检验，用Eviews分析结果如下： Breusch-Godfrey Serial Correlation LM Test:

F-statistic 4.811108 Prob. F(2,15) 0.0243

Obs*R-squared 7.425088 Prob. Chi-Square(2) 0.0244

Test Equation: Dependent Variable: RESID Method: Least Squares Date: 12/26/15 Time: 08:27 Sample: 1 19 Included observations: 19 Presample missing value lagged residuals set to zero.

Variable Coefficient Std. Error t-Statistic Prob. X -0.003275 0.010787 -0.303586 0.7656 C 1.929546 10.35593 0.186323 0.8547 RESID(-1) 0.608886 0.292707 2.080189 0.0551 RESID(-2) 0.089988 0.291120 0.309110 0.7615

R-squared 0.390794 Mean dependent var -1.65E-13

Adjusted R-squared 0.268953 S.D. dependent var 18.89466 S.E. of regression 16.15518 Akaike info criterion 8.587023 Sum squared resid 3914.848 Schwarz criterion 8.785852 Log likelihood -77.57671 Hannan-Quinn criter. 8.620672 F-statistic 3.207406 Durbin-Watson stat 1.570723 Prob(F-statistic) 0.053468

如上表显示，LM=TR2=7.425088，其p值为0.0244，表明存在自相关。

2）对模型进行处理： ①采取广义差分法

a)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: 08:34 Sample (adjusted): 2 19 Included observations: 18 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. E(-1) 0.657352 0.177626 3.700759 0.0018 R-squared 0.440747 Mean dependent var 1.717433

Adjusted R-squared 0.440747 S.D. dependent var 17.85134 S.E. of regression 13.34980 Akaike info criterion 8.074833 Sum squared resid 3029.692 Schwarz criterion 8.124298 Log likelihood -71.67349 Hannan-Quinn criter. 8.081653 Durbin-Watson stat 1.634573

由上可知，ρ=0.657352

b)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-0.657352*Y(-1) Method: Least Squares Date: 12/26/15 Time: 08:41 Sample (adjusted): 2 19 Included observations: 18 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. C 35.97761 8.103546 4.439737 0.0004

X-0.657352*X(-1) 0.668695 0.020642 32.39512 0.0000

R-squared 0.984983 Mean dependent var 278.1002

Adjusted R-squared 0.984044 S.D. dependent var 105.1781 S.E. of regression 13.28570 Akaike info criterion 8.115693 Sum squared resid 2824.158 Schwarz criterion 8.214623 Log likelihood -71.04124 Hannan-Quinn criter. 8.129334 F-statistic 1049.444 Durbin-Watson stat 1.830746 Prob(F-statistic) 0.000000

由上图可知回归方程为： Yt*=35.97761+0.668695Xt* Se=(8.103546)(0.020642) t=(4.439737)(32.39512)