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5.2 （1）

①用图形法检验

绘制e2的散点图，用Eviews分析如下：

30,00025,00020,000E215,00010,0005,00001,0001,5002,0002,500X3,0003,5004,000 由上图可知，模型可能存在异方差，

② Goldfeld-Quanadt检验

1）定义区间为1-7时，由软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 14:52 Sample: 1 7 Included observations: 7

Variable Coefficient Std. Error t-Statistic T 35.20664 4.901492 7.182843 X 0.109949 0.061965 1.774380 C 77.12588 82.32844 0.936807 R-squared 0.943099 Mean dependent var

Adjusted R-squared 0.914649 S.D. dependent var S.E. of regression 31.63265 Akaike info criterion Sum squared resid 4002.499 Schwarz criterion Log likelihood -32.15324 Hannan-Quinn criter. F-statistic 33.14880 Durbin-Watson stat Prob(F-statistic) 0.003238

2 得∑e1i=4002.499

Prob. 0.0020 0.1507 0.4019 565.6857 108.2755 10.04378 10.02060 9.757267 1.426262

2）定义区间为12-18时，由软件分析得：

Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 14:55 Sample: 12 18 Included observations: 7

Variable Coefficient Std. Error t-Statistic Prob. T 52.40588 6.923378 7.569409 0.0016 X 0.068689 0.053763 1.277635 0.2705 C -8.789265 79.92542 -0.109968 0.9177 R-squared 0.984688 Mean dependent var 887.6143

Adjusted R-squared 0.977032 S.D. dependent var 274.4148 S.E. of regression 41.58810 Akaike info criterion 10.59103 Sum squared resid 6918.280 Schwarz criterion 10.56785 Log likelihood -34.06861 Hannan-Quinn criter. 10.30451 F-statistic 128.6166 Durbin-Watson stat 2.390329 Prob(F-statistic) 0.000234

2 得∑e2i=6918.280

3）根据Goldfeld-Quanadt检验，F统计量为： F=∑e2i2 /∑e1i2 =6918.280/4002.499=1.7285

在α=0.05水平下，分子分母的自由度均为4，查分布表得临界值F0.05（4,4）=6.39，因为F=1.7285< F0.05（4,4）=6.39，所以接受原假设，此检验表明模型不存在异方差。

（2）存在异方差，估计参数的方法： ①可以对模型进行变换

②使用加权最小二乘法进行计算，得出模型方程，并对其进行相关检验 ③对模型进行对数变换，进行分析

（3）评价：

3.3所得结论是可以相信的，随机扰动项之间不存在异方差。回归方程是显著的。

5.3

(1)由Eviews软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 16:00 Sample: 1 31 Included observations: 31

Variable Coefficient Std. Error t-Statistic Prob. X 1.244281 0.079032 15.74411 0.0000 C 242.4488 291.1940 0.832602 0.4119 R-squared 0.895260 Mean dependent var 4443.526

Adjusted R-squared 0.891649 S.D. dependent var 1972.072 S.E. of regression 649.1426 Akaike info criterion 15.85152 Sum squared resid 12220196 Schwarz criterion 15.94404 Log likelihood -243.6986 Hannan-Quinn criter. 15.88168 F-statistic 247.8769 Durbin-Watson stat 1.078581 Prob(F-statistic) 0.000000

由上表可知，2007年我国农村居民家庭人均消费支出（x）对人均纯收入（y）的模型为：

Y=1.244281X+242.4488

（2）

①由图形法检验

6,000,0005,000,0004,000,000E23,000,0002,000,0001,000,000002,0004,000X6,0008,00010,000 由上图可知，模型可能存在异方差。

②Goldfeld-Quanadt检验

1）定义区间为1-12时，由软件分析得：

Dependent Variable: Y1 Method: Least Squares Date: 12/24/15 Time: 16:05 Sample: 1 12 Included observations: 12

Variable Coefficient Std. Error t-Statistic X1 1.485296 0.500386 2.968297 C -550.5492 1220.063 -0.451247 R-squared 0.468390 Mean dependent var

Adjusted R-squared 0.415229 S.D. dependent var S.E. of regression 420.9803 Akaike info criterion Sum squared resid 1772245. Schwarz criterion Log likelihood -88.44437 Hannan-Quinn criter. F-statistic 8.810789 Durbin-Watson stat Prob(F-statistic) 0.014087

2 得∑e1i=1772245.

2）定义区间为20-31时，由软件分析得： Dependent Variable: Y1 Method: Least Squares Date: 12/24/15 Time: 16:16 Sample: 20 31 Included observations: 12

Variable Coefficient Std. Error t-Statistic X1 1.086940 0.148863 7.301623 C 1173.307 733.2520 1.600141 R-squared 0.842056 Mean dependent var

Adjusted R-squared 0.826262 S.D. dependent var S.E. of regression 889.3633 Akaike info criterion Sum squared resid 7909670. Schwarz criterion Log likelihood -97.41940 Hannan-Quinn criter. F-statistic 53.31370 Durbin-Watson stat Prob(F-statistic) 0.000026

2 得∑e2i=7909670.

3）根据Goldfeld-Quanadt检验，F统计量为： F=∑e2i2 /∑e1i2 =7909670./ 1772245=4.4631

Prob. 0.0141 0.6614 3052.950 550.5148 15.07406 15.15488 15.04414 2.354167

Prob. 0.0000 0.1407 6188.329 2133.692 16.56990 16.65072 16.53998 2.339767

在α=0.05水平下，分子分母的自由度均为10，查分布表得临界值F0.05（10,10）=2.98，因为F=4.4631> F0.05（10,10）=2.98，所以拒绝原假设，此检验表明模型存在异方差。 （3）

1）采用WLS法估计过程中， ①用权数w1=1/X,建立回归得： Dependent Variable: Y Method: Least Squares Date: 12/24/15 Time: 16:29 Sample: 1 31 Included observations: 31 Weighting series: W1

Variable Coefficient Std. Error t-Statistic Prob. X 1.425859 0.119104 11.97157 0.0000 C -334.8131 344.3523 -0.972298 0.3389 Weighted Statistics R-squared 0.831707 Mean dependent var 3946.082

Adjusted R-squared 0.825904 S.D. dependent var 536.1907 S.E. of regression 536.6796 Akaike info criterion 15.47102 Sum squared resid 8352726. Schwarz criterion 15.56354 Log likelihood -237.8008 Hannan-Quinn criter. 15.50118 F-statistic 143.3184 Durbin-Watson stat 1.369081 Prob(F-statistic) 0.000000

Unweighted Statistics R-squared 0.875855 Mean dependent var 4443.526

Adjusted R-squared 0.871574 S.D. dependent var 1972.072 S.E. of regression 706.7236 Sum squared resid 14484289 Durbin-Watson stat 1.532908