第五章：异方差性(作业)
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为了研究中国出口商品总额EXPORT 对国内生产总值GDP 的影响，搜集了1990～2015年相关的指标数据，如表所示。
资料来源：《国家统计局网站》
(1) 根据以上数据，建立适当线性回归模型。
(2) 试分别用White 检验法与ARCH 检验法检验模型是否存在异方差 (3) 如果存在异方差，用适当方法加以修正。 解：（1）
100,000
200,000300,000400,000500,000600,000700,000X
Y
Dependent Variable: Y Method: Least Squares Date: 04/18/20 Time: 15:38
Sample: 1991 2015
Included observations: 25
Variable
Coefficient
Std. Error t-Statistic Prob.
C X
R-squared Mean dependent var Adjusted R-squared . dependent var . of regression Akaike info criterion
Sum squared resid +10 Schwarz criterion
Log likelihood Hannan-Quinn criter.
F-statistic Durbin-Watson stat Prob(F-statistic)
模型回归的结果：
^
673.0863 4.0611i
X i Y =-+
()(0.043820.1368)t =-
20.9463,25R n ==
（2）white: 该模型存在异方差
Heteroskedasticity Test: White
F-statistic Prob. F(2,22) Obs*R-squared Prob. Chi-Square(2) Scaled explained SS
Prob. Chi-Square(2)
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares Date: 04/18/20 Time: 17:45 Sample: 1991 2015
Included observations: 25
Variable
Coefficient
Std. Error t-Statistic Prob.
C +09
+09
X^2
X
R-squared Mean dependent var+09 Adjusted R-squared. dependent var+09
. of regression+09
Akaike info criterion
Sum squared resid+20Schwarz criterion
Log likelihood
Hannan-Quinn criter.
F-statistic Durbin-Watson stat
Prob(F-statistic)
ARCH检验：该模型存在异方差
Heteroskedasticity Test: ARCH
F-statistic Prob. F(1,22)
Obs*R-squared Prob. Chi-Square(1)
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 04/18/20 Time: 19:55
Sample (adjusted): 1992 2015
Included observations: 24 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C+08+08
RESID^2(-1)
R-squared Mean dependent var+09 Adjusted R-squared. dependent var+09
. of regression+09
Akaike info criterion
Sum squared resid+20Schwarz criterion
Log likelihood
Hannan-Quinn criter.
F-statistic Durbin-Watson stat Prob(F-statistic)
（3）修正：加权最小二乘法修正
Dependent Variable: Y
Method: Least Squares
Date: 04/18/20 Time: 20:46
Sample: 1991 2015
Included observations: 25
Weighting series: W2
Weight type: Inverse variance (average scaling)
Variable Coefficient Std. Error t-Statistic Prob.
C
X
Weighted Statistics
R-squared Mean dependent var
Adjusted R-squared. dependent var
. of regression
Akaike info criterion
Sum squared resid+09Schwarz criterion
Log likelihood
Hannan-Quinn criter.
F-statistic Durbin-Watson stat
Prob(F-statistic)Weighted mean dep.
Unweighted Statistics
R-squared Mean dependent var
Adjusted R-squared. dependent var
. of regression Sum squared resid+10修正后进行white检验：
Heteroskedasticity Test: White
F-statistic Prob. F(2,22)
Obs*R-squared Prob. Chi-Square(2)