第三章第五题
（1）第一种方法
得到可支配收入X和消费性支出Y的散点图
由散点图可以看出，随着可支配收入的增加，消费性支出也不断增加，但其中离散程度也在扩大，表示其中可能存在递增异方差。

第二种方法：残差检验法
建立一元线性回归模型：Y=β0+β1X+u i
Dependent Variable: Y
Method: Least Squares
Date: 10/27/19 Time: 16:05
Sample: 1 28
Included observations: 28
Variable Coefficient Std. Error t-Statistic Prob.
C 735.1080 477.1123 1.540744 0.1355
X 0.666222 0.030558 21.80213 0.0000
R-squared 0.948138 Mean dependent var 10780.65
Adjusted R-squared 0.946144 S.D. dependent var 2823.752
S.E. of regression 655.3079 Akaike info criterion 15.87684
Sum squared resid 11165139 Schwarz criterion 15.97199
Log likelihood -220.2757 Hannan-Quinn criter. 15.90593
F-statistic 475.3327 Durbin-Watson stat 1.778976
Prob(F-statistic) 0.000000
模型残差分布图
由图可见，回归方程的残差分布存在明显的不一致趋势，即表明存在异方差性。

E2对X i的散点图
随即干扰项可能存在异方差性。

第四种方法帕克检验
残差平方的对数回归
Dependent Variable: LNE2
Method: Least Squares
Date: 10/27/19 Time: 16:39
Sample: 1 28
Included observations: 28
Variable Coefficient Std. Error t-Statistic Prob.
C -19.65780 19.42926 -1.011763 0.3210
LNX 3.267028 2.025169 1.613213 0.1188
R-squared 0.090987 Mean dependent var 11.67640 Adjusted R-squared 0.056025 S.D. dependent var 2.581025 S.E. of regression 2.507682 Akaike info criterion 4.745344 Sum squared resid 163.5002 Schwarz criterion 4.840501 Log likelihood -64.43481 Hannan-Quinn criter. 4.774434 F-statistic 2.602455 Durbin-Watson stat 1.560974 Prob(F-statistic) 0.118772
残差平方的对数的回归模型估计结果及帕克检验结果Heteroskedasticity Test: Harvey
F-statistic 2.602455 Prob. F(1,26) 0.1188 Obs*R-squared 2.547639 Prob. Chi-Square(1) 0.1105 Scaled explained SS 3.316334 Prob. Chi-Square(1) 0.0686
Test Equation:
Dependent Variable: LRESID2
Method: Least Squares
Date: 10/27/19 Time: 16:51
Sample: 1 28
Included observations: 28
Variable Coefficient Std. Error t-Statistic Prob.
C -19.65780 19.42926 -1.011763 0.3210
LOG(X) 3.267028 2.025169 1.613213 0.1188
R-squared 0.090987 Mean dependent var 11.67640 Adjusted R-squared 0.056025 S.D. dependent var 2.581025 S.E. of regression 2.507682 Akaike info criterion 4.745344 Sum squared resid 163.5002 Schwarz criterion 4.840501 Log likelihood -64.43481 Hannan-Quinn criter. 4.774434
F-statistic 2.602455 Durbin-Watson stat 1.560974 Prob(F-statistic) 0.118772
（2）根据帕克检验，可得出lne2i=-19.6578+3.267028X I
加权最小二乘的回归模型
Dependent Variable: Y
Method: Least Squares
Date: 10/27/19 Time: 17:06
Sample: 1 28
Included observations: 28
Weighting series: W
Weight type: Inverse standard deviation (EViews default scaling)
Variable Coefficient Std. Error t-Statistic Prob.
C 745.5974 613.3528 1.215609 0.2351
X 0.665574 0.045747 14.54896 0.0000
Weighted Statistics
R-squared 0.890606 Mean dependent var 9991.055 Adjusted R-squared 0.886398 S.D. dependent var 1601.638 S.E. of regression 550.5512 Akaike info criterion 15.52847 Sum squared resid 7880773. Schwarz criterion 15.62362 Log likelihood -215.3985 Hannan-Quinn criter. 15.55756 F-statistic 211.6722 Durbin-Watson stat 1.625011 Prob(F-statistic) 0.000000 Weighted mean dep. 9551.014
Unweighted Statistics
R-squared 0.948137 Mean dependent var 10780.65 Adjusted R-squared 0.946143 S.D. dependent var 2823.752 S.E. of regression 655.3140 Sum squared resid 11165346 Durbin-Watson stat 1.784481
加权最小二乘估计的white检验结果Heteroskedasticity Test: White
F-statistic 1.047596 Prob. F(3,24) 0.3896 Obs*R-squared 3.242043 Prob. Chi-Square(3) 0.3558 Scaled explained SS 1.213267 Prob. Chi-Square(3) 0.7498。