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通过图形看到，回归线向上倾斜，大致判断存在异方差性，但是，图示法并不准确，下面使用White异方差检验法进行检验，分别选择不带有交叉项和带有交叉项的White异方差检验法。得到下面的检验结果：

表5：不带有交叉项的White异方差检验结果

Heteroskedasticity Test: White F-statistic

75.59849 Prob. F(3,26) 26.91450 Prob. Chi-Square(3) 52.75104 Prob. Chi-Square(3)

Coefficient 1.51E+08 -0.029775 0.017419 -2715.996

Std. Error 1.08E+08 0.009593 0.001245 8243.375

t-Statistic 1.398492 -3.103868 13.98776 -0.329476

0.0000 0.0000 0.0000 Prob. 0.1738 0.0046 0.0000 0.7444 77607780 1.80E+08 38.81668 39.00351 38.87645 1.947056

Obs*R-squared Scaled explained SS

Test Equation:

Dependent Variable: RESID^2 Method: Least Squares Date: 1/7/15 Time: 17:53 Sample: 1980 2009 Included observations: 30

C X1^2 X2^2 X3^2

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

0.897150 Mean dependent var 0.885283 S.D. dependent var 61075426 Akaike info criterion 9.70E+16 Schwarz criterion -578.2502 Hannan-Quinn criter. 75.59849 Durbin-Watson stat 0.000000

表6：带有交叉项的White异方差检验结果

Heteroskedasticity Test: White F-statistic

33.57944 Prob. F(9,20) 28.13789 Prob. Chi-Square(9) 55.14882 Prob. Chi-Square(9)

0.0000 0.0009 0.0000

Obs*R-squared Scaled explained SS

Test Equation:

Dependent Variable: RESID^2

Method: Least Squares Date: 1/7/15 Time: 17:54 Sample: 1980 2009 Included observations: 30

C X1 X1^2 X1*X2 X1*X3 X2 X2^2 X2*X3 X3 X3^2

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

Coefficient -2.08E+09 -34576.99 0.189719 -0.297299 127.5161 29147.14 0.033135 -97.11637 55473498 -283697.5

Std. Error 4.06E+09 39720.32 0.224091 0.442472 329.2824 35662.29 0.007760 96.87489 68538734 290382.6

t-Statistic -0.512912 -0.870512 0.846615 -0.671906 0.387254 0.817310 4.270053 -1.002493 0.809374 -0.976978

Prob. 0.6136 0.3943 0.4072 0.5093 0.7027 0.4234 0.0004 0.3281 0.4278 0.3403 77607780 1.80E+08 38.71168 39.17875 38.86110 2.262413

0.937930 Mean dependent var 0.909998 S.D. dependent var 54097636 Akaike info criterion 5.85E+16 Schwarz criterion -570.6752 Hannan-Quinn criter. 33.57944 Durbin-Watson stat 0.000000

使用White检验法不论是否带有交叉项，所得的检验伴随概率均小于5%，均在5%的显著水平下拒绝方程不存在异方差性的原假设，认为模型具有比较严重的异方差性。需要对模型进行修正。

②多重共线性检验： 用逐步回归法检验如下

以?为被解释变量，逐个引入解释变量?1、?2、?3，构成回归模型，进行模型估计。

表7： 被解释变量?与?1最小二乘估计结果

Dependent Variable: Y Method: Least Squares Date: 1/7/15 Time: 18:32 Sample: 1980 2009 Included observations: 30

X1 C

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

Coefficient 6.692086 -334986.1

Std. Error 0.880526 56283.70

t-Statistic 7.600101 -5.951743

Prob. 0.0000 0.0000 85749.31 95692.85 24.75574 24.84915 24.78562 0.096883

0.673513 Mean dependent var 0.661853 S.D. dependent var 55645.78 Akaike info criterion 8.67E+10 Schwarz criterion -369.3361 Hannan-Quinn criter. 57.76153 Durbin-Watson stat 0.000000

表8： 被解释变量?与?2最小二乘估计结果

Dependent Variable: Y Method: Least Squares Date: 1/7/15 Time: 18:34 Sample: 1980 2009 Included observations: 30

X2 C

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

Coefficient 1.688594 19746.45

Std. Error 0.063011 4234.328

t-Statistic 26.79831 4.663420

Prob. 0.0000 0.0001 85749.31 95692.85 22.59239 22.68580 22.62227 0.402624

0.962474 Mean dependent var 0.961134 S.D. dependent var 18865.38 Akaike info criterion 9.97E+09 Schwarz criterion -336.8858 Hannan-Quinn criter. 718.1495 Durbin-Watson stat 0.000000

表9： 被解释变量?与?3最小二乘估计结果

Dependent Variable: Y Method: Least Squares Date: 1/7/15 Time: 18:36 Sample: 1980 2009 Included observations: 30

Coefficient

Std. Error

t-Statistic

Prob.

X3 C

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

-4733.789 586426.4

2602.669 275788.7

-1.818821 2.126361

0.0797 0.0424 85749.31 95692.85 25.76343 25.85685 25.79332 0.120717

0.105663 Mean dependent var 0.073722 S.D. dependent var 92097.98 Akaike info criterion 2.37E+11 Schwarz criterion -384.4515 Hannan-Quinn criter. 3.308109 Durbin-Watson stat 0.079650

由图可以看出，?与?2的拟合优度是最大的，R-squared=0.962474。再做

?与?1和?2的回归模型。

表10： 被解释变量?与?1和?2的最小二乘估计结果

Dependent Variable: Y Method: Least Squares Date: 1/7/15 Time: 18:47 Sample: 1980 2009 Included observations: 30

X1 X2 C

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

Coefficient 1.963607 1.391253 -92084.42

Std. Error 0.218188 0.046055 12611.85

t-Statistic 8.999617 30.20878 -7.301423

Prob. 0.0000 0.0000 0.0000 85749.31 95692.85 21.27282 21.41294 21.31765 0.956357

0.990618 Mean dependent var 0.989923 S.D. dependent var 9606.088 Akaike info criterion 2.49E+09 Schwarz criterion -316.0923 Hannan-Quinn criter. 1425.411 Durbin-Watson stat 0.000000

再做?与?1和?2、?3的回归模型。

表11： 被解释变量?与?1和?2、?3的最小二乘估计结果