3,200,000,0002,800,000,0002,400,000,0002,000,000,000E21,600,000,0001,200,000,000800,000,000400,000,000095100105110X3115120125
图6：初始模型的异方差性检验散点图
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: WhiteF-statisticObs*R-squaredScaled explained SS7.389277 Prob. F(3,31)14.59292 Prob. Chi-Square(3)16.04356 Prob. Chi-Square(3)0.00070.00220.0011Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 06/30/15 Time: 21:21Sample: 1 35Included observations: 35VariableCX1^2X2^2X3^2R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statisticProb(F-statistic)Coefficient-1.75E+080.0587460.00642012409.06Std. Error9.08E+080.0745670.00169669670.68t-Statistic-0.1924210.7878263.7860560.178110Prob. 0.84870.43680.00070.85983.88E+086.60E+0843.1131243.2908743.174481.6214090.416941 Mean dependent var0.360516 S.D. dependent var5.28E+08 Akaike info criterion8.63E+18 Schwarz criterion-750.4796 Hannan-Quinn criter.7.389277 Durbin-Watson stat0.000714 表6：带有交叉项的White异方差检验结果
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Heteroskedasticity Test: WhiteF-statisticObs*R-squaredScaled explained SS7.389277 Prob. F(3,31)14.59292 Prob. Chi-Square(3)16.04356 Prob. Chi-Square(3)0.00070.00220.0011Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 06/30/15 Time: 21:26Sample: 1 35Included observations: 35VariableCX1^2X2^2X3^2R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statisticProb(F-statistic)Coefficient-1.75E+080.0587460.00642012409.06Std. Error9.08E+080.0745670.00169669670.68t-Statistic-0.1924210.7878263.7860560.178110Prob. 0.84870.43680.00070.85983.88E+086.60E+0843.1131243.2908743.174481.6214090.416941 Mean dependent var0.360516 S.D. dependent var5.28E+08 Akaike info criterion8.63E+18 Schwarz criterion-750.4796 Hannan-Quinn criter.7.389277 Durbin-Watson stat0.000714 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。
被解释变量?与?1最小二乘估计结果
Dependent Variable: YMethod: Least SquaresDate: 06/30/15 Time: 21:31Sample: 1 35Included observations: 35VariableCX1R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statisticProb(F-statistic)Coefficient-561739.010.85155Std. Error137253.72.062978t-Statistic-4.0927055.260138Prob. 0.00030.0000149841.8183380.526.5528926.6417626.583570.0554310.456065 Mean dependent var0.439582 S.D. dependent var137280.6 Akaike info criterion6.22E+11 Schwarz criterion-462.6755 Hannan-Quinn criter.27.66905 Durbin-Watson stat0.000009
被解释变量?与?2最小二乘估计结果
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Dependent Variable: YMethod: Least SquaresDate: 06/30/15 Time: 21:32Sample: 1 35Included observations: 35VariableCX2R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statisticProb(F-statistic)Coefficient33329.161.328518Std. Error6383.8270.039847t-Statistic5.22087433.34054Prob. 0.00000.0000149841.8183380.523.6155223.7043923.646200.2223430.971169 Mean dependent var0.970295 S.D. dependent var31605.85 Akaike info criterion3.30E+10 Schwarz criterion-411.2716 Hannan-Quinn criter.1111.591 Durbin-Watson stat0.000000
被解释变量?与?3最小二乘估计结果
Dependent Variable: YMethod: Least SquaresDate: 06/30/15 Time: 21:34Sample: 1 35Included observations: 35VariableCX3R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statisticProb(F-statistic)Coefficient1065014.-8683.079Std. Error523816.04961.716t-Statistic2.033182-1.750015Prob. 0.05010.0894149841.8183380.527.0730727.1619427.103750.0932610.084923 Mean dependent var0.057194 S.D. dependent var178059.2 Akaike info criterion1.05E+12 Schwarz criterion-471.7786 Hannan-Quinn criter.3.062554 Durbin-Watson stat0.089410 由图可以看出，?与?2的拟合优度是最大的，R-squared=0.971169。再做
?与?1和?2的回归模型。
被解释变量?与?1和?2的最小二乘估计结果
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Dependent Variable: YMethod: Least SquaresDate: 06/30/15 Time: 21:35Sample: 1 35Included observations: 35VariableCX1X2R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statisticProb(F-statistic)Coefficient-120767.22.5135151.206225Std. Error24367.000.3912660.032826t-Statistic-4.9561816.42405636.74635Prob. 0.00000.00000.0000149841.8183380.522.8442722.9775822.890290.4196420.987408 Mean dependent var0.986621 S.D. dependent var21211.23 Akaike info criterion1.44E+10 Schwarz criterion-396.7746 Hannan-Quinn criter.1254.644 Durbin-Watson stat0.000000 被解释变量?与?1和?2、?3的最小二乘估计结果
Dependent Variable: YMethod: Least SquaresDate: 06/30/15 Time: 21:37Sample: 1 35Included observations: 35VariableCX1X2X3R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statisticProb(F-statistic)Coefficient-29040.152.4443201.200161-822.2026Std. Error72030.720.3896960.032720608.5734t-Statistic-0.4031636.27236836.67998-1.351033Prob. 0.68960.00000.00000.1865149841.8183380.522.8442023.0219522.905560.5736270.988108 Mean dependent var0.986957 S.D. dependent var20942.89 Akaike info criterion1.36E+10 Schwarz criterion-395.7734 Hannan-Quinn criter.858.6093 Durbin-Watson stat0.000000 观察?与?1和?2最小二乘估计的拟合优度（R-squared =0.987408），与
?与?1最小二乘估计的拟合优度（R-squared =0.456065）比较，变化明显，说明?1对y的影响显著。观察?与?1和?2、?3最小二乘估计的拟合优度（R-squared =0.988108），与?与?1和?2最小二乘估计的拟合优度（R-squared =0.987408）比较，变化不明显，说明?3对y影响不显著。
③序列相关性检验：
方程含有截距项，因此，可以使用DW检验法来检验方程是否具有序列相关性。
该模型中，样本量n=35，解释变量的个数为3个，查DW检验表知5%的上下界为dl=1.283，4-dl=2.717，du=1.653，4-du=2.347，；1%的上下界为dl=1.085，
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4-dl=2.915，du=1.439，4-du=2.561。
本模型的DW检验值为：DW=0.573627，在5%的水平下，0 RESID60,00040,00020,0000-20,000-40,000-60,0005101520253035 20,00010,0000RESID-10,000-20,000-30,000-40,000-20,000-10,0000RESID110,00020,000 由于DW值在5%的上下界条件下正自相关，说明模型存在序列相关性，所以需要对模型进行修正。 2.3 建立修正模型——WLS 加权最小二乘法估计模型系数建立模型能够有效地消除模型的异方差性，同时也可以在一定程度上克服序列相关性，因此，使用WLS方法估计模型参数是修正模型的常用方法。 2.3.1 使用WLS法进行参数估计 加权最小二乘法估计模型参数结果输出表 15 / 24