1、異方差性的檢驗和補救一、 研究目的和要求表1列出了1998年我國主要制造工業銷售收入與銷售利潤的統計資料，請利用統計軟件Eviews建立我國制造業利潤函數模型，檢驗其是否存在異方差，并加以補救。表 1 我國制造工業1998年銷售利潤與銷售收入情況行業名稱銷售利潤Y銷售收入X食品加工業187.253180.44食品制造業111.421119.88飲料制造業205.421489.89煙草加工業183.871328.59紡織業316.793862.9服裝制品業157.71779.1皮革羽絨制品81.71081.77木材加工業35.67443.74家具制造業31.06226.78造紙及紙品業134.4

2、1124.94印刷業90.12499.83文教體育用品54.4504.44石油加工業194.452363.8化學原料紙品502.614195.22醫藥制造業238.711264.1化學纖維制品81.57779.46橡膠制品業77.84692.08塑料制品業144.341345非金屬礦制品339.262866.14黑色金屬冶煉367.473868.28有色金屬冶煉144.291535.16金屬制品業201.421948.12普通機械制造354.692351.68專用設備制造238.161714.73交通運輸設備511.944011.53電子機械制造409.833286.15電子通訊設備508.1

3、54499.19儀器儀表設備72.46663.68二、 參數估計EVIEWS 軟件估計參數結果如下Dependent Variable: YMethod: Least SquaresDate: 06/01/16 Time: 20:16Sample: 1 28Included observations: 28VariableCoefficientStd. Errort-StatisticProb.  C12.0334919.518090.6165300.5429X0.1043940.00844212.366580.0000R-squared0.854694 

4、0;  Mean dependent var213.4639Adjusted R-squared0.849105    S.D. dependent var146.4905S.E. of regression56.90455    Akaike info criterion10.98938Sum squared resid84191.34    Schwarz criterion11.08453Log likelihood-151.8513 &#

5、160;  Hannan-Quinn criter.11.01847F-statistic152.9322    Durbin-Watson stat1.212781Prob(F-statistic)0.000000用規范的形式將參數估計和檢驗結果寫下三、 檢驗模型的異方差（一） 圖形法1. 相關關系圖X Y 相關關系圖2. 殘差圖形生成殘差平方序列，做與解釋變量 X 的散點圖如下。與 X 散點圖3. 判斷由圖可以看出，殘差平方 對解釋變量 X 的散點圖主要分布在圖形中的下三角部分，大致看出殘差平方 隨 X 的變動呈增大的趨勢，因此，

6、模型很可能存在異方差。但是否確實存在異方差還應通過更進一步的檢驗。（二） Goldfeld-Quanadt檢驗1. 排序使用 Sort X 命令對解釋變量 X 進行排序。2. 構造子樣本區間，建立回歸模型樣本容量 n=28，去掉中間 c=8 個樣本值，得到兩個樣本區間 110、1928的兩組樣本值。110區間回歸估計Dependent Variable: YMethod: Least SquaresDate: 06/01/16 Time: 20:35Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-Stati

7、sticProb.  C15.7646614.820221.0637270.3185X0.0858940.0191824.4779370.0021R-squared0.714814    Mean dependent var77.06400Adjusted R-squared0.679166    S.D. dependent var31.70225S.E. of regression17.95685    Akaike info criterion8.7

8、90677Sum squared resid2579.587    Schwarz criterion8.851194Log likelihood-41.95338    Hannan-Quinn criter.8.724289F-statistic20.05192    Durbin-Watson stat2.280129Prob(F-statistic)0.0020611928區間回歸估計Dependent Variable: YMethod: Least Squares

9、Date: 06/01/16 Time: 20:36Sample: 19 28Included observations: 10VariableCoefficientStd. Errort-StatisticProb.  C-11.99687138.6642-0.0865170.9332X0.1105520.0393672.8082090.0229R-squared0.496413    Mean dependent var369.2440Adjusted R-squared0.433465   

10、0;S.D. dependent var118.6175S.E. of regression89.28163    Akaike info criterion11.99833Sum squared resid63769.67    Schwarz criterion12.05884Log likelihood-57.99163    Hannan-Quinn criter.11.93194F-statistic7.886037    D

11、urbin-Watson stat2.489267Prob(F-statistic)0.0229063. F統計量值對樣本 110回歸分析對樣本 1928 回歸分析4. 判斷取顯著性水平 ，子樣本個數為 10，變量個數為 2，因此子樣本的殘差平方和的自由度為 8，查 F 分布表得 所以拒絕原假設，表明模型確實存在異方差性。（三） White檢驗對前文參數檢驗的結果進行 White 檢驗，結果如下圖Heteroskedasticity Test: WhiteF-statistic3.607090    Prob. F(2,25)0.0420Obs*R-sq

12、uared6.270439    Prob. Chi-Square(2)0.0435Scaled explained SS7.630696    Prob. Chi-Square(2)0.0220Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/01/16 Time: 20:38Sample: 1 28Included observations: 28VariableCoefficientStd. Errort-Statist

13、icProb.  C-3279.6692857.119-1.1478940.2619X2-0.0008710.000653-1.3340330.1942X5.6706873.1093661.8237440.0802R-squared0.223944    Mean dependent var3006.833Adjusted R-squared0.161860    S.D. dependent var5144.454S.E. of regression4709.748  &#

14、160; Akaike info criterion19.85361Sum squared resid5.55E+08    Schwarz criterion19.99635Log likelihood-274.9506    Hannan-Quinn criter.19.89725F-statistic3.607090    Durbin-Watson stat2.576402Prob(F-statistic)0.042040故 ，取，則，所以拒絕原假設，表明模

15、型確實存在異方差性。四、 異方差的修正（加權最小二乘法）1. 權數將權數分別設置為2. 最小二乘估計在 Eviews 命令窗口輸入得到如下結果Dependent Variable: YMethod: Least SquaresDate: 06/01/16 Time: 21:39Sample: 1 28Included observations: 28Weighting series: W1Weight type: Inverse standard deviation (EViews default scaling)VariableCoefficientStd. Errort-Statistic

16、Prob.  C5.9883516.4036910.9351410.3583X0.1086050.00815613.316590.0000Weighted StatisticsR-squared0.872130    Mean dependent var123.4049Adjusted R-squared0.867212    S.D. dependent var31.99804S.E. of regression32.07267    Akaike in

17、fo criterion9.842635Sum squared resid26745.07    Schwarz criterion9.937792Log likelihood-135.7969    Hannan-Quinn criter.9.871726F-statistic177.3317    Durbin-Watson stat2.386165Prob(F-statistic)0.000000    Weighted mean

18、 dep.67.92073Unweighted StatisticsR-squared0.853094    Mean dependent var213.4639Adjusted R-squared0.847443    S.D. dependent var146.4905S.E. of regression57.21696    Sum squared resid85118.31Durbin-Watson stat2.472027權數為W1 時的最小二乘估計結果Depend

19、ent Variable: YMethod: Least SquaresDate: 06/01/16 Time: 21:46Sample: 1 28Included observations: 28Weighting series: W2Weight type: Inverse standard deviation (EViews default scaling)VariableCoefficientStd. Errort-StatisticProb.  C6.4971483.4866251.8634490.0737X0.1068900.0109919.7248240.00

20、00Weighted StatisticsR-squared0.784362    Mean dependent var67.92073Adjusted R-squared0.776068    S.D. dependent var75.51949S.E. of regression21.39500    Akaike info criterion9.032941Sum squared resid11901.39    Schwarz

21、criterion9.128098Log likelihood-124.4612    Hannan-Quinn criter.9.062031F-statistic94.57221    Durbin-Watson stat2.826376Prob(F-statistic)0.000000    Weighted mean dep.36.45271Unweighted StatisticsR-squared0.854180    Me

22、an dependent var213.4639Adjusted R-squared0.848571    S.D. dependent var146.4905S.E. of regression57.00507    Sum squared resid84489.02Durbin-Watson stat2.489641權數為W2 時的最小二乘估計結果Dependent Variable: YMethod: Least SquaresDate: 06/01/16 Time: 21:48Sample: 1 28Inc

23、luded observations: 28Weighting series: W3Weight type: Inverse standard deviation (EViews default scaling)VariableCoefficientStd. Errort-StatisticProb.  C8.63927111.187680.7722130.4470X0.1061530.00774613.704300.0000Weighted StatisticsR-squared0.878396    Mean dependent

24、var165.8409Adjusted R-squared0.873718    S.D. dependent var67.13183S.E. of regression42.63779    Akaike info criterion10.41211Sum squared resid47267.52    Schwarz criterion10.50727Log likelihood-143.7695    Hannan-Quinn

25、criter.10.44120F-statistic187.8079    Durbin-Watson stat2.423771Prob(F-statistic)0.000000    Weighted mean dep.123.4049Unweighted StatisticsR-squared0.854451    Mean dependent var213.4639Adjusted R-squared0.848853    S.D

26、. dependent var146.4905S.E. of regression56.95205    Sum squared resid84331.95Durbin-Watson stat2.493962權數為W3 時的最小二乘估計結果3. 判斷由上述三個結果可以看出，W1 的 t 檢驗均顯著，F 檢驗也顯著，即對異方差的修正效果最好。選擇以 W1 為權數建立的回歸模型為4. 對所估計的模型再次進行 White 檢驗，觀察異方差調整情況Heteroskedasticity Test: WhiteF-statistic0.555565    Prob. F(2,25)0.5807Obs*R-squared1.191508    Prob. Chi-Square(2)0.5511Scaled explained SS1.227886