5.3 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5.3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）100,000200,000300,000400,000500,000600,000700,000XYDependent Variable: Y Method: Least Squares Date: 04/18/20 Time: 15:38Sample: 1991 2015 Included observations: 25Variable Coefficient Std. Error t-Statistic Prob. C -673.0863 15354.24 -0.043837 0.9654 X4.0611310.20167720.136840.0000R-squared 0.946323 Mean dependent var 234690.8 Adjusted R-squared 0.943990 S.D. dependent var 210356.7 S.E. of regression 49784.06 Akaike info criterion 24.54540 Sum squared resid 5.70E+10 Schwarz criterion 24.64291 Log likelihood -304.8174 Hannan-Quinn criter. 24.57244 F-statistic 405.4924 Durbin-Watson stat 0.366228Prob(F-statistic) 0.000000模型回归的结果：^673.0863 4.0611iX i Y =-+()(0.043820.1368)t =-20.9463,25R n ==（2）white: 该模型存在异方差Heteroskedasticity Test: WhiteF-statistic4.493068 Prob. F(2,22)0.0231 Obs*R-squared 7.250127 Prob. Chi-Square(2) 0.0266 Scaled explained SS8.361541 Prob. Chi-Square(2) 0.0153Test Equation:Dependent Variable: RESID^2 Method: Least Squares Date: 04/18/20 Time: 17:45 Sample: 1991 2015 Included observations: 25Variable Coefficient Std. Error t-Statistic Prob. C -1.00E+09 1.43E+09 -0.700378 0.4910 X^2 -0.455420 0.420966 -1.081847 0.2910 X102226.260664.191.6851170.1061R-squared 0.290005 Mean dependent var2.28E+09Adjusted R-squared 0.225460 S.D. dependent var 3.84E+09 S.E. of regression 3.38E+09 Akaike info criterion 46.83295 Sum squared resid 2.51E+20 Schwarz criterion 46.97922 Log likelihood -582.4119 Hannan-Quinn criter. 46.87352 F-statistic 4.493068 Durbin-Watson stat 0.749886 Prob(F-statistic) 0.023110ARCH检验：该模型存在异方差Heteroskedasticity Test: ARCHF-statistic 18.70391 Prob. F(1,22) 0.0003 Obs*R-squared 11.02827 Prob. Chi-Square(1) 0.0009Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 04/18/20 Time: 19:55Sample (adjusted): 1992 2015Included observations: 24 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob.C 8.66E+08 6.92E+08 1.251684 0.2238RESID^2(-1) 0.817146 0.188944 4.324802 0.0003R-squared 0.459511 Mean dependent var 2.37E+09 Adjusted R-squared 0.434944 S.D. dependent var 3.90E+09 S.E. of regression 2.93E+09 Akaike info criterion 46.51293 Sum squared resid 1.89E+20 Schwarz criterion 46.61110 Log likelihood -556.1552 Hannan-Quinn criter. 46.53898 F-statistic 18.70391 Durbin-Watson stat 0.888067 Prob(F-statistic) 0.000273（3）修正：加权最小二乘法修正Dependent Variable: YMethod: Least SquaresDate: 04/18/20 Time: 20:46Sample: 1991 2015Included observations: 25Weighting series: W2Weight type: Inverse variance (average scaling)Variable Coefficient Std. Error t-Statistic Prob.C 10781.17 2188.706 4.925821 0.0001X 3.931606 0.192004 20.47667 0.0000Weighted StatisticsR-squared 0.947998 Mean dependent var 51703.40 Adjusted R-squared 0.945737 S.D. dependent var 11816.72 S.E. of regression 8420.515 Akaike info criterion 20.99135 Sum squared resid 1.63E+09 Schwarz criterion 21.08886 Log likelihood -260.3919 Hannan-Quinn criter. 21.01839 F-statistic 419.2938 Durbin-Watson stat 0.539863 Prob(F-statistic) 0.000000 Weighted mean dep. 39406.30Unweighted StatisticsR-squared 0.944994 Mean dependent var 234690.8 Adjusted R-squared 0.942602 S.D. dependent var 210356.7 S.E. of regression 50396.82 Sum squared resid 5.84E+10 修正后进行white检验：Heteroskedasticity Test: WhiteF-statistic 0.261901 Prob. F(2,22) 0.7720 Obs*R-squared 0.581387 Prob. Chi-Square(2) 0.7477 Scaled explained SS 0.211737 Prob. Chi-Square(2) 0.8995Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 04/18/20 Time: 20:41Sample: 1991 2015Included observations: 25Collinear test regressors dropped from specificationVariable Coefficient Std. Error t-Statistic Prob.C 71441488 22046212 3.240534 0.0038 X*WGT^2 -2711.961 5055.773 -0.536409 0.5971 WGT^213536351207148710.6534610.5202R-squared 0.023255 Mean dependent var 65232673 Adjusted R-squared -0.065539 S.D. dependent var 61762160 S.E. of regression 63753972 Akaike info criterion 38.89113 Sum squared resid 8.94E+16 Schwarz criterion 39.03739 Log likelihood -483.1391 Hannan-Quinn criter. 38.93170 F-statistic 0.261901 Durbin-Watson stat 0.898907 Prob(F-statistic) 0.771953修正后的模型为^10781.17 3.931606iX i Y =+(4.925821)(20.47667)t =20.9480,25R n ==5.4 表5.4的数据是2011年各地区建筑业总产值（X ）和建筑业企业利润总额（Y ）。
表5.4 各地区建筑业总产值（X ）和建筑业企业利润总额（Y ） (单位：亿元)数据来源：国家统计局网站根据样本资料建立回归模型，分析建筑业企业利润总额与建筑业总产值的关系，并判断模型是否存在异方差，如果有异方差，选用最简单的方法加以修正。