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 2015Included observations: 25VariableCoefficientStd. Error t-Statistic Prob.C XR-squared Mean dependent var Adjusted R-squared . dependent var . of regression Akaike info criterionSum squared resid +10 Schwarz criterionLog likelihood Hannan-Quinn criter.F-statistic Durbin-Watson stat Prob(F-statistic)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-statistic Prob. F(2,22) Obs*R-squared Prob. Chi-Square(2) Scaled explained SSProb. Chi-Square(2)Test Equation:Dependent Variable: RESID^2 Method: Least Squares Date: 04/18/20 Time: 17:45 Sample: 1991 2015Included observations: 25VariableCoefficientStd. Error t-Statistic Prob.C +09+09X^2XR-squared Mean dependent var+09 Adjusted R-squared. dependent var+09. of regression+09Akaike info criterionSum squared resid+20Schwarz criterionLog likelihoodHannan-Quinn criter.F-statistic Durbin-Watson statProb(F-statistic)ARCH检验：该模型存在异方差Heteroskedasticity Test: ARCHF-statistic Prob. F(1,22)Obs*R-squared Prob. Chi-Square(1)Test 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+08+08RESID^2(-1)R-squared Mean dependent var+09 Adjusted R-squared. dependent var+09. of regression+09Akaike info criterionSum squared resid+20Schwarz criterionLog likelihoodHannan-Quinn criter.F-statistic Durbin-Watson stat Prob(F-statistic)（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.CXWeighted StatisticsR-squared Mean dependent varAdjusted R-squared. dependent var. of regressionAkaike info criterionSum squared resid+09Schwarz criterionLog likelihoodHannan-Quinn criter.F-statistic Durbin-Watson statProb(F-statistic)Weighted mean dep.Unweighted StatisticsR-squared Mean dependent varAdjusted R-squared. dependent var. of regression Sum squared resid+10修正后进行white检验：Heteroskedasticity Test: WhiteF-statistic Prob. F(2,22)Obs*R-squared Prob. Chi-Square(2)Scaled explained SSProb. Chi-Square(2)Test Equation:Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 04/18/20 Time: 20:41 Sample: 1991 2015Included observations: 25Collinear test regressors dropped from specificationVariableCoefficientStd. Error t-Statistic Prob.C X*WGT^2 WGT^2R-squaredMean dependent var Adjusted R-squared . dependent var . of regression Akaike info criterionSum squared resid +16 Schwarz criterionLog likelihood Hannan-Quinn criter.F-statistic Durbin-Watson stat Prob(F-statistic)修正后的模型为^10781.17 3.931606iX i Y =+(4.925821)(20.47667)t =20.9480,25R n ==表的数据是2011年各地区建筑业总产值（X ）和建筑业企业利润总额（Y ）。
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。
解：散点图：0100200300400500600700X Y建立线性回归模型：Dependent Variable: Y Method: Least Squares Date: 04/18/20 Time: 21:16 Sample: 1 31Included observations: 31VariableCoefficientStd. Error t-Statistic Prob.C XR-squared Mean dependent var Adjusted R-squared. dependent var. of regressionAkaike info criterionSum squared resid Schwarz criterionLog likelihoodHannan-Quinn criter.F-statistic Durbin-Watson statProb(F-statistic)white检验：Heteroskedasticity Test: WhiteF-statistic Prob. F(2,28)Obs*R-squared Prob. Chi-Square(2)Scaled explained SS Prob. Chi-Square(2)Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 04/18/20 Time: 21:19Sample: 1 31Included observations: 31Variable Coefficient Std. Error t-Statistic Prob.CX^2XR-squared Mean dependent varAdjusted R-squared. dependent var. of regressionAkaike info criterionSum squared resid Schwarz criterionLog likelihoodHannan-Quinn criter.F-statistic Durbin-Watson stat Prob(F-statistic)模型存在异方差模型修正：加权最小二乘法Dependent Variable: YMethod: Least SquaresDate: 04/18/20 Time: 21:24Sample: 1 31Included observations: 31Weighting series: W2Weight type: Inverse variance (average scaling)Variable Coefficient Std. Error t-Statistic Prob.CXWeighted StatisticsR-squared Mean dependent varAdjusted R-squared. dependent var. of regressionAkaike info criterionSum squared resid Schwarz criterionLog likelihoodHannan-Quinn criter.F-statistic Durbin-Watson stat Prob(F-statistic)Weighted mean dep.Unweighted StatisticsR-squared Mean dependent var Adjusted R-squared. dependent var. of regression Sum squared resid Durbin-Watson stat加权后进行white检验：Heteroskedasticity Test: WhiteF-statistic Prob. F(2,28)Obs*R-squared Prob. Chi-Square(2) Scaled explained SS Prob. Chi-Square(2)Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 04/18/20 Time: 21:25Sample: 1 31Included observations: 31Collinear test regressors dropped from specificationVariableCoefficientStd. Error t-Statistic Prob.C X*WGT^2 WGT^2R-squared Mean dependent var Adjusted R-squared . dependent var . of regression Akaike info criterionSum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter.F-statistic Durbin-Watson stat Prob(F-statistic)修正成功，修正后的模型为：^0.0207340.034505iX i Y =+(0.015338)(14.11049)t =20.8729,31R n ==表是2015年中国各地区人均可支配收入（X ）与居民每百户汽车拥有量（Y ）的数据。