第五章：异方差性(作业)

数应1701B杜军17311101055.3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。表3中国出口商品总额与国内生产总值（单位：亿元）时间出口商品总额EXPORT国内生产总值GDP时间出口商品总额EXPORT国内生产总值GDP19913827.122005.6200449103.3161840.219924676.327194.5200562648.1187318.919935284.835673.2200677597.2219438.5199410421.848637.5200793627.1270232.3199512451.861339.92008100394.9319515.5199612576.471813.6200982029.7349081.4199715160.779715.02010107022.8413030.3199815223.685195.52011123240.6489300.6199916159.890564.42012129359.3540367.4200020634.4100280.12013137131.4595244.4200122024.4110863.12014143883.7643974.0200226947.9121717.42015141166.8685505.8200336287.9137422.0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）0100,000200,000300,000400,000500,000600,000700,000020,00060,000100,000140,000XYDependentVariable:YMethod:LeastSquaresDate:04/18/20Time:15:38数应1701B杜军1731110105Sample:19912015Includedobservations:25VariableCoefficientStd.Errort-StatisticProb.C-673.086315354.24-0.0438370.9654X4.0611310.20167720.136840.0000R-squared0.946323Meandependentvar234690.8AdjustedR-squared0.943990S.D.dependentvar210356.7S.E.ofregression49784.06Akaikeinfocriterion24.54540Sumsquaredresid5.70E+10Schwarzcriterion24.64291Loglikelihood-304.8174Hannan-Quinncriter.24.57244F-statistic405.4924Durbin-Watsonstat0.366228Prob(F-statistic)0.000000模型回归的结果：^673.08634.0611iXiY()(0.043820.1368)t20.9463,25Rn（2）white:该模型存在异方差HeteroskedasticityTest:WhiteF-statistic4.493068Prob.F(2,22)0.0231Obs*R-squared7.250127Prob.Chi-Square(2)0.0266ScaledexplainedSS8.361541Prob.Chi-Square(2)0.0153TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:04/18/20Time:17:45Sample:19912015Includedobservations:25VariableCoefficientStd.Errort-StatisticProb.C-1.00E+091.43E+09-0.7003780.4910X^2-0.4554200.420966-1.0818470.2910X102226.260664.191.6851170.1061R-squared0.290005Meandependentvar2.28E+09数应1701B杜军1731110105AdjustedR-squared0.225460S.D.dependentvar3.84E+09S.E.ofregression3.38E+09Akaikeinfocriterion46.83295Sumsquaredresid2.51E+20Schwarzcriterion46.97922Loglikelihood-582.4119Hannan-Quinncriter.46.87352F-statistic4.493068Durbin-Watsonstat0.749886Prob(F-statistic)0.023110ARCH检验：该模型存在异方差HeteroskedasticityTest:ARCHF-statistic18.70391Prob.F(1,22)0.0003Obs*R-squared11.02827Prob.Chi-Square(1)0.0009TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:04/18/20Time:19:55Sample(adjusted):19922015Includedobservations:24afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.C8.66E+086.92E+081.2516840.2238RESID^2(-1)0.8171460.1889444.3248020.0003R-squared0.459511Meandependentvar2.37E+09AdjustedR-squared0.434944S.D.dependentvar3.90E+09S.E.ofregression2.93E+09Akaikeinfocriterion46.51293Sumsquaredresid1.89E+20Schwarzcriterion46.61110Loglikelihood-556.1552Hannan-Quinncriter.46.53898F-statistic18.70391Durbin-Watsonstat0.888067Prob(F-statistic)0.000273（3）修正：加权最小二乘法修正数应1701B杜军1731110105DependentVariable:YMethod:LeastSquaresDate:04/18/20Time:20:46Sample:19912015Includedobservations:25Weightingseries:W2Weighttype:Inversevariance(averagescaling)VariableCoefficientStd.Errort-StatisticProb.C10781.172188.7064.9258210.0001X3.9316060.19200420.476670.0000WeightedStatisticsR-squared0.947998Meandependentvar51703.40AdjustedR-squared0.945737S.D.dependentvar11816.72S.E.ofregression8420.515Akaikeinfocriterion20.99135Sumsquaredresid1.63E+09Schwarzcriterion21.08886Loglikelihood-260.3919Hannan-Quinncriter.21.01839F-statistic419.2938Durbin-Watsonstat0.539863Prob(F-statistic)0.000000Weightedmeandep.39406.30UnweightedStatisticsR-squared0.944994Meandependentvar234690.8AdjustedR-squared0.942602S.D.dependentvar210356.7S.E.ofregression50396.82Sumsquaredresid5.84E+10修正后进行white检验：HeteroskedasticityTest:WhiteF-statistic0.261901Prob.F(2,22)0.7720Obs*R-squared0.581387Prob.Chi-Square(2)0.7477ScaledexplainedSS0.211737Prob.Chi-Square(2)0.8995TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:04/18/20Time:20:41Sample:19912015Includedobservations:25CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticProb.数应1701B杜军1731110105C71441488220462123.2405340.0038X*WGT^2-2711.9615055.773-0.5364090.5971WGT^213536351207148710.6534610.5202R-squared0.023255Meandependentvar65232673AdjustedR-squared-0.065539S.D.dependentvar61762160S.E.ofregression63753972Akaikeinfocriterion38.89113Sumsquaredresid8.94E+16Schwarzcriterion39.03739Loglikelihood-483.1391Hannan-Quinncriter.38.93170F-statistic0.261901Durbin-Watsonstat0.898907Prob(F-statistic)0.771953修正后的模型为^10781.173.931606iXiY(4.925821)(20.47667)t20.9480,25Rn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)地区建筑业总产值X建筑业企业利润总额Y地区建筑业总产值X建筑业企业利润总额Y北京6046.22216.78湖北5586.45231.46天津2986.4579.54湖南3915.02124.77河北3972.66127.00广东5774.01251.69山西2324.9149.22广西1553.0726.24内蒙古1394.68105.37海南255.476.44辽宁6217.52224.31重庆3328.83155.34吉林1626.6589.03四川5256.65177.19黑龙江2029.1658.92贵州824.7214.39上海4586.28166.69云南1868.4061.88江苏15122.85595.87西藏124.475.75浙江14907.42411.57陕西3216.63104.38安徽3597.26127.12甘肃925.8429.33福建36