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第一题进行初步的回归分析DependentVariable:YMethod:LeastSquaresDate:04/22/14Time:19:22Sample:137Includedobservations:37VariableCoefficientStd.Errort-StatisticProb.X11.6198450.15491810.456160.0000X2-0.2878610.407309-0.7067400.4854X3-0.8026800.504260-1.5918000.1223X40.3226140.5372180.6005280.5528X50.3486730.4714110.7396360.4655X6-0.3081160.327959-0.9394940.3552X70.1219560.1670290.7301470.4712C0.0151660.0310550.4883680.6290R-squared0.976425Meandependentvar-0.105784AdjustedR-squared0.970734S.D.dependentvar1.037483S.E.ofregression0.177484Akaikeinfocriterion-0.431061Sumsquaredresid0.913518Schwarzcriterion-0.082754Loglikelihood15.97463F-statistic171.5877Durbin-Watsonstat2.155171Prob(F-statistic)0.000000检验异方差的（White检验）WhiteHeteroskedasticityTest:F-statistic1.594691Probability0.158634Obs*R-squared18.63593Probability0.179332TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:04/22/14Time:22:37Sample:137Includedobservations:37VariableCoefficientStd.Errort-StatisticProb.C0.0258880.0101172.5588710.0179X1-0.0206360.041636-0.4956250.6251X1^2-0.0240520.016490-1.4585760.1588X20.0511830.1082380.4728750.6410X2^20.0468570.0300551.5590360.1333X3-0.0550530.134011-0.4108100.6852X3^2-0.0834800.043951-1.8993850.0707X4-0.0540180.151870-0.3556860.7255X4^20.1769010.0651202.7165270.0126X50.2372260.1758171.3492810.1910X5^2-0.2110740.081481-2.5904670.0167X6-0.2649590.148345-1.7860960.0879X6^20.1176030.0548052.1458610.0432X70.0903730.0600951.5038320.1468X7^2-0.0264070.024525-1.0767430.2933R-squared0.503674Meandependentvar0.024690AdjustedR-squared0.187830S.D.dependentvar0.037460S.E.ofregression0.033760Akaikeinfocriterion-3.648171Sumsquaredresid0.025074Schwarzcriterion-2.995096Loglikelihood82.49116F-statistic1.594691Durbin-Watsonstat2.595797Prob(F-statistic)0.158634根据F检验值及其伴随频率，可以判断接受原假设：不存在异方差模型的多重共线性检验从t检验及其伴随p值可以看出，只有变量x1显著，其余解释变量均不显著；并且方程的拟合优度R-squard为0.976425，方程整体的F检验显著。因此怀疑x2x3x4x5x6x7存在多重共线性。x2x3x4x5x6x7简单相关系数X2X3X4X5X6X7X21.0000000.9664970.8588020.7185010.5710820.453453X30.9664971.0000000.9575020.8590410.7197760.581063X40.8588020.9575021.0000000.9634820.8473600.696322X50.7185010.8590410.9634821.0000000.9456510.821318X60.5710820.7197760.8473600.9456511.0000000.950976X70.4534530.5810630.6963220.8213180.9509761.000000对多重共线性进行处理（逐步回归法）（1）对yx1做线性回归DependentVariable:YMethod:LeastSquaresDate:04/23/14Time:11:42Sample:137Includedobservations:37VariableCoefficientStd.Errort-StatisticProb.X10.9091470.04841718.777540.0000C-0.0173510.052194-0.3324310.7415R-squared0.909700Meandependentvar-0.105784AdjustedR-squared0.907120S.D.dependentvar1.037483S.E.ofregression0.316186Akaikeinfocriterion0.587566Sumsquaredresid3.499076Schwarzcriterion0.674643Loglikelihood-8.869973F-statistic352.5958Durbin-Watsonstat2.621934Prob(F-statistic)0.000000（2）对yx2做线性回归DependentVariable:YMethod:LeastSquaresDate:04/23/14Time:11:43Sample:137Includedobservations:37VariableCoefficientStd.Errort-StatisticProb.X20.7100520.0833478.5191820.0000C-0.0712600.098750-0.7216170.4753R-squared0.674650Meandependentvar-0.105784AdjustedR-squared0.665354S.D.dependentvar1.037483S.E.ofregression0.600169Akaikeinfocriterion1.869327Sumsquaredresid12.60710Schwarzcriterion1.956404Loglikelihood-32.58256F-statistic72.57646Durbin-Watsonstat2.806281Prob(F-statistic)0.000000（2）对yx3做线性回归DependentVariable:YMethod:LeastSquaresDate:04/23/14Time:11:44Sample:137Includedobservations:37VariableCoefficientStd.Errort-StatisticProb.X30.5980770.1068615.5967670.0000C-0.0882940.125699-0.7024260.4871R-squared0.472286Meandependentvar-0.105784AdjustedR-squared0.457208S.D.dependentvar1.037483S.E.ofregression0.764359Akaikeinfocriterion2.352980Sumsquaredresid20.44858Schwarzcriterion2.440057Loglikelihood-41.53014F-statistic31.32380Durbin-Watsonstat2.737167Prob(F-statistic)0.000003（3）对yx4做线性回归DependentVariable:YMethod:LeastSquaresDate:04/23/14Time:11:45Sample:137Includedobservations:37VariableCoefficientStd.Errort-StatisticProb.X40.4847760.1339033.6203530.0009C-0.0983810.147560-0.6667190.5093R-squared0.272455Meandependentvar-0.105784AdjustedR-squared0.251668S.D.dependentvar1.037483S.E.ofregression0.897487Akaikeinfocriterion2.674102Sumsquaredresid28.19191Schwarzcriterion2.761179Loglikelihood-47.47089F-statistic13.10696Durbin-Watsonstat2.600144Prob(F-statistic)0.000921（4）对yx5做线性回归DependentVariable:YMethod:LeastSquaresDate:04/23/14Time:11:46Sample:137Includedobservations:37VariableCoefficientStd.Errort-StatisticProb.X50.3595400.1534122.3436180.0249C-0.1007700.160836-0.6265380.5350R-squared0.135643Meandependentvar-0.105784AdjustedR-squared0.110947S.D.dependentvar1.037483S.E.ofregression0.978238Akaikeinfocriterion2.846411Sumsquaredresid33.49325Schwarzcriterion2.933488Loglikelihood-50.65861F-statistic5.492545Durbin-Watsonstat2.437027Prob(F-statistic)0.024905（5）对yx6做线性回归DependentVariable:YMethod:LeastSquaresDate:04/23/14Time:11:47Sample:137Includedobservations:37VariableCoefficientStd.Errort-StatisticProb.X60.2542560.1732651.4674350.1512C-0.0900820.168234-0.5354570.5957R-squared0.057959Meandependentvar-0.105784AdjustedR-squared0.031043S