应用回归分析-多重共线性

1、实 验 报 告实验课程 应用回归分析 第 七 次实验 实验日期 12.17 班级 学号 姓名 成绩 要求：将所有要提交的数据、结果等文件按学号+姓名上传一、实验目的掌握SPSS中找出并消除数据共线性方法. 掌握SPSS中的岭回归分析方法.二、实验内容1在训练中氧气消耗能力问题的研究中，我们想要建立一个关系式，以便根据训练测试的数据来预报肺活量，而不必进行昂贵和笨重的氧气消耗测试。考察的因变量y为OXY(氧气消耗能力)，自变量有x1(age,年龄)、x2(weight,体重)、x3(RunTime,1.5英里跑的时间)、x4(RstPulse, 休息时脉博)、x5(RunPulse,跑步时脉博)

2、、x6(RunPulse, 跑步时最大脉博)。(数据在“回归人大数据12_学生.xls的第2题”中 )，利用统计软件计算(1) 用方差扩大因子法分析数据的多重共线性；(2) 用特征根法分析数据的多重共线性；(3) 本题是否适用剔除变量的方法消除共线性，如果适用，进行变量剔除（要求写出回归方程，及主要的统计量）；三、实验结果与分析（包括运行结果及其数据分析、解释等）(1) 用方差扩大因子法分析数据的多重共线性；CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.Collinearity Statis

3、ticsBStd. ErrorBetaToleranceVIF1(Constant)102.93412.4038.299.000x1-.227.100-.222-2.273.032.6611.513x2-.074.055-.116-1.359.187.8661.155x3-2.629.385-.685-6.835.000.6291.591x4-.022.066-.031-.326.747.7061.416x5-.370.120-.711-3.084.005.1198.437x6.303.136.5222.221.036.1148.744a. Dependent Variable: y由于x5,

4、x6的VIF8，x1-x4的VIF都1.5，故猜测可能存在多重共线性。(2) 用特征根法分析数据的多重共线性；Collinearity DiagnosticsaModelDimensionEigenvalueCondition IndexVariance Proportions(Constant)x1x2x3x4x5x6116.9501.000.00.00.00.00.00.00.002.01919.291.00.15.01.03.39.00.003.01521.501.00.15.24.13.03.00.004.00927.621.01.03.18.61.19.00.005.00633.82

5、9.00.11.44.13.36.02.016.00182.638.80.50.10.10.02.07.017.000196.786.19.06.02.01.01.91.98a. Dependent Variable: y特征值全都十分接近0，故认为变量间有严重的多重共线性。由方差比例阵，x5-x6间可能存在共线性(3) 本题是否适用剔除变量的方法消除共线性，如果适用，进行变量剔除（要求写出回归方程，及主要的统计量）；剔除x6ANOVAaModelSum of SquaresdfMean SquareFSig.1Regression696.0525139.21022.406.000bResid

6、ual155.329256.213Total851.38230a. Dependent Variable: yb. Predictors: (Constant), x5, x2, x3, x1, x4CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.Collinearity StatisticsBStd. ErrorBetaToleranceVIF1(Constant)116.48811.61810.027.000x1-.285.104-.279-2.753.011.7101.408x2-.05

7、2.058-.081-.898.378.8961.116x3-2.704.412-.704-6.561.000.6341.579x4-.027.071-.039-.382.706.7071.414x5-.126.052-.243-2.414.023.7201.389a. Dependent Variable: yCollinearity DiagnosticsaModelDimensionEigenvalueCondition IndexVariance Proportions(Constant)x1x2x3x4x5115.9531.000.00.00.00.00.00.002.01917.8

8、57.00.16.01.02.39.003.01420.503.00.15.37.10.02.014.00926.002.01.04.07.74.27.015.00535.652.03.17.45.03.30.266.00177.546.96.48.10.10.01.72a. Dependent Variable: y此时VIF全部小于10，1.，但从回归系数的显著性看，存在不显著变量.。剔除x4ANOVAaModelSum of SquaresdfMean SquareFSig.1Regression695.1474173.78728.921.000bResidual156.235266.0

9、09Total851.38230a. Dependent Variable: yb. Predictors: (Constant), x5, x2, x3, x1CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.Collinearity StatisticsBStd. ErrorBetaToleranceVIF1(Constant)115.66211.22610.303.000x3-2.772.365-.722-7.597.000.7811.280x1-.276.099-.270-2.783.0

10、10.7481.338x2-.049.056-.077-.875.390.9081.102x5-.129.051-.249-2.544.017.7371.356a. Dependent Variable: yCollinearity DiagnosticsaModelDimensionEigenvalueCondition IndexVariance Proportions(Constant)x3x1x2x5114.9671.000.00.00.00.00.002.01418.529.00.03.30.29.013.01120.838.01.83.12.04.004.00629.476.03.

11、06.11.59.215.00170.426.96.09.46.09.79a. Dependent Variable: y剔除x2ANOVAaModelSum of SquaresdfMean SquareFSig.1Regression690.5513230.18438.643.000bResidual160.831275.957Total851.38230a. Dependent Variable: yb. Predictors: (Constant), x5, x3, x1CoefficientsaModelUnstandardized CoefficientsStandardized

12、CoefficientstSig.Collinearity StatisticsBStd. ErrorBetaToleranceVIF1(Constant)111.71810.23510.915.000x3-2.825.358-.736-7.886.000.8041.244x1-.256.096-.251-2.664.013.7901.267x5-.131.051-.252-2.588.015.7381.355a. Dependent Variable: yCollinearity DiagnosticsaModelDimensionEigenvalueCondition IndexVaria

13、nce Proportions(Constant)x3x1x5113.9781.000.00.00.00.002.01218.340.00.50.38.013.00920.800.03.42.19.104.00160.601.96.08.42.90a. Dependent Variable: yModel SummaryModelRR SquareAdjusted R SquareStd. Error of the Estimate1.901a.811.7902.440634a. Predictors: (Constant), x5, x3, x1此时所有回归系数显著R2=0.811F=38.

14、643，sig=0.000 故回归方程显著。y=111.718-2.825x3-0.256x1-0.131x56.61) 根据多重共线性剔除变量CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.Collinearity StatisticsBStd. ErrorBetaToleranceVIF1(Constant)1348.3382211.463.610.552x1-.641.167-1.125-3.840.002.003319.484x2-.317.204-1.306-1.551.143.00

15、02636.564x3-.413.548-.270-.752.464.002479.288x4-.002.024-.007-.087.932.03727.177x5.671.1283.7065.241.000.0011860.726x6-.008.008-.020-.928.369.5741.743a. Dependent Variable: y剔除x2CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.Collinearity StatisticsBStd. ErrorBetaTolerance

16、VIF1(Constant)-1252.8321507.836-.831.419x1-.735.163-1.291-4.524.000.004276.969x3-.923.459-.604-2.012.063.003306.617x4.026.017.0931.591.132.08611.605x5.510.0782.8156.527.000.002632.896x6-.011.008-.028-1.274.222.6081.645a. Dependent Variable: y 剔除x5CoefficientsaModelUnstandardized CoefficientsStandard

17、ized CoefficientstSig.Collinearity StatisticsBStd. ErrorBetaToleranceVIF1(Constant)-2715.0462829.351-.960.352x1-.047.235-.083-.202.843.006160.513x31.463.526.9572.781.013.009111.949x4.036.031.1281.160.263.08711.507x6.003.015.008.206.839.6491.540a. Dependent Variable: y 剔除x1CoefficientsaModelUnstandar

18、dized CoefficientsStandardized CoefficientstSig.Collinearity StatisticsBStd. ErrorBetaToleranceVIF1(Constant)-2296.3221869.710-1.228.236x31.359.097.88914.036.000.2494.018x4.031.019.1111.649.117.2224.509x6.004.014.010.256.801.6731.485a. Dependent Variable: y此时所有方差扩大因子VIF都小于10。ANOVAaModelSum of Square

19、sdfMean SquareFSig.1Regression134661374.115344887124.705328.215.000bResidual2324941.06817136761.239Total136986315.18320a. Dependent Variable: yb. Predictors: (Constant), x6, x3, x4回归方程为：y=-2296.322+1.359x3+0.31x4+0.04x6但此时x4 x5回归系数的t检验都不通过。从实际意义看，建筑业影响最大，人口数也有一定影响，但受灾面积越大，财政收入反而越大，不符合实际，故此方程无法使用。 2) 逐步回归法选择变量Model SummaryModelRR SquareAdjusted R SquareStd. Error of the Estimate1.994a.989.988285.68272.996b.992.991247.77503.998c.996.995183.1330a. Predictors: (Const