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1、回归分析一实验描述：中国民航客运量的回归模型。为了研究我国民航客运量的变化趋势及其成因，我们以民航客运量作为因变量Y，以国民收入（X1)、消费额（X2）、铁路客运量（X3）、民航航线里程（X4）、来华旅游入境人数（X5）、为主要影响因素。数据如下表。试建立Y与X1-X5之间的多元线性回归模型。年份Y (万人) X1 (亿元)X2 (亿元)X3 (万人)X4 (万公里)X5 (万人)1978231301018888149114.89180.921979298335021958638916.00420.391980343368825319220419.53570.25198140139412799
2、9530021.82776.711982445425830549992223.27792.4319833914736335810604422.91947.7019845545652390511035326.021285.2219857447020487911211027.721783.3019869977859555210857932.432281.95198713109313638611242938.912690.231988144211738803812264537.383169.481989128313176900511380747.192450.14199016601438496639
3、571250.682746.201991217816557109699508155.913335.651992288620223129859969383.663311.5019933383248821594910545896.084152.70二实验过程描述及实验结果(1)Descriptive StatisticsMeanStd. DeviationNY1.1591E3960.6723916X19.6117E36643.5403816X26.4472E34251.9460716X31.0233E511010.5699316X438.400023.6201816X51.9309E31244.0
4、009416该表格中输出了5个自变量和1个因变量的一般统计结果，包括各自变量与因变量的平均值，标准差和个案数16。(2)CorrelationsYX1X2X3X4X5Pearson CorrelationY1.000.989.985.227.987.924X1.9891.000.999.258.984.930X2.985.9991.000.289.978.942X3.227.258.2891.000.213.504X4.987.984.978.2131.000.882X5.924.930.942.504.8821.000Sig. (1-tailed)Y.000.000.199.000.000X
5、1.000.000.168.000.000X2.000.000.139.000.000X3.199.168.139.214.023X4.000.000.000.214.000X5.000.000.000.023.000.NY161616161616X1161616161616X2161616161616X3161616161616X4161616161616X5161616161616该表格中列出了各个变量之间的相关性，从该表格可以看出因变量Y和自变量X1之间的相关系数为0.989，相关性最大,。因变量Y与自变量X3之间相关系数为0.227，相关性最小。(3)Variables Entered
6、/RemovedbModelVariables EnteredVariables RemovedMethod1X5, X3, X4, X2, X1a.Entera. All requested variables entered.b. Dependent Variable: Y该表格输出的是被引入或从回归方程中被剔出的各变量。说明进行线性回归分析时所采用的方法是全部引入法Enter。因变量为Y。(4)Model SummarybModelRR SquareAdjusted R SquareStd. Error of the Estimate1.999a.998.99749.49240a. Pr
7、edictors: (Constant), X5, X3, X4, X2, X1b. Dependent Variable: Y该表格输出的是常用统计量。从该表看出相关性系数R为0.999，判定系数R2为0.998，调整的判定系数为0.997，回归估计的标准误差为49.49240。(5)ANOVAbModelSum of SquaresdfMean SquareFSig.1Regression1.382E752763775.3541.128E3.000aResidual24494.981102449.498Total1.384E715a. Predictors: (Constant), X5,
8、 X3, X4, X2, X1b. Dependent Variable: Y该表格输出的是方差分析表。从这部分结果看出：统计量F为1.128E3;相伴概率值小于0.01，拒绝原假设说明多个自变量与因变量Y之间存在线性回归关系。Sum of Squares一栏中分别代表回归平方和(1.382E7)，残差平方和(24494.981)以及总平方和(1.384E7)，df为自由度。判定系数R2=0.99855。(6)CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.BStd. ErrorBeta1(C
9、onstant)450.909178.0782.532.030X1.354.0852.4474.152.002X2-.561.125-2.485-4.478.001X3-.007.002-.083-3.510.006X421.5784.030.5315.354.000X5.435.052.5648.440.000a. Dependent Variable: Y该表格为回归系数分析。其中Unstandardized Coefficients为非标准化系数，Standardized Coefficients为标准化系数，t为回归系数检验统计量，sig为相伴概率值。由表知t检验的相伴概率值均小于0.
10、01，拒绝原假设，说明个变量与因变量之间均有显著线性相关关系。从表格中可以看出该多元线性回归方程为：y=450.909+0.354 X1-0.561 X2-0.007 X3+21.578 X4+0.435 X5(7)Residuals StatisticsaMinimumMaximumMeanStd. DeviationNPredicted Value264.96983.4170E31.1591E3959.8220916Std. Predicted Value-.9322.352.0001.00016Standard Error of Predicted Value19.56938.80229
11、.5766.83716Adjusted Predicted Value293.81173.4674E31.1604E3960.3004416Residual-5.02250E179.79993.0000040.4103816Std. Residual-1.0151.612.000.81616Stud. Residual-1.3361.851-.0111.10916Deleted Residual-8.77748E11.39989E2-1.2551776.6936516Stud. Deleted Residual-1.3982.166.0331.20116Mahal. Distance1.4088.2834.6882.45916Cooks Distance.001.820.183.21916Centered Leverage Value.094.552.313.16416a. Dependent Variable: Y该表格为残差统计结果表。列出了预测值，标准预测值，预测值标准差等指标的最小值，最大值，平均值，方差和N数。(8) 该图为回归因变量Y和自变量X1之间的关系点图。