应用回归分析 第五章习题.doc

应用回归分析 第五章习题5.10(1)建立y对的线性回归方程CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.BStd. ErrorBeta1(Constant)5922.8272504.3152.365.040x24.8642.507.6771.940.081x32.374.842.7822.818.018x4-817.901187.279-1.156-4.367.001x514.539147.078.050.099.923x6-846.867291.634-.899-2.904.016a. Dependent Variable: y由上可知，线性回归方程是：（2）用后退法选择变量CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.BStd. ErrorBeta1(Constant)-2530523.6511053982.823-2.401.040x2-27.45813.588-3.823-2.021.074x33.321.7971.0944.169.002x4-1506.217324.836-2.128-4.637.001x5212.489146.255.7371.453.180x6-477.930284.609-.507-1.679.127x11304.787542.1845.1042.407.0392 3(Constant)-445380.948110447.795-4.033.002x32.310.457.7615.055.000x4-971.882174.101-1.373-5.582.000x6-827.999220.276-.879-3.759.003x1232.20256.138.9084.136.002a. Dependent Variable: yANOVAdModelSum of SquaresdfMean SquareFSig.1Regression1983863635912.485.001aResidual2383520.7839264835.643Total22222156.937152Regression19279614.03353855922.80713.104.000bResidual2942542.90410294254.290Total22222156.938153Regression18750376.89244687594.22314.852.000cResidual3471780.04611315616.368Total22222156.93715a. Predictors: (Constant), x1, x3, x6, x4, x5, x2b. Predictors: (Constant), x1, x3, x6, x4, x2c. Predictors: (Constant), x1, x3, x6, x4d. Dependent Variable: yModel SummaryModelRR SquareAdjusted R SquareStd. Error of the Estimate1.945a.893.821514.6222.931b.868.801542.4523.919c.844.787561.797a. Predictors: (Constant), x1, x3, x6, x4, x5, x2b. Predictors: (Constant), x1, x3, x6, x4, x2c. Predictors: (Constant), x1, x3, x6, x4由上三表可知，用后退法选出的变量及其回归方程为：（3）用逐步回归法选择自变量Model SummaryModelRR SquareAdjusted R SquareStd. Error of the Estimate1.498a.248.1941092.8322.697b.485.406937.9503.811c.657.572796.609a. Predictors: (Constant), x3b. Predictors: (Constant), x3, x5c. Predictors: (Constant), x3, x5, x4ANOVAdModelSum of SquaresdfMean SquareFSig.1Regression5502210.09015502210.0904.607.050aResidual16719946.847141194281.918Total22222156.937152Regression10785395.10825392697.5546.130.013bResidual11436761.83013879750.910Total22222156.937153Regression14607124.51934869041.5067.673.004cResidual7615032.41812634586.035Total22222156.93715a. Predictors: (Constant), x3b. Predictors: (Constant), x3, x5c. Predictors: (Constant), x3, x5, x4d. Dependent Variable: yCoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.BStd. ErrorBeta1(Constant)5161.2591142.7444.517.000x31.511.704.4982.146.0502(Constant)472.2982150.138.220.830x33.188.9131.0503.492.004x5212.32586.643.7372.451.0293(Constant)1412.8071865.912.757.464x33.440.7821.1334.398.001x5348.72992.2201.2103.782.003x4-415.136169.163-.587-2.454.030a. Dependent Variable: y逐步回归法可得：(4)根据以上计算结果分析后退法与逐步回归法的差异：两个方法得到的最终模型是不同的。在后退法中首先剔除了，第二步剔除了；而逐步回归法则在第二步引入了，第三步引入了。说明两种方法对自变量重要性的认可是不同的，这与自比那两之间的相关性有关。相比之下，后退发首先做全模型的回归，每个自变量都有机会展示自己的作用，所得结果更值得信服。如，在本题中可以看到，是之后六个月的最惠利率，对因变量的影响似乎并不大。第四章习题习题4.14（1） 用普通最小二乘法建立y与x1和x2的回归方程，用残差图以及DW检验诊断序列的自相关性。CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.BStd. ErrorBeta1(Constant)-574.062349.271-1.644.107每周演出场次X1191.09873.309.3452.607.012周点击率X22.045.911.2972.246.029a. Dependent Variable: 销售额yModel SummarybModelRR SquareAdjusted R SquareStd. Error of the EstimateDurbin-Watson1.541a.293.264329.6930247.745a. Predictors: (Constant), 周点击率X2, 每周演出场次X1b. Dependent Variable: 销售额y由上表可知，回归方程为： 认为误差项呈正自相关（2） 用迭代法处理序列相关，并建立回归方程。应用迭代法原理，在SPSS中执行以下步骤：新命名x11和x12，分别将x1的前n-1和后n-1个数据复制在这两列对x21和x22作相同的处理，同处理的还有y1和y2Transform-compute variables，在taeget Variable中命名Y3。在Numegric expression中输入，得到新列Y3.同处理自变量列，得到X1改和X2改列。对Y3和X1改、X2改进行线性回归CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.BStd. ErrorBeta1(Constant)-179.04090.458-1.979.054X1改211.10747.758.5214.420.000X2改1.437.629.2692.285.027a. Dependent Variable: Y3建立回归方程： （3） 用一阶差分法处理数据，并建立回归方程。类同上述数据处理方法，得到：Coefficientsa,bModelUnstandardized CoefficientsStandardized CoefficientstSig.BStd. ErrorBeta1X111210.11743.692.5444.809.000X2221.397.577.2742.421.019a. Dependent Variable: Y33b. Linear Regression through the Origin（4） 比较以上各方法所建立回归方程的优良性。差分法：ANOVAc,dModelSum of SquaresdfMean SquareFSig.1Regression4036879.69622018439.84825.564.000aResidual3868812.3764978955.355Total7905692.072b51a. Predictors: X222, X111b. This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.c. Dependent Variable: Y33d. Linear Regression through the Origin迭代法：ANOVAbModelSum of SquaresdfMean SquareFSig.1Regression2864465.70921432232.85521.540.000aResidual3191575.2874866491.152Total6056040.99650a. Predictors: (Constant), X2改, X1改b. Dependent Variable: Y3通过上表可以看到，两种方法都可以有效地消除序列自相关性。两种方法建立起的回归方程都能通过整体的显著性检验，但就单个变量而言，从p值考虑，在迭代法中得到的回归系数的显著性要弱于差分法。4.16 对第三章思考与练习第11题作异常值检验。Correlations残差绝对值工业总产值x1农业总产值x2居民非商品支出x3Spearmans rho残差绝对值Correlation Coefficient1.000-.134-.117-.421Sig. (2-tailed).712.748.226N10101010工业总产值x1Correlation Coefficient-.