应用回归分析第五章习题

应用回归分析第五章习题5.10(1)建立y对26x~x的线性回归方程CoefficientsaModelUnstandardizedCoefficientsStandardizedCoefficientstSig.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.DependentVariable:y由上可知，线性回归方程是：2345659228274864237481790114539846867y..x.x.x.x.x（2）用后退法选择变量CoefficientsaModelUnstandardizedCoefficientsStandardizedCoefficientstSig.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-.879-3.759.003x1232.20256.138.9084.136.002CoefficientsaModelUnstandardizedCoefficientsStandardizedCoefficientstSig.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.DependentVariable:yANOVAdModelSumofSquaresdfMeanSquareFSig.1Regression19838636.15463306439.35912.485.001aResidual2383520.7839264835.643Total22222156.937152Regression19279614.03353855922.80713.104.000bResidual2942542.90410294254.290Total22222156.938153Regression18750376.89244687594.22314.852.000cResidual3471780.04611315616.368Total22222156.93715a.Predictors:(Constant),x1,x3,x6,x4,x5,x2b.Predictors:(Constant),x1,x3,x6,x4,x2c.Predictors:(Constant),x1,x3,x6,x4d.DependentVariable:yModelSummaryModelRRSquareAdjustedRSquareStd.ErroroftheEstimate1.945a.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：34614453809482310971882827999232202y..x.x.x.x（3）用逐步回归法选择自变量ModelSummaryModelRRSquareAdjustedRSquareStd.ErroroftheEstimate1.498a.248.1941092.8322.697b.485.406937.9503.811c.657.572796.609a.Predictors:(Constant),x3b.Predictors:(Constant),x3,x5c.Predictors:(Constant),x3,x5,x4ANOVAdModelSumofSquaresdfMeanSquareFSig.1Regression5502210.09015502210.0904.607.050aResidual16719946.847141194281.918Total22222156.937152Regression10785395.10825392697.5546.130.013bResidual11436761.83013879750.910Total22222156.937153Regression14607124.51934869041.5067.673.004cResidual7615032.41812634586.035Total22222156.93715ANOVAdModelSumofSquaresdfMeanSquareFSig.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.DependentVariable:yCoefficientsaModelUnstandardizedCoefficientsStandardizedCoefficientstSig.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.DependentVariable:y逐步回归法可得：35414128073440348729415136y..x.x.x(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5x，第二步剔除了2x；而逐步回归法则在第二步引入了5x，第三步引入了4x。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，5x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。CoefficientsaModelUnstandardizedCoefficientsStandardizedCoefficientstSig.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.DependentVariable:销售额yModelSummarybModelRRSquareAdjustedRSquareStd.ErroroftheEstimateDurbin-Watson1.541a.293.264329.6930247.745ModelSummarybModelRRSquareAdjustedRSquareStd.ErroroftheEstimateDurbin-Watson1.541a.293.264329.6930247.745a.Predictors:(Constant),周点击率X2,每周演出场次X1b.DependentVariable:销售额y由上表可知，回归方程为：125740621910982045y..x.x0745DW.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-computevariables，在taegetVariable中命名Y3。在Numegricexpression中输入12YY，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CoefficientsaModelUnstandardizedCoefficientsStandardizedCoefficientstSig.BStd.ErrorBeta1(Constant)-179.04090.458-1.979.054X1改211.10747.758.5214.420.000X2改1.437.629.2692.285.027a.DependentVariable:Y3建立回归方程：121790402111071437y..x.x（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,bModelUnstandardizedCoefficientsStandardizedCoefficientstSig.BStd.ErrorBeta1X111