第五章数据分析(梅长林)习题.doc

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1、【精品文档】如有侵权，请联系网站删除，仅供学习与交流第五章数据分析(梅长林)习题.精品文档.第五章习题1.习题5.1解：假定两总体服从正态分布，且协方差矩阵，误判损失相同又先验概率按比例分配，通过SAS计算得到先验概率如表：Class Level InformationgroupVariableNameFrequencyWeightProportionPriorProbabilityG1G166.00000.4285710.428571G2G288.00000.5714290.571429即： 又计算可得：有计算的总体协防差距矩阵S为：Pooled Within-Class Covarianc

2、e Matrix, DF = 12Variablex1x2x11.081944444-0.310902778x2-0.3109027780.174756944并且：计算广义平方距离函数：并计算后验概率：回代判别结果如下:Posterior Probability of Membership in groupObsFrom groupClassified into groupG1G21G1G10.93870.06132G1G10.93030.06973G1G10.99990.00014G1G2*0.42070.57935G1G10.98930.01076G1G11.00000.00007G2G2

3、0.00070.99938G2G20.00260.99749G2G20.00080.999210G2G20.05860.941411G2G20.03500.965012G2G20.00060.999413G2G20.00380.996214G2G20.00120.9988由此可见误判的回代估计：若按照交叉确认法，定义广义平方距离如下：逐个剔除, 交叉判别，后验概率按下式计算：通过SAS计算得到表所示结果。发现同样也是属于G1的4号被误判为G2，因此误判率的交叉确认估计为Posterior Probability of Membership in groupObsFrom groupClassi

4、fied into groupG1G21G1G10.90600.09402G1G10.76410.23593G1G11.00000.00004G1G2*0.19500.80505G1G10.97430.02576G1G11.00000.00007G2G20.00120.99888G2G20.00510.99499G2G20.00140.998610G2G20.07130.928711G2G20.04220.957812G2G20.00090.999113G2G20.00590.994114G2G20.00220.9978其中=12.1138，又因为，所以，最后可得后验概率p为：0.048709

5、习题5.3解：（1）在并且先验概率相同的的假设前提下，建立矩离判别的线性判别函数。利用SAS的proc discrim过程首先计算得到总体的协方差矩阵，如表：Pooled Within-Class Covariance Matrix, DF = 25Variablex1x2x3x4x5x6x7x8x12.25705591-0.915133110.34259974-0.6084399-0.9576508-0.8929719-0.0539445-0.2192724x2-0.915133125.2318255-0.3390873-2.5515272-5.09663710.78571637-0.083

6、55864.37529806x30.34259974-0.339087343.300631231.422760171.786923430.40208409-0.0676655-0.0732213x4-0.6084399-2.551527261.422760176.078458635.781008572.32039331-0.32051160.48605897x5-0.9576508-5.096637141.786923435.781008578.158547433.44983429-0.10966510.08904743x6-0.89297190.785716370.402084092.320

7、393313.449834294.16657066-0.22362780.87862549x7-0.0539445-0.08355869-0.0676655-0.3205116-0.1096651-0.22362780.26009291-0.0767347x8-0.21927244.37529806-0.07322130.486058970.089047430.87862549-0.07673472.51054423各个总体的马氏平方距离见表：Generalized Squared Distance to groupFrom groupG1G2G1024.61468G224.614680线性判

8、别函数为：得到训练样本回判法判别结果如表：Error Count Estimates for groupG1G2TotalRate0.00000.00000.0000Priors0.50000.5000训练样本的交叉确认判别结果：Posterior Probability of Membership in groupObsFrom groupClassified into groupG1G217G1G2*0.45010.549919G1G2*0.09200.9080Error Count Estimates for groupG1G2TotalRate0.10000.00000.0500Pri

9、ors0.50000.5000（2）假设两总体服从正态分布，先验概率按比例分配且误判损失相同，在两总体协方差矩阵相同，即的条件下进行Bayes判别分析，通过SAS discrim过程得到结果：Error Count Estimates for groupG1G2TotalRate0.00000.00000.0000Priors0.74070.2593交叉确认判别结果：Posterior Probability of Membership in groupObsFrom groupClassified into groupG1G219G1G2*0.22460.775425G2G1*0.52820

10、.4718Error Count Estimates for groupG1G2TotalRate0.05000.14290.0741Priors0.74070.2593在，并且先验概率按比例分配的假设前提下利用SAS的proc discrim过程进行Bays判别分析，这时以个总体的训练样本单独估计各总体的协方差矩阵，可到的训练样本的回判和交叉确认结果：回判结果：Error Count Estimates for groupG1G2TotalRate0.00000.00000.0000Priors0.74070.2593交叉确认判别结果：Posterior Probability of Mem

11、bership in groupObsFrom groupClassified into groupG1G221G2G1*1.00000.000022G2G1*1.00000.000023G2G1*1.00000.000024G2G1*1.00000.000025G2G1*1.00000.000026G2G1*1.00000.000027G2G1*1.00000.0000Error Count Estimates for groupG1G2TotalRate0.00001.00000.2593Priors0.74070.2593（3）在不同的假设前提，采用不同判别方法得到待判样本的判别结果：1

12、.距离判别分析得到西藏、上海、广东的判别结果：Posterior Probability of Membership in groupObsClassified into groupG1G21G20.00001.00002G20.00001.00003G20.00001.00002.在协方差矩阵相同的前提下，Bayes对西藏、上海、广东的判别结果：Posterior Probability of Membership in groupObsClassified into groupG1G21G20.00001.00002G20.00001.00003G20.00001.00003在协方差不同矩

13、阵相同的前提下，Bayes对西藏、上海、广东的判别结果：Posterior Probability of Membership in groupObsClassified into groupG1G21G11.00000.00002G11.00000.00003G11.00000.00003.习题5.4解：（1）假设两总体服从正态分布且在两总体协方差矩阵相同，即，先验概率按相同的条件下进行Bayes判别分析，通过SAS discrim过程得到结果：首先得到线性判别函数：回代误判结果：Posterior Probability of Membership in groupObsFrom grou

14、pClassified into groupG1G29G1G2*0.34010.659929G2G1*0.85710.1429由计算结果发现，第9号样本被误判到G2,29号样本被误判到G1.误判率为6.34%Error Count Estimates for groupG1G2TotalRate0.08330.04350.0634Priors0.50000.5000交叉确认判别结果：由计算发现总共有四个样本被判错，分别是9、28、29、35号样品。累计误判率为10.69%Posterior Probability of Membership in groupObsFrom groupClass

15、ified into groupG1G29G1G2*0.09730.902728G2G1*0.61300.387029G2G1*0.96430.035735G2G1*0.84700.1530Error Count Estimates for groupG1G2TotalRate0.08330.13040.1069Priors0.50000.5000（1）假设两总体服从正态分布且在两总体协方差矩阵相同，即，先验概率按比例分配且误判损失相同的条件下进行Bayes判别分析，通过SAS discrim过程得到结果：首先得到线性判别函数：Linear Discriminant Function for

16、groupVariableG1G2Constant-99.91796-95.41991x130.3506029.87680x2-0.15214-0.15210x3-0.78868-0.22662x41.951761.39528x50.589640.06490x6-108.10195-85.33735x7-0.31156-0.25957回代误判结果Posterior Probability of Membership in groupObsFrom groupClassified into groupG1G29G1G2*0.21190.788129G2G1*0.75790.2421Error C

17、ount Estimates for groupG1G2TotalRate0.08330.04350.0571Priors0.34290.6571交叉确认误判结果：Posterior Probability of Membership in groupObsFrom groupClassified into groupG1G25G1G2*0.34360.65649G1G2*0.05320.946811G1G2*0.40520.594812G1G2*0.35190.648129G2G1*0.93380.066235G2G1*0.74280.2572Error Count Estimates for groupG1G2TotalRate0.33330.08700.1714Priors0.34290.6571