陈振坤 2015020141 判别分析

陈振坤 2015020141 判别分析习题4.8解：SPSS过程：（1） 先创建一个变量，命名为group，根据销售情况取值，畅销是group=1，平销则group=2，滞销则group=3.并将待判别的数据也输入到表格中。（2） 点击analyse-classify-discriminant-将类别放进grouping variable中，将将销售价格、口味评分、信任度评分放入independents中，点击statistics，选中Fishers和unstandardized,点击continue-点击classify，选中casewise results和summary table，点击continue，最后点OK。结果分析：表1-1分析案例处理摘要Analysis Case Processing SummaryUnweighted CasesNPercentValid1045.5ExcludedMissing or out-of-range group codes14.5At least one missing discriminating variable0.0Both missing or out-of-range group codes and at least one missing discriminating variable1150.0Total1254.5Total22100.0表1-1为分析案例处理摘要，反映的是邮箱样本量基变量缺失的情况。题目中有一个待检验的样本，所以有1个样本变量值缺失。表1-2组均值的均等性检验Tests of Equality of Group MeansWilks LambdaFdf1df2Sig.销售价格.4124.99527.045口味评分.3556.35227.027信任度评分.18815.16727.003从表1-2可以看出，p值均小于0.05，所以在0.05的置信（改为显著）水平下，销售价格、口味评分、信任度评分都是的均值差异是显著的。表1-3典型判别函数的分析结果EigenvaluesFunctionEigenvalue% of VarianceCumulative %Canonical Correlation119.911a93.393.3.97621.435a6.7100.0.768a. First 2 canonical discriminant functions were used in the analysis.从表1-3可以看出，第一判别函数解释了93.3%的方差，第二判别函数解释了6.7%的方差。表1-4 Wilks Lambda表Wilks LambdaTest of Function(s)Wilks LambdaChi-squaredfSig.1 through 2.02023.5806.0012.4115.3392.069从表1-4可以看出，卡方统计量为23.580，P值为0.001d | G=g)P(G=g | D=d)Squared Mahalanobis Distance to CentroidGroupP(G=g | D=d)Squared Mahalanobis Distance to CentroidFunction 1Function 2pdfOriginal111.4752.9941.4902.00611.7613.345-1.901211.8512.982.3242.0188.2802.880-1.443311.6442.963.8792.0377.3951.569-1.204412*.6162.654.9681.3462.2382.166.431522.2642.6042.6601.3963.5081.170.3006221.0002.950.0001.0505.8692.3821.391722.2642.9962.6601.00413.5493.5942.482833.33721.0002.1781.00048.756-4.490-.860933.77421.000.5132.00079.570-6.416-.0771033.58921.0001.0592.00073.917-6.200.88311ungrouped2.2002.8293.2141.1716.376.705.757*. Misclassified case从表1-9 最后一行可以看出，新品牌饮料的判定销售情况为平销。习题4.9解：SPSS过程：（1）先创建一个变量，命名为group，根据是否履行还贷责任设置1和2，已履行责任设为1，未履行责任设为2，并将待判别的数据也输入到表格中。（2）点击analyse-classify-discriminant-将类别放进grouping variable中，将申请人的年龄、受教育程度、从事工作的年数、未变更住址的年数、收入、负债收入比例、信用卡债务、其他债务等变量放入independents中，点击statistics，选中Fishers和unstandardized,点击continue-点击classify，选中casewise results和summary table，点击continue，最后点OK。结果分析;表2-1分析案例处理摘要Analysis Case Processing SummaryUnweighted CasesNPercentValid1090.9ExcludedMissing or out-of-range group codes19.1At least one missing discriminating variable0.0Both missing or out-of-range group codes and at least one missing discriminating variable0.0Total19.1Total11100.0从表2-1中可以看出，这次判别分析中有10个是已分类样本，有1 个是待分类样本。表2-2 典型判别分析函数的分析结果EigenvaluesFunctionEigenvalue% of VarianceCumulative %Canonical Correlation17.422a100.0100.0.939a. First 1 canonical discriminant functions were used in the analysis.Wilks LambdaTest of Function(s)Wilks LambdaChi-squaredfSig.1.1198.5238.384 从表2-2中的eigenvalues表中可以看出，第一判别函数解释了100%的方差。Wilks Lambda 表是对第一个判别函数的显著性检验。从表中可以看出，卡方统计量为8.523，P值为0.3840.05，所以第一判别函数是不显著的。表2-3 标准化典型判别函数Standardized Canonical Discriminant Function CoefficientsFunction1X1-.190X23.344X3.968X4-2.358X5.418X63.869X71.694X8-6.847表2-4结构矩阵Structure MatrixFunction1X3-.205X6.191X7.159X1-.145X4-.112X2.082X5-.052X8.052Pooled within-groups correlations between discriminating variables and standardized canonical discriminant functions Variables ordered by absolute size of correlation within function.表2-3 和表2-4 反映的是判别函数和判别载荷。表2-3是标准化后的判别函数，表2-4反映的是结构矩阵，即判别载荷。由表2-4可知判别函数为：其中，是标准化后的变量值，标准化变量的系数即为判别权重。通过判别权重和判别载荷可以看出哪些解释变量的贡献比较大。表2-5 费希尔判别函数系数Canonical Discriminant Function CoefficientsFunction1X1-.032X26.687X3.173X4-.357X5.024X6.710X7.792X8-2.383(Constant)-10.794Unstandardized coefficients从表2-5中可以看出，费希尔判别函数为：其中，X1X8是实际的8个解释变量， Y是判别得分。表2-6 贝叶斯判别函数值Classification Function Coefficientsgroup1.002.00X1.340.184X294.070126.660X31.0331.874X4-4.943-6.681X52.9693.086X613.72317.182X7-10.994-7.133X8-37.504-49.116(Constant)-118.693-171.296Fishers linear discriminant functions从表2-6中可以看出，两类的贝叶斯判别函数分别为：（2）Casewise StatisticsCase NumberActual GroupHighest GroupSecond Highest GroupDiscriminant ScoresPredicted GroupP(Dd | G=g)P(G=g | D=d)Squared Mahalanobis Distance to CentroidGroupP(G=g | D=d)Squared Mahalanobis Distance to CentroidFunction 1pdfOriginal111.77311.000.0832.00026.645-2.725211.48511.000.4882.00017.431-1.738311.57011.000.3222.00029.605-3.004411.86711.000.0282.00022.151-2.270511.99311.000.0002.00023.840-2.446622.81011.000.0581.00021.4622.196722.0361.8384.4101.1627.691.337822.84111.000.0401.00025.7492.638922.48711.000.4831.00031.0073.1321022.14911.0002.0871.00039.9193.88111ungrouped1.00011.00036.1542.000118.509-8.450表2-7 按照案例顺序的统计表从表2-7 中可以看出，新客户的类别为1，即可以认为新客户会履行还贷责任。习题4.10解：SPSS过程：（1） 先创建一个变量，命名为group，根据病症将其分为类别1、2、3，胃癌患者为1，萎缩性胃炎患者为2，非胃炎患者为3，（2）点击analyse-classify-discriminant-将类别放进grouping variable中，将,病人的思想生化指标（血清铜蛋白、蓝色反应、鸟吲哚乙酸、中兴硫化物）的变量放入independents中，点击statistics，选中Fishers和unstandardized,点击continue-点击classify，选中casewise results和summary table，点击continue，最后点OK。结果分析：表3-1分析案例处理摘要Analysis Case Processing SummaryUnweighted CasesNPercentValid15100.0ExcludedMissing or out-of-range group codes0.0At least one missing discriminating variable0.0Both missing or out-of-range group codes and at least one missing discriminating variable0.0Total0.0Total15100.0从表3-1中可以看出，本案例总共有15个已分类样本。表3-2 标准化典型判别函数Standardized Canonical Discriminant Function CoefficientsFunction12X1.453-.175X2.596-.811X3.662.600X4.299.608表3-3 结构矩阵Structure MatrixFunction12X3.638*.327X1.234*.057X2.643-.645*X4.295.478*Pooled within-groups correlations between discriminating variables and standardized canonical discriminant functions Variables ordered by absolute size of correlation within function.*. Largest absolute correlation between each variable and any discriminant function表3-2、表3-3 反映的是判别函数和判别载荷。表3-2是标准化的判别函数，表3-3反映的是结构矩阵，即为判别载荷。由表3-2可知判别函数为：其中，X1