多元统计分析(期末试题)聚类分析主成分分析因子分析.pdf
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1、2011-2012学年第一学期多元统计分析上机考试试卷班级:金融工程2009 级学号:2009310283 姓名:田睿电脑序号:考试说明:1、打开本试卷的WORD 文件后,首先将本 WORD 文档“另存”,将文件名设为你的“学号+姓名”(注意,学号在前),并在本试卷中再次填好班级、姓名、学号、电脑序号,再根据题目要求将必要的结果复制到本文件中并进行必要的分析。考试结束时,提交该WORD 文档,请不要提交SPSS的结果文件。2、考试时间120 分钟,16:00 18:00。考试结束后,将本试卷上传至ftp:/(用户名和密码:mengjie2010)的“多元统计期末考试提交”子目录。注意,请务必到
2、教师工作台向监考教师确认你的试卷已经上传成功后,再离开教室。上机操作题:1、(32 分)为了从1 张心电图的5 项不同指标(X1X5)中找出区分健康人(group=1)、硬化症患者(group=2)和冠心病患者(group=3)这 3 类人的方法,对3 类人分别取容量为 n1=11、n2=7、n3=5 的 3 个样本,原始数据见表1。请对此案例进行判别分析,并回答以下问题:(1)简述 Fisher 判别分析的基本原理。(2)本题中,请分析三组人群在各项指标的取值上是否有显著差异。(显著性水平取0.1)(3)请写出贝叶斯判别函数的表达式。(先验概率按各组的样本容量比重确定)(4)请写出未标准化的
3、Fisher 判别函数的表达式。(5)分析三组人群被错判的情况。(6)画出表示三组人群的两个Fisher 判别式得分的散点图,用不同颜色的符号区别表示不同的人群。(7)新测得某人的5 项指标值为(9.11,231.99,12.62,5.73,6.49),请给出其贝叶斯判别的后验概率值,以及Fisher 判别函数的得分值,则他属于哪类?(8)贝叶斯判别方法的判别准则并不唯一,请说明在SPSS软件中,所输出的Bayes 判别函数的结果是在怎样的假设条件以及准则下计算得到的。答:1.Fisher 判别分析的基本原理是:通过投影,用 p 维变量的少数几个线性组合(即判别函数),来代替原始的p 维变量,
4、以达到降维的目的,再根据样品在这些判别函数上的取值,对样品的归属做出判别。2.由 SPSS输出表格:组均值的均等性的检验Wilks 的 Lambda F df1 df2 Sig.X1.853 1.729 2 20.203 X2.598 6.713 2 20.006 X3.773 2.939 2 20.076 X4.751 3.310 2 20.057 X5.701 4.272 2 20.029 看各个总体在均值等指标上除了x1 均小于 0.1,说明 x2 到 x5之间有显著的差异,而 x1的检验值大于0.1,拒绝原假设,说明其总体之间指标差异不大3.由SPSS输出表格分类函数系数group 1
5、 2 3 X1 8.005 7.446 7.284 X2-.463-.401-.434 X3.091.121.365 X4 108.180 103.481 103.183 X5 30.148 28.316 29.247(常量)-388.026-361.993-361.866 Fisher 的线性判别式函数通过上表写出 Bayes判别函数分别为:F1=-388.026+8.005x1-0.463x2+0.091x3+108.180 x4+30.148x5 F2=-361.993+7.446x1-0.401x2+0.121x3+103.481x4+28.316x5 F3=-361.866+7.28
6、4x1-0.434x2+0.365x3+103.183x4+29.247x5 4.由SPSS输出表格:典型判别式函数系数文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5
7、ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3
8、U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3
9、文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:C
10、X10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y
11、4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2
12、HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3函数1 2 X1.299.110 X2-.024
13、.016 X3-.060-.137 X4 2.319.329 X5.710-.456(常量)-12.716-1.091 非标准化系数F1=-12.716+0.299x1-0.024x2-0.06x3+2.319x4+0.710 x5 F2=-1.091+0.110 x1+0.016x2-0.137x3+0.329x4-0.456x5 5.由SPSS输出表格分类结果agroup 预测组成员合计1 2 3 初始计数1 11 0 0 11 2 0 6 1 7 3 1 0 4 5%1 100.0.0.0 100.0 2.0 85.7 14.3 100.0 3 20.0.0 80.0 100.0 a.已
14、对初始分组案例中的 91.3%个进行了正确分类。由上图可知,第一组成员全部判断正确;第二组错判为第一组的概率是14.3%;第三组错判成第一组的概率是20%6.由SPSS输出表格文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档
15、编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX1
16、0T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M
17、3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC
18、7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I
19、4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW
20、10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5
21、J8Y37.某人的 5 项指标值为(9.11,231.99,12.62,5.73,6.49)将各样品的自变量值代入上述三个Bayes判别函数:F1=-388.026+8.005x1-0.463x2+0.091x3+108.180 x4+30.148x5 F2=-361.993+7.446x1-0.401x2+0.121x3+103.481x4+28.316x5 F3=-361.866+7.284x1-0.434x2+0.365x3+103.183x4+29.247x5 得到:F1=F2=F3=两个 Fisher判别函数分别为:F1=-12.716+0.299x1-0.024x2-0.06x3+
22、2.319x4+0.710 x5 F2=-1.091+0.110 x1+0.016x2-0.137x3+0.329x4-0.456x5 F1=1.567 F2=0.9058.距离判别法虽然简单、便于使用,但是该方法也有它明显的不足之处。一,把总体等同看待,没有考虑到各总体会以不同的概率(先验概率)出现,也即判别方法与总体各自出现的概率的大小无关。第二,判别方法与错判之后所造成的损失无关,没有考虑误判之后所造成的损失的差异文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码
23、:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T
24、1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J
25、2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I8Z2I4J5 ZW10U3U5J8Y3文档编码:CX10T1Y4M3J2 HC7I
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