主成分分析实验报告.docx

1、主成分分析实验报告项 目 名 称 实验4主成分分析 所属课程名称 多元统计分析（英） 项 目 类 型 综合性实验 实验(实训)日期 2012年 4 月 15 日 一、实验（实训）概述：【目的及要求】主成分分析利用指标之间的相关性，将多个指标转化为少数几个综合指标，从而达到降维和数据结构简化的目的。这些综合指标反映了原始指标的绝大部分信息，通常表示为原始指标的某种线性组合，且综合指标间不相关。利用矩阵代数的知识可求解主成分。按具体的题目要求完成实验报告,并及时上传到给定的FTP和课程网站！【基本原理】利用指标之间的相关性，将多个指标转化为少数几个综合指标。【实施环境】（使用的材料、设备、软件）S

2、AS、SPSS、EXCEL软件二、实验（实训）内容：【项目内容】主成分分析。【方案设计】题目:由原始数据求主成分。【实验（实训）过程】（步骤、记录、数据、程序等）附后【结论】（结果、分析）附后三、指导教师评语及成绩：评语：成绩： 指导教师签名： 批阅日期：实验报告4主成分分析（综合性实验）(Principal component analysis)实验原理：主成分分析利用指标之间的相关性，将多个指标转化为少数几个综合指标，从而达到降维和数据结构简化的目的。这些综合指标反映了原始指标的绝大部分信息，通常表示为原始指标的某种线性组合，且综合指标间不相关。利用矩阵代数的知识可求解主成分。实验题目：下

3、表中给出了不同国家及地区的男子径赛记录： (t8a6)Country100m (s)200m (s)400m (s)800m (min)1500m (min)5000m (min)10,000m (min)Marathon (mins)Argentina10.3920.8146.841.813.714.0429.36137.72Australia10.3120.0644.841.743.5713.2827.66128.3Austria10.4420.8146.821.793.613.2627.72135.9Belgium10.3420.6845.041.733.613.2227.45129.9

4、5Bermuda10.2820.5845.911.83.7514.6830.55146.62Brazil10.2220.4345.211.733.6613.6228.62133.13Burma10.6421.5248.31.83.8514.4530.28139.95Canada10.1720.2245.681.763.6313.5528.09130.15Chile10.3420.846.21.793.7113.6129.3134.03China10.5121.0447.31.813.7313.929.13133.53Columbia10.4321.0546.11.823.7413.4927.8

5、8131.35Cook Islands12.1823.252.942.024.2416.735.38164.7Costa Rica10.9421.948.661.873.8414.0328.81136.58Czechoslovakia10.3520.6545.641.763.5813.4228.19134.32Denmark10.5620.5245.891.783.6113.528.11130.78Dominican Republic10.1420.6546.81.823.8214.9131.45154.12Finland10.4320.6945.491.743.6113.2727.52130

6、.87France10.1120.3845.281.733.5713.3427.97132.3German (D.R.)10.1220.3344.871.733.5613.1727.42129.92German (F.R.)10.1620.3744.51.733.5313.2127.61132.23Great Brit.& N. Ireland10.1120.2144.931.73.5113.0127.51129.13Greece10.2220.7146.561.783.6414.5928.45134.6Guatemala10.9821.8248.41.893.814.1630.11139.3

7、3Hungary10.2620.6246.021.773.6213.4928.44132.58India10.621.4245.731.763.7313.7728.81131.98Indonesia10.5921.4947.81.843.9214.7330.79148.83Ireland10.6120.9646.31.793.5613.3227.81132.35Israel10.712147.81.773.7213.6628.93137.55Italy10.0119.7245.261.733.613.2327.52131.08Japan10.3420.8145.861.793.6413.412

8、7.72128.63Kenya10.4620.6644.921.733.5513.127.38129.75Korea10.3420.8946.91.793.7713.9629.23136.25D.P.R Korea10.9121.9447.31.853.7714.1329.67130.87Luxembourg10.3520.7747.41.823.6713.6429.08141.27Malaysia10.420.9246.31.823.814.6431.01154.1Mauritius11.1922.4547.71.883.8315.0631.77152.23Mexico10.4221.346

9、.11.83.6513.4627.95129.2Netherlands10.5220.9545.11.743.6213.3627.61129.02New Zealand10.5120.8846.11.743.5413.2127.7128.98Norway10.5521.1646.711.763.6213.3427.69131.48Papua New Guinea10.9621.7847.91.94.0114.7231.36148.22Philippines10.7821.6446.241.813.8314.7430.64145.27Poland10.1620.2445.361.763.613.

10、2927.89131.58Portugal10.5321.1746.71.793.6213.1327.38128.65Rumania10.4120.9845.871.763.6413.2527.67132.5Singapore10.3821.2847.41.883.8915.1131.32157.77Spain10.4220.7745.981.763.5513.3127.73131.57Sweden10.2520.6145.631.773.6113.2927.94130.63Switzerland10.3720.4645.781.783.5513.2227.91131.2Taipei10.59

11、21.2946.81.793.7714.0730.07139.27Thailand10.3921.0947.911.833.8415.2332.56149.9Turkey10.7121.4347.61.793.6713.5628.58131.5USA9.9319.7543.861.733.5313.227.43128.22USSR10.072044.61.753.5913.227.53130.55Western Samoa10.8221.86492.024.2416.2834.71161.83（数据来源：1984年洛杉机奥运会IAAF/AFT径赛与田赛统计手册）实验要求：（1）试用Princo

12、mp过程求主成分；并对结果进行解释；（2）试用方差累积贡献率和Scree图确定主成分的个数；（3）计算各国第一主成分的得分并排名；（4）试对结果进行解。实验题目分析报告：（1）试用Princomp过程求主成分；并对结果进行解释；如上就是主成分分析截图，利用sas处理数据后我们可以知道：有8个主成分。（2）试用方差累积贡献率和Scree图确定主成分的个数；从上面的主成分累计贡献率截图和碎石图我们可以分析：选取两个主成分的贡献率就已经达到0.9375.所以我们选取2个主成分个数。（3）计算各国第一主成分的得分并排名；（4）试对结果进行解。对上述的各个国家的第一主成分得分排名，排在第一的是Coook

13、 Island,排名中也有出现第一主成分得分负数的，这主要是因为求出来的数据与对应的数据相乘的结果。相关程序：（1） 导入数据程序PROC IMPORT OUT= WORK.b DATAFILE= f:sastest.xls DBMS=EXCEL REPLACE; RANGE=Sheet1$; GETNAMES=YES; MIXED=NO; SCANTEXT=YES; USEDATE=YES; SCANTIME=YES;RUN;（2） 得到主成分并且画图分析程序： title; footnote;* Principal Components Analysis * ;options pageno

14、=1;ods output Eigenvalues = work._eigen;proc princomp data=WORK.b out=WORK.SCORE outstat=WORK.STATS; var A B C D E F G H;run; quit;goptions reset=all device=WIN;* Scree Plot *;data work._eigen; set work._eigen; if eigenvalue 0; rename number=Component; drop difference proportion cumulative;run; titl

15、e; footnote;goptions ftext=SWISS ctext=BLACK htext=1 cells;axis1 minor=none major=(number=5) label=(Eigenvalue);pattern1 value=SOLID color=BLUE;proc gchart data=work._eigen ; format eigenvalue best8.; vbar component / type=sum sumvar=eigenvalue discrete raxis=axis1 frame cframe=CXF7E1C2 caxis=BLACK coutline=BLACK name=SCREE description=Scree plot;run;quit;goptions reset=pattern ftext= ctext= htext=;goptions reset=all device=WIN ;