主成分分析实验报告

1、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）SAS、SPSS EXCEL软件二、实验（

2、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）（Pri ncipal comp onent an alysis）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：下表中给出了不同国家及地区

3、的男子径赛记录：（t8a6）1500500010,000MarathCountry100m200m400m800mmmmon(s)(s)(s)(mi n)(mi n)(mi n)(mi n)(mi ns)Arge nti na10.3920.8146.841.813.714.0429.36137.72Australia10.3120.0644.841.743.5713.2827.66128.3Austria10.4420.8146.821.793.613.2627.72135.9Belgium10.3420.6845.041.733.613.2227.45129.95Bermuda10.282

4、0.5845.911.83.7514.6830.55146.62Brazil10.2220.4345.211.733.6613.6228.62133.13Burma10.6421.5514.4530.28139.95Canada10.1720.2245.681.763.6313.5528.09130.15Chile10.3420.846.21.793.7113.6129.3134.03China10.5121.0447.31.813.7313.929.13133.53Columbia10.4321.0546.11.823.7413.4927.88131.35Cook Is

5、lands12.1823.252.942.024.2416.735.38164.7Costa 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 Republic10.1420.6546.81.823.8214.9131.45154.12Finland10.4320.6945.491.743.6113.2727.52130.87France10.11

6、20.3845.281.733.5713.3427.97132.3German (D.R.)10.1220.3344.871.733.5613.1727.42129.92German (F.R.)10.1620.3744.51.733.5313.2127.61132.23Great Brit.& N.Ireland10.1120.2144.931.73.5113.0127.51129.13Greece10.2220.7146.561.783.6414.5928.45134.6Guatemala10.9821.8248.41.893.814.1630.11139.33Hungary10.2620

7、.6246.021.773.6213.4928.44132.58India10.621.4245.731.763.7313.7728.81131.98Indonesia10.5921.4947.81.843.9214.7330.79148.83Ireland10.6120.9646.31.793.5613.3227.81132.35Israel10.712147.81.773.7213.6628.93137.55Italy10.0119.7245.261.733.613.2327.52131.08Japan10.3420.8145.861.793.6413.4127.72128.63Kenya

8、10.4620.6644.921.733.5513.127.38129.75Korea10.3420.8946.91.793.7713.9629.23136.25D.P.R Korea10.9121.9447.31.853.7714.1329.67130.87Luxembourg10.3520.7747.41.823.6713.6429.08141.27Malaysia10.420.9246.31.823.814.6431.01154.1Mauritius11.1922.4547.71.883.8315.0631.77152.23Mexico10.4221.3513.462

9、7.95129.2Netherlands10.5220.9545.11.743.6213.3627.61129.02New Zealand10.5120.8846.11.743.5413.2127.7128.98Norway10.5521.1646.711.763.6213.3427.69131.48Papua New Guinea10.9621.78114.7231.36148.22Philippines10.7821.6446.241.813.8314.7430.64145.27Poland10.1620.2445.361.763.613.2927.89131.58Po

10、rtugal10.5321.1746.71.793.6213.1327.38128.65Rumania10.4120.9845.871.763.6413.2527.67132.5Singapore10.3821.2847.41.883.8915.1131.32157.77Spain10.4220.7745.981.763.5513.3127.73131.57Sweden10.2520.6145.631.773.6113.2927.94130.63Switzerland10.3720.4645.781.783.5513.2227.91131.2Taipei10.5921.2946.81.793.

11、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Princomp过程求主成分；并对结果进

12、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;KbcdeT Eh5Prin2Prin3PrinA3rin53rin63rin?PrinBft.66R7Sfi ?2?628.127628Pt內尸旺-5=J3704R.11G741A.1R554?B.461520.3605S7-.259116-.1533570.656137-.112643-.eg60540.24B273-.5604670-652341-.21S3230. IS6625-.952

13、354-.0&0127G.0L2+33-.532432-4-7939S0.5+0353-.314692-.23301603&165-.U9W-.153+43-451-.4-37715-.157&43Q.&100119.13S29L-.zS二上廿旳-.253979-.141299H.54fab9/-.306K600.1&1752飢 08O06S-13317C219017-.176371-.796795-.4 J 63263.2 990.2395120.4373280.315285O.3988220.1SS164tigenvectors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

14、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;Eigenvalues of the Correlation MatrixEigenvalueDifferenutProportionCurrulative15.744527849.82739.327320.877618290+718297159.10979.937S315932114e.0352717608199e.?574斗B * 124049390.044169110+01559.972950.079S3027G,01191512e.eiw9.9S29石0.067965156.021545620.0085B. 99147

15、0 046419530.023S19430.005S0.997280.00281.0012:52 Thursday, April 23, 2&122igenslue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;得分排名国家得分得分排名国家得分得分排名国家得分1Cook Islands10.5556320 Argentina0.26189639Brazil-1.558262 Western Sam7.o23121621Luxembourg0.22050940New Zealand

16、 -1.599713Mauritius4.25865822Korea0.20754541Sweden-1.603234Papua New 3G.90919323India-0.1652442Switzerland-1.638975Singapore3.12211124Greece-0.3795943Finland-1.692026Thailand2.76181725Chile-0.3810844Canada-1.746357Indonesia2.74779926Columbia-0.3900745Poland-2.000618Guatemala2.67243527Mexico-0.678534

17、6Belgium-2.041269Costa Rica2.29664728 Austria-0.8076447Kenya-2.1683210Philippines2.07042229Norway-0.8114948France-2.171911Burma1.9718730Ireland-0.884249Australia-2.4463712Dominican R1e.71488631Portugal-0.9163750German (F.R.-)2.5527413Malaysia1.70828332Denmark-1.1132451German (D.R.-)2.5900914D.P.R Ko

18、rea1.68368733Rumania-1.1964952USSR-2.6268515Taipei0.95050234Hungary-1.2051953Italy-2.7269516Bermuda0.73925735 Japan-1.2378754Great Brit.& N- 3.0242317Israel0.43458636Czechoslova-k1.3725655USA-3.4305618China0.4089737Spain-1.4805919Turkey0.2660838Netherlands-1.55543（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

19、是 Coook 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.bDATAFILE= f:sastest.xlsDBMS=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=1;ods output Eigenvalues = work._eigen;proc princomp data=WORK.b out=WORK.SCORE