数据分析实验报告8 主成分分析

学号：100111114班级：信息101姓名：赵永光实验八主成分分析一、实验目的和要求能利用原始数据与相关矩阵、协主差矩阵作主成分分析,并能理解标准化变量主成分与原始数据主成分的联系与区别；能根据SAS输出结果选出满足要求的几个主成分．实验要求:编写程序，结果分析．实验内容：书上4.54.64.5dataexamp4_5;inputidx1-x8;cards;18.3523.537.518.6217.4210.001.0411.2129.2523.756.619.1917.7710.481.7210.5138.1930.504.729.7816.287.602.5210.3247.7329.205.429.4319.298.492.5210.0059.4227.938.208.1416.179.421.559.7669.1627.989.019.3215.999.101.8211.35710.0628.6410.5210.0516.188.391.9610.8189.0928.127.409.6217.2611.122.4912.6599.4128.205.7710.8016.3611.561.5312.17108.7028.127.2110.5319.4513.301.6611.96116.9329.854.549.4916.6210.651.8813.61128.6736.057.317.7516.6711.682.3812.88139.9837.697.018.9416.1511.080.8311.67146.7738.696.018.8214.7911.441.7413.23158.1437.759.618.4913.159.761.2811.28167.6735.718.048.3115.137.761.4113.25177.9039.778.4912.9419.2711.052.0413.29187.1840.917.328.9417.6012.751.1414.80198.8233.707.5910.9818.8214.731.7810.10206.2535.024.726.2810.037.151.9310.392110.6052.417.709.9812.5311.702.3114.69227.2752.653.849.1613.0315.261.9814.572313.4555.855.507.459.559.522.2116.302410.8544.687.3214.5117.1312.081.2611.57257.2145.797.6610.3616.5612.862.2511.69267.6850.3711.3513.3019.2514.592.7514.87277.7848.448.0020.5122.1215.731.1516.61287.9439.6520.9720.8222.5212.411.757.90298.2864.348.0022.2220.0615.120.7222.893012.4776.395.5211.2414.5222.005.4625.50;run;proccorrcovnosimpledata=examp4_5;varx1-x8;run;procprincompdata=examp4_5prefix=yout=bb;varx1-x8;run;procplotdata=bb;ploty2*y1$id='*';procsortdata=bb;bydescendingy1;run;procprintdata=bb;varidy1y2x1-x8;run;输出结果：1、样本相关系数矩阵CorrelationMatrixx1x2x3x4x5x6x7x8x11.00000.3336-.0545-.0613-.28940.19880.34870.3187x20.33361.0000-.02290.3989-.15630.71110.41360.8350x3-.0545-.02291.00000.53330.49680.0328-.1391-.2584x4-.06130.39890.53331.00000.69840.4679-.17130.3128x5-.2894-.15630.49680.69841.00000.2801-.2083-.0812x60.19880.71110.03280.46790.28011.00000.41680.7016x70.34870.4136-.1391-.1713-.20830.41681.00000.3989x80.31870.8350-.25840.3128-.08120.70160.39891.00002、调用主成分分析的princomp过程，从相关系数矩阵出发进行主成分分析，输出集bbThePRINCOMPProcedureObservations30Variables8SimpleStatisticsx1x2x3x4Mean8.70666666739.056000007.62900000010.86566667StD1.61472819012.438758283.0527165403.89495579SimpleStatisticsx5x6x7x8Mean16.5890000011.626000001.90200000013.06100000StD2.997854813.058108050.8515762263.647070961）样本相关系数矩阵R的特征值、各主成分贡献率及累计贡献率EigenvaluesoftheCorrelationMatrix特征值Difference贡献率%累计贡献率%13.096288290.729065220.38700.387022.367223071.447235720.29590.6829已达68.29%30.919987350.214061990.11500.797940.705925360.207483030.08820.886250.498442330.268554030.06230.948560.229888310.099112540.02870.977270.130775770.079306230.01630.993680.051469540.00641.0000

SAS系统14:09Monday,October22,200122ThePRINCOMPProcedure2）样本相关系数矩阵R特征值的正交化特征向量TheSASSystem17:30Tuesday,October26,20124ThePRINCOMPProcedureEigenvectorsy1y2y3y4y5y6y7y8x10.249607-.2412380.693918-.3767700.502313-.018418-.0365430.045052x20.519234-.037607-.071261-.224871-.4244530.001760-.2824670.642950x3-.0184800.4754390.5778190.032379-.510472-.1733440.381416-.050854x40.2540920.538081-.021777-.2310660.0103580.399113-.471680-.458432x50.0216950.575449-.0480870.2853680.5162700.1461090.1591920.520977x60.4926630.134676-.1453480.2242220.177156-.754966-.081452-.244442x70.317147-.2606820.2863910.768116-.0907590.355165-.130720-.089297x80.509332-.087081-.271279-.1769900.0260150.3047200.708416-.1808213）按第一主成分对各省份进行排序TheSASSystem17:30Tuesday,October26,20126Obsidy1y2x1x2x3x4x5x6x7x81306.89591-2.2783312.4776.395.5211.2414.5222.005.4625.502293.248422.560958.2864.348.0022.2220.0615.120.7222.893271.792142.888097.7848.448.0020.5122.1215.731.1516.614261.515071.373537.6850.3711.3513.3019.2514.592.7514.875231.40116-3.1784013.4555.855.507.459.559.522.2116.306211.15390-1.3742010.6052.417.709.9812.5311.702.3114.697221.05651-1.235247.2752.653.849.1613.0315.261.9814.578240.435430.4740910.8544.687.3214.5117.1312.081.2611.579250.153290.113207.2145.797.6610.3616.5612.862.2511.6910170.045200.980567.9039.778.4912.9419.2711.052.0413.291128-0.133244.908447.9439.6520.9720.8222.5212.411.757.901218-0.134890.343637.1840.917.328.9417.6012.751.1414.801319-0.141120.681978.8233.707.5910.9818.8214.731.7810.101412-0.17044-0.589628.6736.057.317.7516.6711.682.3812.88158-0.39220-0.295629.0928.127.409.6217.2611.122.4912.651610-0.430400.645708.7028.127.2110.5319.4513.301.6611.961714-0.51802-0.552276.7738.696.018.8214.7911.441.7413.23189-0.61274-0.282579.4128.205.7710.8016.3611.561.5312.171913-0.66670-0.295489.9837.697.018.9416.1511.080.8311.672011-0.81850-0.421286.9329.854.549.4916.6210.651.8813.61217-1.11335-0.0181510.0628.6410.5210.0516.188.391.9610.812215-1.11496-0.440438.1437.759.618.4913.159.761.2811.28236-1.18223-0.192969.1627.989.019.3215.999.101.8211.35242-1.25819-0.132249.2523.756.619.1917.7710.481.7210.512516-1.25934-0.428277.6735.718.048.3115.137.761.4113.25263-1.29370-0.860338.1930.504.729.7816.287.602.5210.32274-1.32567-0.102397.7329.205.429.4319.298.492.5210.00285-1.48595-0.351569.4227.938.208.1416.179.421.559.76291-1.684480.167438.3523.537.518.6217.4210.001.0411.213020-1.96091-2.108276.2535.024.726.2810.037.151.9310.3由输出结果可以看出：前两个主成分的累计贡献率已达68.29%，因此，取前两个主成分做进一步分析即可．给出了对应于和的正交单位化特征向量和，由此得到标准化指标的前两个样本主成分为为8个指标加权平均，反映各省份在生活基本消费的消费水平能力的综合指标．值大，则各省份的生活水平越低，反映各省份在生活消费品德消费能力综合指标，值大，则各省份的消费水平越高。第一主成分样本得分降序排列依次为：广东上海北京浙江海南福建广西天津江苏辽宁西藏四川山东湖北河北宁夏湖南陕西云南新疆青海安徽甘肃内蒙古贵州吉林黑龙江河南山西江西。4.6dataexamp4_6;inputidx1-x3y1-y3;cards;1606962976998256538410378107380697666991304558090808511456275681161309167464701091011037647166771021308737064115110109968677576851191069827472133127116067611301341211270747815015810013667478150131142148370749998105156866901198510916786375164981381710377771601171211877687414471153196677687782892070707211493122217565717770109229174931181151502366757317014712124758276153132115257471661431051002676706411411312927749086731061162874778011681772967716963877030787580105132803164667183941333271807681878633637573120895934901037410710910135607661991119836487775113124973766939713611212238747076109881053960747172907140637566130101904166808613011714442776774839210743706710015014214644737681119120119457890771221551494673688010290122477283681046996486560701199489495270769294100;run;proccorrcovnosimpledata=examp4_6;varx1-x3y1-y3;run;procprincompdata=examp4_6prefix=yout=bb;varx1-x3y1-y3;run;procprincompcovdata=examp4_6;varx1-x3y1-y3;run;procsortdata=bb;bydescendingy1;run;输出结果：1、调用主成分分析的princomp过程，从相关系数矩阵出发进行主成分分析，输出集bb1）样本相关系数矩阵R的特征值、各主成分贡献率及累计贡献率EigenvaluesoftheCorrelationMatrixEigenvalueDifferenceProportionCumulative12.121571661.037363700.35360.353621.084207960.086246200.18070.534330.997961760.126282980.16630.700640.871678770.292251460.14530.845950.579427310.234274770.09660.942560.345152540.05751.00002）样本相关系数矩阵R特征值的正交化特征向量Eigenvectorsy1y2y3y4y5y6x10.3446250.1487210.4541790.7393800.146362-.291088x20.2618130.843332-.066937-.051728-.1154850.446936x30.3681410.0502500.487105-.6432350.410527-.205892y10.469630-.325477-.3950130.1536280.5484700.439382y20.4919500.085830-.552875-.096822-.253064-.609535y30.463241-.3883890.300440-.062561-.6571510.3294462、调用主成分分析的princomp过程，从协方差阵出发进行主成分分析1）样本协方差矩阵R的特征值、各主成分贡献率及累计贡献率EigenvaluesoftheCovarianceMatrixEigenvalueDifferenceProportionCumulative11097.39817699.402130.54230.54232397.9960484.897030.19670.73903313.09901213.354190.15470.8938499.7448229.626820.04930.9