数据分析试验三

1、中北大学理学院实验报告实验课程：数据分析专业：信息与计算科学班级：13080241学号:1308024101姓名：潘娟中北大学理学院实验三美国50个州七种犯罪比率的数据分析87【实验目的】通过使用SAS软件对实验数据进行主成分分析和因子分析，熟悉数据分析方法，培养学生分析处理实际数据的综合能力。【实验内容】表3给出的是美国50个州每100000个人中七种犯罪的比率数据。这七种犯罪是：Murder（杀人罪），Rape（强奸罪），Robbery（抢劫罪），Assault（斗殴罪），Burglary（夜盗罪），Larceny（偷盗罪），Auto（汽车犯罪）表3美国50个州七种犯罪的比率数据State

2、MurderRapeRobberyAssaultBurglaryLarcenyAutoAlabama14.225.296.8278.31135.51881.9280.7Alaska10.851.696.8284.01331.73369.8753.3Arizona9.534.2138.2312.32346.14467.4439.5Arkansas8.827.683.2203.4972.61862.1183.4California11.549.4287.0358.02139.43499.8663.5Colorado6.342.0170.7292.91935.23903.2477.1Connecti

3、cut4.216.8129.5131.81346.02620.7593.2Delaware6.024.9157.0194.21682.63678.4467.0Florida10.239.6187.9449.11859.93840.5351.4Georgia11.731.1140.5256.51351.12170.2297.9Hawaii7.225.5128.064.11911.53920.4489.4Idaho5.519.439.6172.51050.82599.6237.6Illinois9.921.8211.3209.01085.02828.5528.6Indiana7.426.5123.

4、2153.51086.22498.7377.4Iowa2.310.641.289.8812.52685.1219.9Kansas6.622.0100.7180.51270.42739.3244.3Kentucky10.119.181.1123.3872.21662.1245.4Louisiana15.530.9142.9335.51165.52469.9337.7Maine2.413.538.7170.01253.12350.7246.9Maryland8.034.8292.1358.91400.03177.7428.5Massachusetts3.120.8169.1231.61532.22

5、311.31140.1Michigan9.338.9261.9274.61522.73159.0545.5Minnesota2.719.585.985.81134.72559.3343.1Mississippi14.319.665.7189.1915.61239.9144.4Missouri9.628.3189.0233.51318.32424.2378.4Montana5.416.739.2156.8804.92773.2309.2Nebraska3.918.164.7112.7760.02316.1249.1Nevada15.849.1323.1355.02453.14212.6559.2

6、NewHampshire3.210.723.276.01041.72343.9293.4NewJersey5.621.0180.4185.11435.82774.5511.5NewMexico8.839.1109.6343.41418.73008.6259.5NewYork10.729.4472.6319.11728.02782.0745.8NorthCarolina10.617.061.3318.31154.12037.8192.1Ohio7.827.3190.5181.11216.02696.8400.488NorthDakota0.99.013.343.8446.11843.0144.7

7、Oklahoma8.629.273.8205.01288.22228.1326.8Oregon4.939.9124.1286.91636.435061388.9Pennsylvania5.619.0130.3128.0877.51624.1333.2RhodeIsland3.610.586.5201.01489.52844.1791.4SouthCarolina11.933.0105.9485.31613.62342.4245.1SouthDakota2.013.517.9155.7570.51704.4147.5Tennessee10.129.7145.8203.91259.71776.53

8、14.0Texas13.333.8152.4208.21603.12988.7397.6Utah3.520.368.8147.31171.63004.6334.5Vermont1.415.930.8101.21348.22201.0265.2Virginia9.023.392.1165.7986.22521.2226.7Washington4.339.6106.2224.81605.63386.9360.3WestVirginia6.013.242.290.9597.41341.7163.3Wisconsin2.812.952.263.7846.92614.2220.7Wyoming5.421

9、.939.7173.9811.62772.2282.01、1）分别用样本协方差矩阵和样本相关矩阵作主成分分析，二者的结果有何差异？2）原始数据的变化可否由三个或者更少的主成分反映，对所选取的主成分给出合理的解释。3）计算从样本相关矩阵出发计算的第一样本主成分的得分并予以排序.2、从样本相关矩阵出发，做因子分析。【实验所使用的仪器设备与软件平台】sAsa件【实验方法与步骤】（阐述实验的原理、方案、方法及完成实验的具体步骤等，附上自己编写的程序）1 .1）主成分分析样本协方差矩阵procprincompdata=work.crimecovariance;run;|样本相关矩阵procprincom

10、pdata=work.crime;|run;3）计算从样本相关矩阵出发计算的第一样本主成分的得分并予以排序.89procprincompdata=crimeout=defen;run;procsortdata=defen;byprinl;run;procprintdata=defen;run;2 .从样本相关矩阵出发，做因子分析。procfactordata=work.crimescore;|run;【实验结果】1.1）分别用样本协方差矩阵和样本相关矩阵作主成分分析，二者的结果有何差异？样本协方差矩阵各变量的均值及其标准差：ThePRINDOMPProcedureObservations50V

11、ariables7SiRpleSUH-lesNundsrRapeRobbsr>As»ulI6urslaryLurcenyAuIdMean25.73400000I24.0SW0211,30000001291.9D400U33029iGD00377.52COODOSW拜阳41105962935I加小能u州?432.4557114638,5750WIBB.394417$样本协方差矩阵：CovarianceMatrix样本协方差矩阵的特殊指标：特征值、差额、贡献率、累计贡献率90MurderRapeRobberyAssaultBUrleiryLarcenyAutnNbrderNUrde

12、rUpSS25.011IG5.?5”L4I645J7-1352B205L4EFfepeFfepe25J1115.775E2酉790.513313.53”9电15RobberyFtobbery165.25562,647805.74934.16MW,0026655.9210032.42归转ullAsssajII251.41738.51羽10050.6727OCe,2078112.075348.14Burt1aryBur#"。E15J73313.592然4工。2700S.20187017,94470512.9946664,15Lsrcen/L方rcw-135M013918.1528655.

13、927BI12.07470512,99215U37S.1163681,55AutoAuto5L46726-0110093.425348.1446664/1569B8L5537401.40TotdlVariance21756784.3112EigenvaluesoftheCovarianceMatrixE1oenvelueDifferenceProportionCbPniu1ative121527321.E21330145.00.88940J8842197178.8172678-30.00810.9384324498.417744.00.00110.999646754.33765.70JD030

14、.389852350.10.0001LOOOO630.532.20i00001.000078,9O.OOOD1.0000可以得出主成分为Murder（杀人罪）。Ei&enveclorsPriplPrin;Prin3Prin4prin5PrlnGPrin?MurderMurder-.0000620.003595-.005980瞄邮0.0038770.1574100.98775Rape0.0006500.01G208,0088010.047812004149O.BOEI-J50545RobberyRobbe：d0.0C13530.1369900.1319940.4E4E4I0.964629

15、-.021719-.011875AssaultAssaull0.0C3C58d.197992-,1130560.363075-.463548-.049145-.019849BurglaryEkjrglary0.U22C5Ck94087G-.201253-.1的物-.003217-,U0S672LarcenyLarceny0.99/43-.0223620.0033410.000423(MW?吓-刈侬70.000108AutoAuto0.0032910.3761780.34的的-.016798-J78ESS口04m0.005010Larceny（偷盗罪）与Murder（杀人罪）高度相关，Burgl

16、ary（夜盗罪）与Rape（强奸罪）高度相关，Robbery（抢劫罪）与Auto（汽车犯罪）高度相关，Robbery（抢劫罪）与Larceny（偷盗罪）高度相关，Murder（杀人罪）与Auto（汽车犯罪）高度相关。样本相关矩阵ThePRINCOMPProcedure60ObservfttiartsVariablesteanStDMurderRblpbRabbsryAtthuItBursldryLarcenyAuto7.444DUOOOO25.7344)0000IU.D920000211.30000001291.904000一罐泮比加037?.Sf60000IU.75962995EE.3567

17、2433455”148$吼575皿8133.3H4175SimpleStatI-siitsCorrelationMatrixMurderRspeRobberyA&snulLBui总l&ryLircen/AdtciMurderMurder1.00000.G012L邨"(M郦0.3858-.0754O,Q68BRapeRap©0.60121.Q0Q0Q,限190JU30,71215,27090,3488RobberyRobbery0.48370.5919i.ncoa0.56710.6372。，崛g015907AssauItAssauIt口4跖0.74030-55

18、711.0000LEK90.16800.?758BurglaryBurglary0.33580.71J10.697?0.62231.0000D.2346Q.EE3OLarcenyLarceny-.07540.2789L0C99u.i颁U.23461,0)000.0777AutoAuto0.OS890.34A80.59070.27580.55800.077?1.000091EIgenvaIuesoftheCorrelationMMrixEIgenvalueDifferenceProportionCumu1etive19.707457682.563374860.52880.528621.14408

19、3000.123506800.1G340.693131.020576200.636576110.14530.838940.385001100.107103210.05500.893950*277897890.023078740.03970,833650.254819150.04465437Q3E40.870070.210164780.0300L0000可以看出主成分为Murder（杀人罪），Rape（强女干罪），Robbory（抢劫罪）Ei?envetlorsrlnnrid!-uu-HuOu-nDftoAUQOB-AbrrflcUrUTInui.1OD-Quon.Du*u/_rRUAHL-1A

20、hOu/14Fhvr-nkuAH*_rhH.QurftuAv-1,Tflrtv69iJInuro.Ou,1OuOuQunu.1_rkuMUI-TJcdr(flflflJu-fld-Fhu-LTV!®,uMnclr以什，aryny"3®eDelus.ceo.rpQs,rrIL.u驾Jus-uMHPMJIilHnD1Hrarynygflvu-,e出因此SArgrchuanuos-uAMuMHPMnhHHpunH各成分间没有很高的相关性，没有两个成分的相关度达到0.9以上。Robbory（抢劫罪）与Larceny（偷盗罪）的相关系数为0.736050Rape（强奸罪）与

21、Auto（汽车犯罪）的相关系数为0.750208两者的差别：<1>主成分发生了变化。用样本协方差矩阵求得主成分为Murder（杀人罪）用样本相关矩阵求得主成分为Murder（杀人罪），Rape（强奸罪），Robbory（抢劫罪）。<2>各成分间的相关系数不不相同。所以由样本协方差矩阵，样本相关矩阵求得的主成分一般是不同的。2）原始数据的变化可否由三个或者更少的主成分反映，对所选取的主成分给出合理的解释。<1>用样本协方差矩阵求出的主成分Murder（杀人罪），它的贡献率为98.94%可以用它来代替其他六个变量，其信息损失量是很小的。<2>用样本相

22、关矩阵求出的主成分为Murder（杀人罪），Rape（强奸罪），Robbory（抢劫罪）。Murder（杀人罪）的贡献率为52.96%,Murder（杀人罪）和Rape（强奸罪）的累计贡献率为69.31%,Murder（杀人罪），Rape（强奸罪），Robbory（抢劫罪）三个的累计贡献率为83,89%。可以用这三个主成分来代替7个原始变量，而且也不至于损失原始变量中的太多信息。3）计算从样本相关矩阵出发计算的第一样本主成分的得分并予以排序92ObsStateMurderRapeRobberyAssftu1tBurglaryLarceny1NorthDakota0.99.013.343.fl4

23、4C.11043.0ZSouthDskota2.0E617.9155.7570.51704.J3loft2.310.841.2帆E8122685.14lestVirginia6.013,242,230,9537.411341.75Wisconsin2,a12,952,263.7S4C.92614.26hfewHampshire3.210.729.276.ID1041.77Nebraska3.916.164,7112.7760.02816.1&Vermont1.416.330,H101.21348.22201.03怖in日?.413.538J170.01253J235C.710Monta

24、na5.416.733.21565904.32773.211Minresota2.719.5S5.9SE.81134.72559,312doming5.421.939.7173.fi61l.£2772.213Idaho5.619.439,6172.51050.82G89.G14Utah3.&20.968.8147.3I1W.E3004.615Pencsy1vania5.619.0130.9128.0877.51624.116Kentucl</Yirinia1QJ18JSI.1123.3872.21662,1173.023.392.1165.7986.22521.2ISM

25、ississippi14.919.665.7189.1915.61288.819Kftrksas6.E2240100.7130.51270.42733.320Arkansas3.»2LE降2208.4972.B18B2J21Connecticut4.216.81129.5131.S1846.02(20.722Indiana7.4练5123.2153.51036.22498.723RhodeIsland印10.566.5201.ID1489.52844.124NorthCstrO'lIna10,617.061,931g.21154.12037.825Ok1ahoma»

26、,6294273.H205.01288.2222S.i26阳wJerseyR.62L0100.4185J1435#?74,527Haaii7.2£5.512S.064.11911.53920.42SOhio7.S27.3190.5131.11218,02696.S29Tennessee10.129.7145.82*91259.?1776.590Alabaza14.?26.296,H278.31135.51891.331Dsloart6.02448157.0194.21B82.68G78.4SAS系统2016年。制旧星期三上午。场ObsAutoPrinlPrin2PrinSPrinlP

27、riMPrinSPrin71144.7-3.823930.223660.0545?0.23310-0.10104-OJ0195-0.435162147.5-2.89759-0.17857Q.32568-C.142501.35&12-0.SS349-0.442533219.$-2.732710.385370.003040,05178-0.13318-0.307630.032344163.3-2.87196-0.603610.100050.43749-1.088560.1004S-0.098085220.7-2,S660Q1.37462-0,042230.13374-0.39222-0.0

28、8091-0,073776293.42504580”525450.21564-C.,213965-0J71SS0.12530Q.see421249.1-2.125890.06620Q.02502C.1S190*0.05399-0.09270-Q.43459g265.2-2.03424O,.7717S-0.10537-0.82610-0.57322-0J75530.21957924S.3-1.830710.405540.05353-C.75E03-a.iooes-D.5848S0.4025210309.2-1.929S4-0.0459S0.106080,091730.48091k顺30-D.06

29、55411348.1-1.S54750.77129-0.3E03G-C.16310-0U92E70.08590-0.2407712282.0-1.56779-0.185670.31673-C,0i74770.422750.05493-g.4105013237.6'1.60014-L.201140.39222-Q.3和的0.07754-0.060930.0613914334.5-1.327430.53535-0.0510S-0*37274-0.11851-C.11009-0.1020E15333.2-1.320780.01118-0.462730.57334-0.14641<0.1

30、154030655IE246.4-1.30764-0.827200.0425SC.65887-0.10024C.568790.1748117226.7-0.38129-0J66870.3225(U5第。-0J44000.25240-0,0499918H4.4'0.81874畸80.600600.100910644?0.G3G1S19244.3-0.72378-0.21492Q.19778-0.14301-0.87664-0.170330.1546720163.4-0.69403-L.056640.522080.05519-0.062910.013002-0.3698621538.2-O

31、.G2012L.2423D1.1214SC.053270.090190.136450.3027522377.4-0.46S53-0.05824-0.197140.235250.134310,32850-0.3596423791.4-0.30022L784线-1.G0096-0.407941.137590.071210.9639724192.1-0.38399-L.417540.62093-0.150360,71897-0.49389Q.B693525326.8'0.12009-L.462700.2?429-0.382710.010B0H.4326S-0.101302G511.50.12

32、9880/6988-0.84133C.1S421-0J7061-0.264200.2118927469.40.170271.04430-0.57074-0.34414-1.225701.035790.6537626400.40.2加150.0108?-0.333840.57098-0-34999-0.04418-0.2991S29314.00,30359-0.75340-5,014440.23550-0.301560.25268-0,1477630280.70.399G2-1.894610.412050.377550-533710.411980-52368314E7.00.4S5950.754

33、72-0.41699-C.28279*0,43264-0.08G870,338642.从样本相关矩阵出发，做因子分析93於S系统201RTheFACTORProcedureRawData505050InputLtttaTypeNumberofRecordsReadNumbernfRecordsUsedNforSignificanceTestsEicenvalueDifferenceProportionCumu1atIve13J07457882,563374860.52960.G29621.144083000J23506300.1G840,B83131.020576200,635575110.14580.898940.385001100JO71