实验3美国50个州七种犯罪比率的数据分析

1、资料.实验三 美国50个州七种犯罪比率的数据分析【实验目的】L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个州七种犯釜的比率数据State Murder Rape RobberyAssaultBurglaryLarcenyAutoAlabama

2、 Alaska Arizona Arkonsos California Colorado Conn ecticut Delaware Florida Georgia Hawaii Idaho Illinois Indiana Iowa Konsos Ken tucky Louisi ono Maine Maryla nd Mossochuse 卄 s Michig on Minn esota Mississippi Missouri Mont ono Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carol

3、ina Ohio North Dakota Oklahoma Oregon Penn sylva nio.2.858.5320.2.7259436J.540137.3649.8M1 09.8.1 16.46.1 01 17.59.7.2&1 01 528.3.9.2M9.53.1 523.6 8758.10.6Ci2626408961548560195889563711 5L47.9.26.49.L59.L6.o.29.o.3.408.9.9.8.6.8.9.25324412332122121313231121140 14 19 92 3 2o71.3O.28Q27929391988.22Q7

4、.5Q.9.5Q6.3.2271.97 .997Q27 J96.96.13883.28717012915718714012839.211123益引14238.29216926185.65.18939.64.32323.24 6 6CJ9.28 0 711453 319013.73.1241303034098215150535350966315870 8.423.8.2L49.&4.29.3.?.Q35Q8.1 .45.9.S&25 78105939456470539823753735835152232321142612181131322812113o76.5 3 98 4 113 338138

5、 0-9-0.1 M 5 6 88430 8 214 2 2 11135.51881.9280.71331.73369.8753.32346.14467.4439.5972.61862183.42139.43499.8663.51935.23903.2477.11346.02620.7593.21682.63678.4467.01859.93840.5351.413512170.2297.91911.53920.4489.41050.82599.6237.61085.02828.5528.61086.22498.7377.4812.52685.1219.91270.42739.3244.387

6、2.21662.1245.41165.52469.9337.71253.12350.7246.91400.03177.7428.51532.22311.31140.11522.73159.0545.51134.72559.3343.1915.61239.9144.41318.32424.2378.4804.92773.2309.2760.02316.124924534212.6559.21041.72343.9293.41435.82774.5511.51418.73008.6259.51728.02782.0745.81154.12037.8192.11216.02696.8400.4446

7、.11843.0144.71288.22228.1326.81636.435061388.9877.51624.1333.2Rhode IslondSouthCarolinaSouth DakotaTenn esseeTexasUtahVerm ontVirginiaWashi ngtonWest VirginiaWisconsinWyoming6.9O.35 4 o 3 o 8 43.1 2 OI33.1 .9.46.2 55 o03.1 357.8.3.9.3.6.28.93.9.3.053.9.3.2L123212311286.5201.01489.52844791.4105.9485.

8、31613.62342.424517.9155.7570.51704.4147.5145.8203.91259.71776.5314.0152.4208.216032988.7397.668.8147.31171.63004.6334.530.8101.21348.22201.0265.292165.7986.22521.2226.7106.2224.81605.63386.9360.342.290.9597.41341.7163.352.263.7846.92614.2220.739.7173.9811.62772.2282.01、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

9、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】计算机、SAS9.4（简体中文）【实验方法或步骤】1. 先将数据输入到Excel中，再通过SAS系统导入数据。融代码：proc princomp doto二work.crime covarianee;run;proc princomp doto二work.crime out二defen;run;proc sort data=defen;by prinl;run;pr

10、oc print data=defen;run;proc factor data=work.crime simple corr;run;proc factor data=work.crime priors=smc msa scree residual preplot rotate=promax reorder plot outstat=fact_all;run;【实验原理】因子分析与主成分分析有区别：主成分分析只是简单的变量代换，而因子分析要构造因子模型；主成分分析时将一组具有相关关系的变量变换为一组互不相 关的变量，而因子分析的目的是要用尽可能少的因子构造一个结构简单的因子模 型，主成分分析

11、是将主成分表示成原始变量的线性组合，而因子分析时将原始变 量表示成公共因子和特殊因子的线性组合。【实验结果】1、丨）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：均值和标准差：SAS系铳PRINCOMP 过召观测5087MurderRapeRobberyAssaultBurglaryLarcenyAuto均危7 44400000025 73400000124 0920000211 30000001291 9040003302 386000377S260000StD386676894110 7596299588 3485672100 2530492432

12、4557114638 575008193 3944175协方差矩阵和总方差:MurderRapeRobberyAssauKBurglaryLarcenyAutoMurder材 urder14 9525.01165 25251 41645 17-1352 2051 46RapeRape250111577562 64796513313591391815726 01RobberyRobbery165.25562 6478(474934 1624347 0028655 9210092 42AssauliAssault251 41798 514934 1610050 6727006 2078112 07

13、5348 14BurglaryBurglary645 173313 5924347 0027006 2018701794470512 9946664 15LarcenyLarceny-1352 2013918 1528655 9278112 0747051299215163781169681 55AinoAuto51 467260110092 4253481446664 1569681 5537401 40总右差 217S8784 312协方差矩阵的待征值：待征值、差分、比例、累积:协方差矩阵旳W4Efi特征3差分比例累积121527321.621330145.00.98940.9894219

14、71766172678.300D910 984324498.417744.00.00110.999645754.33765.70.00030.999952G88 62950.1000011 0000638.532.20.00001.000076.30.00001.0000可以得岀主成分为Murder （杀人罪）。PnnlPrin2Prin3Prin4PrinSPrin6Prin7MurderMurder-.0000620.003595-.0059000.0253860.0039770.1574100.987175RapeRape0.0006500.016206-.0089080.047612-

15、.0041490.986021153545RobberyRobbery00013590135900131040 4646410 864629-021719-011675AssaultAssault0.0036580.137992.1138860.863075-.469548-.049145-.013&49BurglaryBurglaty00220S60 940376 2812S3-189782 003217-0096720 001172LarcenyLarceny0.999743-.0223620.0033410.0004230 001205-.0002470.000188AutoAuto0

16、0032910 2781780 943599-0167891765960 0048160 005010待征向量:Larceny（偷盗罪）与Murderf杀人罪）髙度相关；Burglary依盗罪）与Rape（强奸罪）高度相关；Robbery（抢劫罪）与Auto（汽车犯罪）髙度相关;Robberyf抢劫罪）与Larceny盗罪）高度相关；Murde（杀人罪）与Auto（汽车犯罪）高度相关。陡坡图和已解释方差:。样本相关矩阵:均值和标准差：SAS系统PRINCOMP 过稈50713单统计fiiMurderRapeRobberyAssaultBurglaryLarcenyAuto均値7.4440000

17、002S.73400000124.0920000211.30000001291.9040003302386000377.5260000StD3 86676894110 7S96299S88 348S672100 2S30492432 4SS7114638 S7SOO8193 394417S相关矩阵:相关矩阵MurderRapeRobberyAssaultBurglaryLarcenyAutoMurderMurder1.00000.50120.43370.64860.3858-.07540.0688RapeRape0.60121.00000.59190.74030.71210.27890.348

18、9RobberyRobbery0 48370 59191 00000 5571 63720 0690 5907AssaultAssault0 64860 74030 55711 00000 62290 16800 2758BurglaryBurglary0.38580.71210.53720.62291.00000.23450.5560LarcenyLarceny-.07540.27890.06990.16800.23461.00030.0777AutoAuto0.0688034890.59070.27S80.SS8O0.07771.0000相关矩阵的特征值：特征值、差分、比例、累积:相关距阵

19、的特征值特征（a差分比例累枳13.707457082.563374880.52950.529621.144083000.123505800.16340.693131.020576200 635575110.145B0838940385001100.107103210.05500.893950 277897890 023078740 03970933660.2S4819150.0446S4370.03640.970070 210164780 03001 0000可以看出主成分为Murderf杀人罪），Rape（强奸罪），Robboryf抢劫罪）。待征向量:待征冋fitPrinlPrin2Prin

20、3Prin4Prin5Prin6Prin7MurderMurder0.348772-.5882470.0863510.3673B20.0734860.5017910.364284RapeRape0.456744-.0687280.222472-.238040-.1561600.305460-.750208RobberyRettery0.4242980.071135-.3022560.596935-.389075-.446584-.128080AssaultAssault0.4355S4-.2336390.189765-.2236540.580589-.5736570.059380Burglar

21、yBurglaiy0.4421700.208589.045298-.531074-46138S0.0289600.S13001LarcenyLarceny0.1222050.S453330.7360S00.3412020.06S1340.0621920.146218AutoAuto0 2992#04863-S214010.0596400S144240 348818-002066由上图可知，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。Robboryf抢劫罪）与Larceny （偷盗罪）的相关系数为0.736050; Rape（强 奸罪）与Auto （汽车犯罪）的相关系数为0.

22、750208。样本协方差矩阵和样本相关矩阵的差别：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。陡坡图和已解释方差:e UR2）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。 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%可以用它来代菩其他六个变童，其信息损失是很小的。 用样本相关矩阵求出的主成分为Murd

23、er（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），Robboryf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，而且也不至于损失原始变中的太多信息。3）计算从样本相关矩阵岀发计算的第一样本主成分的得分并予以排序。SAS系统ObtStateMurderRapeRobberyAscaultBurglaryLarcenyAutoPnnlPnn2Pnn3Prin4PnnSPrin6Prin71No 曲

24、 DaKcia0.99.013.343.8446.119430144.7-3.823930.223660.054570.23310-0.101C4-0.30195-0.435182South Dakota20135V91S57570 51704 4147 5-2.89759-0 178570 32568-O142J035512-0 683480 442533lowa2310.641.289.8812.52685.1219.9-2.782710.385370.003040.05178-0.13318-0.3D7530.032344West Virginia6013242290959741341

25、7163 3-2 67195-0 603510100050 49796-0 03856010048-0 0960&5vvisccrsin2.812.952.263.7846.92614.2220.7-2.666000.37452-0.0422B0.13374-0.39222-0.0B091-0.073776New Hampshire321072327601041.72343 92934-2 504580S2545-0 21564-0 23965-0171990125300 388427Nebraska3.91B.1W.7112.7760.02316.1249.1-2.125890.056200

26、.025020.19190-0.05359-0.09270-0.434598Vermont1 41593081012134822201 02652-2.034240.77178-0 10537-0 926180.57322-0175530219579Maine2413 538717001253.12350 7246 9-1 B30710 405540053590 75603-0.100BS-0 SWB80 4025210Montana541673921568804.92773 23092-1 &2994-0 045960106080 091730 480910 05630-0 0655411M

27、innesota2719 5BS985 a1134 72559 3343 1-1.654750 77129035036-0 16310-0 492570 02598-02407712Wyomng54219397V39811 62772 2282 0-1 56779-0 185670 31673-0 074770422750054930 41Q5013Id3ho5519419 6172 51050S2S99 6237 6-1 50014-0 201140332220 327650 07754-0 060930 0513314Utah35203668M7 31171 530045334 5-1.3

28、27430 53535-0 05106-0 37274-O 11351-0 11003-0 1020615Pemsylvania5619 01303128 0877 51624 1332 2-1320780 01118-0 462730 57334-O 14641-0 11540-03D6S516Kentucky10.119.1Bl.l123.3872.2166Z1245.4-1.30764-0.927200.042550.65B97-0.100240.588790.1748117Virginia9023392 116S79B6 22521 2226 7-O.B8129-0 768B70322

29、250 3SB70-0 144300 25248-0 0499918MlSSISSItXI14319.6&S.7189.1915.51239 9144.4-0. Bl 8742.024220.5246B0.680600.100310.6&1420.6361819Kansas6622 0100 7iaos1270 42739 3244 2-0 72378-0 21492019776-0 14301-0 37654-070230 1546720Arkansas8.827.683.2203.4972.6186Z1183.4-0.59403-1.056M0.5220B0.05519-0.062910.

30、09002-0.3696521ComcctKut42168129Sm a134602620 7S93 2-0 620121 24230-1 121460 0S3270 0901901364S0 3027522Irdiana7.426.5123.2153.510B6.224SB.7377.4-O.45S53-0.05824-0.197140.29525-0.134910.326500.3596423Rhode Island3610586520101489528441791 4-0 38221 784491 50096-0 407941.137590 071210 9639724No 曲 Caro

31、lina10.617.051.3318.31154.12037.8192.1-0.38399-1.417540.62093-0.150360.71897-0.493B90.8593525Oklahcma8629273820501288 2222813268-012809-0 482700224290382710.010600.43253-01013026New Jersey5.621.0180.4185.11435.82774.5511.50.129660.76993-0.841330.19421-0.17051-0.2M200.2118327Hawaii7.225 S12806411911.

32、53920448940V0271 04480-0 57074-0 34414-1 225701 0357906537628ONO7.827.3190.5181.11216.02695 B400.40.228150.010B7-0.393840.57096-0.34999-0.04416-0.2991929Tennessee101297145 8203.91259.717765314 00 30ftS9-0 75340-0 014440 23550-0 301580 2S268-0 147783031Alabama14225 296S278 31135 51881 9280 70399S2-1

33、694610 412050 377550 533710411980 5236BDelaware6024 91570194 216S2636784467 00 465950 75472-0 41693-0 28279-0432840 086970 3386432Illinoisgg21 8211 3209 010B5 0282B5523 60 47312-0 038B7-0 750031 18(60 322340 0316S0 1158933Washington43396106222481605.633869360 30 574060 460680 33025-1 14081-0 48333-0

34、 0100908M0934Missouri9628 31fl9 0233 S131832424 237B40 71676-0 43211-0 223310 44036-0.19172-0 11093-0 0531335Georgia11 731.11405256 51351.12170229790 79430？ 083740 26424011514-0 098350 206230 0651836Massachusens3 120 ft169 1231 61S32.22311 3114011.102812 64709-2 55296-G 177581 666550 330770 1272137N

35、ew8839 J1095343 41418 73OOB 5259 51.13323-0 898920 8645B-0 773200 20728-0 33554-0 5625238Texas1333381524208 21603 1298B7397 61 33407-0 747290 058340 17707-O 431410916410 3054739Louisiana15.530.9142.9335.5116532469.9337.71.36301-1.794390.445980.582820.731E00.2WB70.2692940Oregon4939 9124 1236 g1636.43

36、5061 038B91 06aa4 049545.351881 192330 292500 108790 2270241South Carolina11.933.0105.3485.31613.523424245.11.91203-1.676681.00163-0.976070.93720-0.921540.4546142Cokzado6342 0170729291935 23903 2477 11 992310SS51800652B-1 05077-0 40354-0 15846-0 XB01643Maiyiand8.034.8292.1358.91400.03177.742B.52.069

37、22-0.18228-0.254070.531940.01240-1.26679-0.6121344Michigan033S0261 Q274 61522.721 SOOS4552 1SS28012460-OS37770 43278-OW756-0 12767-0 637064546Alaska10.85).696.8284.01331.73369B753.32.209480.12894-0.16583-0.528011.187621.57313-1.35938Arizona9534213823123234614467 443952 255840 214380 27123-1 31174-0

38、504520 055900 9293847Fiends10.239.6187.9449.11859.93840 5351.42.73122-0.740790.67640-0.310300.27936-0.933B30.0322148Nev; York10729447263191172802782 0745 83加60 0)944-1 9608ft1 88223-039479-V16S4101 067349Cairfcmia11.549.4287.0358.02133.43499 8663.54.104450.19049-0.52819-0.30283-0.274580.11051-0.4087

39、650Nevada158491 |323135502453 14212 65592481801-0 45953-0 20611-0 00202 -0 967370 337140358862、从样本相关矩阵出发，做因子分析。50个观测的均值和标准差:SAS系统FACTOR过程逾入ar is妾型读取的记录数50便用的记录敬50用于显苦性检验的N5050个观刘站均值和标准走变丘均8标准差Murder7 44403 8668Rape25.734010.7596Robbery124.0920&8.3486Assault211.3000100 2530Burglary1291.9040432.4557La

40、rceny3302 38604638 5750Auio377.5260193.3944相关性:相关性MurderRapeRobberyAssaultBurglaryLarcenyAutoMurderMurder1.000000.601220.483710.648550.38582-0.075390.05381RapARape0 601221 000000.591880 740260 712130 278870 34BQ0RobberyRobbery0.483710.591831.000000.557080.637240.069920.59068AssaultAssault0.648550.74

41、0260.557081.000000.622910.167970.27584BurglaryBurglary0.385820.712130.637240.622911.000000.234560.55795LarcenyLarce ny-0.075390.278870.069920.167970.234561.000300.07768AutoAuto0.068810.348900.590680.27SB40.557950.077681.00000相关矩阵的特征值：特征值、差分、比例、累积：SAS系统FACTOR过程初始因子方法：丰成分先验公因子方差估计：ONE相关矩阵旳倚征值：总计二7平均值=

42、1特征值差分比例察积13.707457882.563374380.52960.529621 14408300012350680016340 693131.020576200.535575110.14580.838940.385001100.107103210.05500.893950.277897890.023078740.03970.933660.254819150.D44554370.03640.970070 210164780 03001 00003个囚子将被MINEIGEN准则保国。因子模式:因子模式FactorlFactor?Factor3MurderMurder0.67155-0.

43、629200.08724RapeRap0 87045-0 07351 22475RobberyRobbery0.816980.07509-0.30535AssaultAW 合 Uli0 83861-0 24990 19171BurglaryBurglary0.851390.22311-0.04576LarcenyLarcany0 235300 58330 74358AutoAutc0.576280.53341-0.52674每个因子的已解释方差:毎个因子巳辉釋方差FactorlFacror2Factor33.70745791 14408301.0205762最终的公因子方差估计:品终的公因子方

44、差怙计：总计=5.872117MurderRapeRobberyAssaultBurglaryLarcenyAUtO0.854484480.829348420.766475970.602469570.776733880.948520770.89403400控制所有其他变重的偏相关和Kaiser抽样适当性测度:SAS糸统FACTOR过程初拾囚子方法主SJ子枝別所Q其他变说的偏相关MurderRapeRobberyAssaultBurglaryLarcenyAuioMurderMurder1 ooooo0 30570273520 35684-0 09623-0 30244-0 28340RapeR

45、ape0309571 ooooo0 065140318550 378930 270580 00279RobberyRobbery0.273520.085141 ooooo0 00052017480-0 039930 46396AssaultAssault0.3S6840.318S50.080S21.000000.204110.06S38-0.03891BurglaryBurglary-0.095230.378930.174800.204111.000000.071350.31941Larcenygceny-0.30244.270580.039930.055380.071351.000000.08316AuioAuco-0.283400.002790.46396-0.038910.31941-0.083161.00000Kaiser抽样适当性31疳 总体MSA二0 79445530MurderRapeRobberyAssaultBurglaryLarcenyAuto0.&81S00S30.710446360.823533890.031219020.862347070.845396110.