数据分析实验三

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【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100 000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

2、七种犯罪的比率数据StateMurderRapeRobberyAssaultBurglaryLarcenyAutoAlabama14.225.296.8278.31135.51881.9280.7Alaska10.851.696.8284.01331.73369.8753.3Arizona9.534.2138.2312.32346.14467.4439.5Arkansas8.827.683.2203.4972.61862.1183.4California11.549.4287.0358.02139.43499.8663.5Colorado6.342.0170.7292.91935.23903.

3、2477.1Connecticut4.216.8129.5131.81346.02620.7593.2Delaware6.024.9157.0194.21682.63678.4467.0Florida10.239.6187.9449.11859.93840.5351.4Georgia11.731.1140.5256.51351.12170.2297.9Hawaii7.225.5128.064.11911.53920.4489.4Idaho5.519.439.6172.51050.82599.6237.6Illinois9.921.8211.3209.01085.02828.5528.6Indi

4、ana7.426.5123.2153.51086.22498.7377.4Iowa2.310.641.289.8812.52685.1219.9Kansas6.622.0100.7180.51270.42739.3244.3Kentucky123.3872.21662.1245.4Louisiana15.530.9142.9335.51165.52469.9337.7Maine2.413.538.7170.01253.12350.7246.9Maryland8.034.8292.1358.91400.03177.7428.5Massachusetts3.120.8169

5、.1231.61532.22311.31140.1Michigan9.338.9261.9274.61522.73159.0545.5Minnesota2.719.585.985.81134.72559.3343.1Mississippi14.319.665.7189.1915.61239.9144.4Missouri9.628.3189.0233.51318.32424.2378.4Montana5.416.739.2156.8804.92773.2309.2Nebraska3.918.164.7112.7760.02316.1249.1Nevada15.849.1323.1355.0245

6、3.14212.6559.2New Hampshire3.210.723.276.01041.72343.9293.4New Jersey5.621.0180.4185.11435.82774.5511.5New Mexico8.839.1109.6343.41418.73008.6259.5New York10.729.4472.6319.11728.02782.0745.8North Carolina10.617.061.3318.31154.12037.8192.1Ohio7.827.3190.5181.11216.02696.8400.4North Dakota0.99.013.343

7、.8446.11843.0144.7Oklahoma8.629.273.8205.01288.22228.1326.8Oregon4.939.9124.1286.91636.435061388.9Pennsylvania5.619.0130.3128.0877.51624.1333.2Rhode Island3.610.586.5201.01489.52844.1791.4South Carolina11.933.0105.9485.31613.62342.4245.1South Dakota2.013.517.9155.7570.51704.4147.5Tennessee10.129.714

8、5.8203.91259.71776.5314.0Texas13.333.8152.4208.21603.12988.7397.6Utah3.520.368.8147.31171.63004.6334.5Vermont1.415.930.8101.21348.22201.0265.2Virginia9.023.392.1165.7986.22521.2226.7Washington4.339.6106.2224.81605.63386.9360.3West Virginia6.013.242.290.9597.41341.7163.3Wisconsin2.812.952.263.7846.92

9、614.2220.7Wyoming5.421.939.7173.9811.62772.2282.01、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】SAS软件【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proc princomp data=work.crime covarian

10、ce;run;样本相关矩阵proc princomp data=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.proc princomp data=crime out=defen; run;proc sort data=defen;by prinl;run;proc print data=defen;run;2.从样本相关矩阵出发，做因子分析。proc factor data=work.crime score; 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:

11、The PRINCOMP ProcedureUbserYat i ons50Ya r i abIes7Si rnp I e Stat ist icsMurderRapeRobberyAssau1tBurglaryLa rcenyAutoMean7.44400000025.73400000124.0920000211.30000001291.9040003302.386000377.5260000StD3.86676894110.7596299588.3485672100.2530492432.4557114638.575008193.3944175样本协方差矩阵:Covar i ance Ma

12、t r i :：:MurderRapeRobberyAssauItBurg 1 aryLarcenyAutoMurderMurder14.9525.01165.25251.41645.17-1352.2051.46RapeRape25.01115.77562.64798.513313.5913918.15726.01RobberyRobbery165.25562.647805.474934.1624347.0028655.9210092.42AssauItAssauIt251.41798.514934.1610050.6727006.2078112.075348.14Burg I aryBn

13、rg I a ry645.173313.5924347.0027006.20187017.94470512.9946664.15LarcenyLa rceny-1352.2013918.1528655.9278112.07470512.9921516378.1169681.55AutoAuto51.46726.0110092.425348.1446664.1569681.5537401.40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Total Variance 21758784.312EigenvaIues of the Covariance MatrixEigenvalueD

14、ifferenceProport ionCumulat ive121527321.621330145.00.98940.98942197176.6172678.30.00910.9984324498.417744.00.00110.999646754.33765.70.00030.999952988.62950.10.00011.0000638.532.20.00001.000076.30.00001.0000可以得出主成分为Murder （杀人罪）。EigenvectorsPrinlPrin2PrinSPrin4Prin5Print；Prin?MurderMurder-.0000620.11

15、03595-.0059000.0253860.0039770.1574100.987175RapeRape0.0006500.016206-.0089080.047612-.0041490.986021-.158545RobberyRobbery0.0013590.1359900.1319940.4646410.864629-.021719-.011675Assau1tAssau1t0.0036580.137992-.1138860.863075-.469548-.049145-.013649BurglaryBurglary0.0220560.940376-.281253-.189782-.0

16、03217-.0086720.001172LarcenyLarceny0.999743-.0223620.0033410.0004230.001205-.0002470.000188AutoAuto0.0032910.2781780.943599-.016789-.1785960.0048160.005010Larceny （偷盗罪）与Murder （杀人罪）高度相关，Burglary （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）

17、高度相关。样本相关矩阵201606月01日 星期三 上午。8时58分02杪12The PRINCOMP Procedure507Ubservat i ons Va r i abIesS i mpIe Stat i st i csMurderRapeRobberyAssauItBurglaryLa rcenyiutoilean7.444000UUU25.73400000124.0920000211.30000001291.9040003302.386000377.5260000StD3.86676894110.7596299588.3485672100.2530492432.4557114638

18、.575008193.3944175Correlation Matri:MurderRapeRobberyAssau1tBurglaryLarcenyAutoMurderMurder1.00000.60120.48370.64860.3858-.07540.0688RapeRape0.60121.00000.59190.74080.71210.27890.3489RobberyRobbery0.48370.59191.00000.55710.63720.06990.5907Assau1tAssau1t0.64860.74030.55711.00000.62290.16800.2758Burgl

19、aryBurglary0.38580.71210.68720.62291.00000.23460.5580LarcenyLa rceny-.07540.27890.06990.1680LI.284E：1.00000.0777AutoAuto0.0G880.34890.59070.27580.55800.07771.0000EigenvaIues of the Correlat ion MatrixEigenva1ueDifferenceProport ionCumulat ive13.707457882.563374880.52960.529621.144083000.123506800.16

20、340.693131.020576200.635575110.14580.838940.385001100.107103210.05500.893950.277897890.023078740.03970.933660.254819150.044654370.03640.970070.210164780.03001 .0000可以看出主成分为Murder（杀人罪）,Rape（强奸罪），Robbory（抢劫罪）。E i genvectorsPrin1Prin2Prin8Prin4PrinbPrint；Prin7MurderMurder0.348772-.5882470.0863510.36738

21、20.0734860.5017910.364284RapeRape0.456744-.0687280.222472-.238040-.1561600.305460-.750208RobberyRobbery0.4242980.071135-.3022560.596935-.389075-.446584-.128080Assau1tAssauIt0.435534-.2336390.189765-.2236540.580589-.5736570.059380BurglaryBurglary0.4421700.208589-.045298-.531074-.4613850.0289600.51300

22、1LarcenyLarceny0.1222050.5453330.7360500.3412020.0651340.0621920.146218AutoAuto0.2992940.498695-.5214010.0596400.5144240.348818-.002066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Auto （汽车犯罪）的相关系数为0.750208两者的差别：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

23、（杀人罪），Rape（强奸罪），Robbory（抢劫 罪）。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。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。用样本相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

24、），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.ObsStateMurder RapeRobberyAssauItBurglaryLarceny1North Dakota0.99.013.343.8446.11843.02South Dakota2.013.517.9155.7570.51704.43Iowa2.310.641.209.8812.52685.14West Virginia6.013.242.290.959

25、7.41341.75Wisconsin2.812.952.263.7846.92614.26New Hampsh i re3.210.723.276.01041.72343.97Nebraska3.918.164.7112.7760.02316.18Vermont1.415.930.8101.21348.22201.09Maine2.413.538.7170.01253.12350.710Montana5.416.739.2156.8804.92773.211Minnesota2.719.585.905.81134.72559.312Wyoming5.421.939.7173.9811.627

26、72.213Idaho5.519.439.6172.51050.82599.614Utah3.520.368.8147.31171.63004.615Pennsylvania5.619.0130.3128.0877.51624.116Kentucky123.3872.21662.117Virginia9.023.392.1165.7986.22521.218Mississippi14.319.665.7109.1915.61239.919Kansas6.622.0100.7100.51270.42739.320Arkansas8.827.683.2203.4972.61

27、862.121Connect i cut4.216.8129.5131.81346.02620.722Indiana7.426.5123.2153.51086.22498.723Rhode Island3.610.586.5201.01489.52844.124North Carol ina10.617.061.3318.31154.12037.825Ok 1ahoma8.629.273.8205.01288.22228.126New Jersey5.621.0180.4105.11435.82774.527Hawai i7.225.5128.064.11911.53920.428Ohio7.

28、827.3190.5101.11216.02696.829Tennessee10.129.7145.8203.91259.71776.530Alabama14.225.296.8278.31135.51881.931Delaware6.024.9157.0194.21682.63678.4ObsAutoPrinlPrin2Prin3Prin4Prin5PrinBPrin71144.7-3.823930.223660.054570.23310-0.10104-0.30195-0.435182147.5-2.89759-0.178570.32568-0.142600.35512-0.68348-0

29、.442533219.9-2.782710.385370.003040.05178-0.13318-0.307630.032344163.3-2.67195-0.603510.100050.49798-0.038560.10048-0.098085220.7-2.666000.37462-0.042280.13374-0.39222-0.08091-0.073776293.4-2.504580.52545-0.21564-0.23965-0.171990.125300.388427249.1-2.125890.066200.025020.19190-0.05399-0.09270-0.4345

30、98265.2-2.034240.77178-0.10537-0.92618-0.57322-0.175530.219579246.9-1.830710.405540.05359-0.75603-0.10085-0.584880.4025210309.2-1.82994-0.045980.106080.091730.480910.05630-0.0655411343.1-1.654750.77129-0.35036-0.16310-0.492570.03598-0.2407712282.0-1.56779-0.185670.31673-0.074770.422750.05493-0.41050

31、13237.6-1.50014-0.201140.33222-0.327650.07754-0.060930.0513314334.5-1.327430.53535-0.05106-0.37274-0.11351-0.11003-0.1020615333.2-1.320780.01118-0.462730.57334-0.14641-0.11540-0.3065516245.4-1.30764-0.927200.042560.65897-0.100240.588790.1748117226.7-0.88129-0.768870.322250.35070-0.144300.25240-0.049

32、9918144.4-0.81874-2.024220.5280.680600.100310.664420.6361819244.3-0.72378-0.214820.19776-0.14301-0.37654-0.170330.1546720183.4-0.68403-1.056640.522080.05518-0.062910.09002-0.3698621593.2-0.620121.24230-1.121460.053270.090190.136450.3027522377.4-0.45853-0.05824-0.197140.29525-0.134910.32650-0.3598423

33、791.4-0.388221.78449-1.50096-0.407941.137590.071210.9639724192.1-0.38399-1.417540.62093-0.150060.71097-0.493090.8593525326.8-0.12809-0.482700.22429-0.382710.010600.43253-0.1013026511.50.128880.76888-0.841330.19421-0.17061-0.264200.2118327489.40.170271.04480-0.57074-0.34414-1.225701.035790.6537628400

34、.40.228150.01087-0.393840.57096-0.34999-0.04416-0.2991929314.00.30859-0.75340-0.014440.23550-0.301580.25268-0.1477830280.70.39952-1.694610.412050.377550.533710.411980.5236831467.00.465950.75472-0.41693-0.20279-0.43204-0.006970.330642.从样本相关矩阵出发，做因子分析。烬系统2016The FACTOR ProcedureInput Data TypeNumber of Records ReadNumber of Records UsedN for Sign if icance TestsRaw Data505050Eigenvalues of theCorre 1 at ion Matrix： Total = 7Average = 1EigenvalueDifferenceProport ionCumulat ive13.707457882.563374880.52960.529621.144083000