数据分析期末题.doc

数据分析方法课程设计题目概述：3、调查美国50个州7种犯罪率，得结果列于表1，其中给出的是美国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1 美国50个州七种犯罪的比率数据state州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ALABAMA14.225.296.8278.31135.51881.9280.7ALASKA10.851.696.8284.01331.73369.8753.3ARIZONA9.534.2138.2312.32346.14467.4439.5ARKANSAS8.827.683.2203.4972.61862.1183.4CALIFORNIA11.549.4287.0358.02139.43499.8663.5COLORADO6.342.0170.7292.91935.23903.2477.1CONNECTICUT4.216.8129.5131.81346.02620.7593.2DELAWARE6.024.9157.0194.21682.63678.4467.0FLORIDA10.239.6187.9449.11859.93840.5351.4GEORGIA11.731.1140.5256.51351.12170.2297.9HAWAII7.225.5128.064.11911.53920.4489.4IDAHO5.519.439.6172.51050.82599.6237.6ILLINOIS9.921.8211.3209.01085.02828.5528.6INDIANA7.426.5123.2153.51086.22498.7377.4IOWA2.310.641.289.8812.52685.1219.9KANSAS6.622.0100.7180.51270.42739.3244.3KENTUCKY10.119.181.1123.3872.21662.1245.4LOUISIANA15.530.9142.9335.51165.52469.9337.7MAINE2.413.538.7170.01253.12350.7246.9MARYLAND8.034.8292.1358.91400.03177.7428.5MASSACHUSETTS3.120.8169.1231.61532.22311.31140.1MICHIGAN9.338.9261.9274.61522.73159.0545.5MINNESOTA2.719.585.985.81134.72559.3343.1MISSISSIPPI14.319.665.7189.1915.61239.9144.4MISSOURI9.628.3189.0233.51318.32424.2378.4MONTANA5.416.739.2156.8804.92773.2309.2NEBRASKA3.918.164.7112.7760.02316.1249.1NEVADA15.849.1323.1355.02453.14212.6559.2NEW 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 CAROLINA10.617.061.3318.31154.12037.8192.1NORTH DAKOTA0.99.013.343.8446.11843.0144.7OHIO7.827.3190.5181.11216.02696.8400.4OKLAHOMA8.629.273.8205.01288.22228.1326.8OREGON4.939.9124.1286.91636.43506.1388.9PENNSYLVANIA5.619.0130.3128.0877.51624.1333.2RHODE ISLAND3.610.586.5201.01489.52844.1791.4SOUTH CAROLINA11.933.0105.9485.31613.62342.4245.1SOUTH DAKOTA2.013.517.9155.7570.51704.4147.5TENNESSEE10.129.7145.8203.91259.71776.5314.0TEXAS13.333.8152.4208.21603.12988.7397.6UTAH3.520.368.8147.31171.63004.6334.5VERMONT1.415.930.8101.21348.22201.0265.2VIRGINIA9.023.392.1165.7986.22521.2226.7WASHINGTON4.339.6106.2224.81605.63386.9360.3WEST VIRGINIA6.013.242.290.9597.41341.7163.3WISCONSIN2.812.952.263.7846.92614.2220.7WYOMING5.421.939.7173.9811.62772.2282.01) 基于变量(Murder,rape,robbery,assault,burglary,larceny,auto)的观测值，求样本协方差矩阵和样本相关系数矩阵;2) 分别从和。出发做主成分分析：（1） 求样本主成分的贡献率、累计贡献率和各个样本主成分；（2） 在两种情况下，你认为应该保留几个主成分，其意义如何解释？（提示：要求累计贡献率达到80%以上）就此题而言，你认为基于和的分析结果哪个更合理？（3） 按第一主成分得分将美国50个州排序，结果如何？（4） 作以第一主成分得分为横坐标，第二主成分得分为纵坐标的散点图。3) 对表1的美国50个州七种犯罪的比率数据，分别试用快速聚类和类平均距离谱系聚类法将美国50个州分4类，并对聚类结果进行分析和比较。从聚类结果看，你认为哪种分类方法好？问题一采用sas得到样本协方差矩阵S：MurderRaperobberyassaultburglarylarcenyautoMurder14.951925.0138165.2459251.4141645.1653286.080951.4603rape25.0138115.7696562.6393798.50733313.5864795.56726.0126robbery165.2459562.63937805.4694934.1612434728650.7710092.42assault251.4141798.50734934.16110050.6727006.229427.365348.142burglary645.16533313.5862434727006.2187017.9248665.346664.15larceny286.08094795.5628650.7729427.36248665.3526943.562356.95auto51.4603726.012610092.425348.14246664.1562356.9537401.4样本相关系数矩阵R：Pearson相关系数，N=50MurderRaperobberyassaultburglarylarcenyautoMurder10.601220.483710.648550.385820.101920.06881rape0.6012210.591880.740260.712130.613990.3489robbery0.483710.5918810.557080.637240.446740.59068assault0.648550.740260.5570810.622910.404360.27584burglary0.385820.712130.637240.6229110.792120.55795larceny0.101920.613990.446740.404360.7921210.44418auto0.068810.34890.590680.275840.557950.444181问题二1、从R进行主成分分析：（1）、求样本主成分的贡献率、累计贡献率和各个样本主成分。贡献率：Eigenvalues of the Correlation MatrixEigenvalueDifferenceProportionCumulative14.114962.8762380.58790.587921.2387220.5129050.1770.764830.7258170.4093850.10370.868540.3164320.0584580.04520.913750.2579740.0359350.03690.950660.2220390.0979830.03170.982370.1240560.01771（2）累计贡献率到达80%以上，需保留三个主成分，前三个成分的累计贡献率已达到86.9%。Prin1Prin2Prin3Prin4Prin5Prin6Prin7Murder0.300279-0.629170.178245-0.232110.5381230.2591170.267593rape0.431759-0.16944-0.24420.0622160.188471-0.77327-0.29649robbery0.3968750.0422470.495861-0.55799-0.51998-0.11439-0.0039assault0.396652-0.34353-0.069510.629804-0.506650.1723630.191745burglary0.4401570.203341-0.2099-0.057560.1010330.535987-0.64812larceny0.357360.402319-0.53923-0.234890.0300990.0394060.60169auto0.2951770.5024210.5683840.4192380.369753-0.05730.147046由此三个主成分：PRIN1=0.300279murder + 0.431759 rape +0.396875 robbery +0.396652assault + 0.440157 burglary +0.357360arceny +0.295177autoPRIN2=-0.629174muder-0.169435rape+0.042247robbery-0.343528asault+0.203341burglary+ 0.402319larceny+0.502421 autoPRIN3=0.178245muder-0.2442rape+0.495861robbery-0.06951asault- 0.2099burglary-0.5392larceny+0.568auto从S进行主成分分析：贡献率：Eigenvalues of the Correlation MatrixEigenvalueDifferenceProportionCumulative1672099.9608440.30.87360.8736263659.6739443.590.08270.9563324216.0817902.620.03150.987846313.4643295.8140.00820.99653017.652980.4680.00390.9999637.18331.510175.67301 特征向量：Prin1Prin2Prin3Prin4Prin5Prin6Prin7Murder0.0008640.007077-0.007380.0222360.0050320.1849110.982437rape0.0087730.011477-0.01040.051813-0.005990.981012-0.18595robbery0.0569930.1659210.1103010.4572110.864522-0.02224-0.01101assault0.0591960.174243-0.150510.849046-0.46866-0.0536-0.00917burglary0.4653460.774439-0.34551-0.25358-0.00125-0.0039-0.0021larceny0.872863-0.481780.0597030.0491050.001277-0.003610.002712auto0.1213840.3317520.917649-0.0136-0.181370.0052530.00464累计贡献率：第一个成分贡献率已达到87.36%。主成分表达式：PRIN1=0.000864muder+0.008773rape+0.056993robbery+0.059196asault+0.465346burglary+0.872863larceny+0.121384auto分析：由于第一主成分对所有变量都有近似相等的载荷，因此可认为第一主成分是对所有犯罪率的总度量。第二主成分在变量auto和larceny上有高的正载荷，而在变量murder和assault上有高的负载荷；在burglary上存在小的正载荷，而在rape上存在小的负载荷。可以认为，这个主成分是用于度量暴力犯罪在犯罪性质上占的比重。第三主成分很难给出明显的解释。在依PRIN1排序的结果表中，排在前面的PRIN1值较小的州犯罪率较低，即北达科他NORTH DAKOTA（PRIN1= -3.96408）州犯罪率最低，PRIN1值较大的州，犯罪率较高，即内华达NEVADA（PRIN1= 5.26699）州犯罪率最高。在依PRIN2排序的结果表35.4中，排在前面的PRIN2值较小州的暴力犯罪性质比重较大。由此得出采用基于R的主成分分析 更合理，不仅能从总体度量犯罪率还能得到不同犯罪率组合的比重，更能突显地区不同犯罪率的高低。（3） 按第一主成分将50个州排序：statePrin1Prin2Prin3Prin4Prin5Prin6Prin7NORTH DAKOTA-3.964077650.387671-0.08603-0.18059-0.38235-0.40470.096798SOUTH DAKOTA-3.17202684-0.25446-0.138420.487677-0.71435-0.32213-0.03645WEST VIRGINIA-3.14772196-0.814250.536901-0.166690.042973-0.16643-0.20532IOWA-2.581561930.824753-0.51548-0.30085-0.291870.0946440.442398WISCONSIN-2.502960980.780831-0.42647-0.5309-0.10821-0.057710.253503NEWHAMPSHIRE-2.465622860.82503-0.20949-0.088070.1907370.391119-0.0941NEBRASKA-2.150707450.225739-0.11052-0.1684-0.16361-0.421950.184246VERMONT-2.06432760.944967-0.510790.104676-0.128990.310747-0.91333MAINE-1.826310780.578785-0.532410.337634-0.477060.553981-0.39406KENTUCKY-1.72690862-1.146630.657767-0.383110.5586670.023296-0.10775PENNSYLVANIA-1.72006943-0.19591.009178-0.19285-0.21512-0.34819-0.38228MONTANA-1.668012930.270992-0.3680.1479620.092177-0.049330.769386MINNESOTA-1.554342371.056437-0.14623-0.31594-0.01757-0.22692-0.27826MISSISSIPPI-1.50735805-2.546710.703693-0.209810.7095550.46267-0.19614IDAHO-1.43245398-0.00801-0.634140.121909-0.014950.1063640.165056WYOMING-1.424634680.062683-0.577520.2227650.043421-0.377980.62723ARKANSAS-1.05441043-1.34544-0.018340.0215360.022688-0.38604-0.31067UTAH-1.049956980.936561-0.64009-0.03263-0.09174-0.030470.180693VIRGINIA-0.91620755-0.69265-0.20438-0.42960.226637-0.100140.30802NORTH CAROLINA-0.69925167-1.67027-0.090410.650179-0.297950.9541930.20695KANSAS-0.63406694-0.02804-0.49573-0.32463-0.146450.20564-0.02609CONNECTICUT-0.541329491.501230.7838850.086190.1848860.2814-0.08962INDIANA-0.49989552.6E-050.24333-0.267450.249195-0.42050.030475OKLAHOMA-0.32136304-0.62429-0.121340.2626410.433196-0.13097-0.4257RHODE ISLAND-0.201555152.1465760.95681.1303510.3161220.9998670.297514TENNESSEE-0.13659511-1.134980.652999-0.163980.182649-0.21754-0.6823ALABAMA-0.04988023-2.09610.5016450.2509850.4984860.4336180.118075NEW JERSEY0.2178738250.9642090.603874-0.19902-0.24450.242962-0.078OHIO0.2395303350.0905270.459642-0.57002-0.13419-0.326060.073085GEORGIA0.490407599-1.380790.244629-0.062480.2021010.025782-0.33221ILLINOIS0.5129024950.094231.121196-0.431250.0182620.0377820.825377MISSOURI0.556366491-0.558510.563358-0.30673-0.15163-0.06676-0.12561HAWAII0.8231313251.823918-0.78176-1.180251.0932920.544922-0.1003WASHINGTON0.9305796340.737764-1.303870.156067-0.08755-0.72808-0.46312DELAWARE0.9645806541.296743-0.52586-0.41732-0.018720.4035610.206165MASSACHUSETTS0.9784389792.6310542.542251.8131030.4407390.09248-0.20652LOUISIANA1.12020258-2.083270.3674580.2033960.3592190.2019580.644098NEW MEXICO1.214170935-0.95076-1.072760.53541-0.34152-0.41341-0.02135TEXAS1.396960942-0.68131-0.07992-0.603750.9295480.167733-0.01221OREGON1.449002120.586025-1.245050.418182-0.35117-0.58967-0.2375SOUTH CAROLINA1.60336057-2.16211-0.552611.387271-0.721920.691138-0.22241MARYLAND2.182798286-0.194740.381652-0.18256-1.35485-0.431690.360049MICHIGAN2.2733343990.1548740.535674-0.33238-0.24676-0.628670.066708ALASKA2.421514980.166523-0.069731.1604721.470051-1.497810.464808COLORADO2.5092925190.916596-1.151580.112603-0.16923-0.33103-0.24066ARIZONA3.0141382810.844945-1.75195-0.116210.2802111.070440.057515FLORIDA3.111753982-0.60392-1.215410.495075-0.819670.2895850.35866NEW YORK3.4524801810.4328932.736615-0.99366-1.268020.1262460.033301CALIFORNIA4.2838037330.1431870.2761550.0251220.057931-0.37708-0.46401NEVADA5.26698533-0.25262-0.30241-0.980080.3572160.339124-0.12412（4）作图问题三1、快速聚类由SAS处理得到：(1)、初始聚点Initial SeedsClusterMurderraperobberyassaultburglarylarcenyauto14.339.6106.2224.81605.63386.9360.323.120.8169.1231.61532.22311.31140.139.534.2138.2312.32346.14467.4439.54613.242.290.9597.41341.7163.3（2）、分类结果：ClusterObsDistance from Seed12359.3120170.512291.6614130329.5131278.4132473.5137430.7139360.4143186.1144363.7147327.827280.8210379.3212195.3213348.821465.936215387.5216284.6218154.6219222.5221807.4223122.9225200.4226408.6227420.1229220.5235212.9236300240546.4245364246216.6249346.3250406.433561.735473.436132.438441.539283.1311251.1328453.641325.144203.841756.4826424439.2433442434450.6438130.7441304442402.7448407.74个类的距离矩阵如下：Cluster12341.659.7157969.55381502.3832659.7157.1623.102852.59163969.55381623.102.2452.15741502.383852.59162452.157.从聚类结果看出第一类是以盗窃罪为主；第二类是以强奸、抢劫、斗殴罪为主，且所属城市较多，说明该类犯罪是较普片的；第三类是以汽车犯罪为主；第四类是以杀人、斗殴罪为主。由距离矩阵可以看出各类之间的差异较小，说明分类比较合理。2、类平均谱系聚类法聚类结果：类的数目频数类平均距离49MONTANAWYOMING20.026848IOWAWISCONSIN20.067547KENTUCKYPENNSYLVANIA20.08746INDIANAMINNESOTA20.092845IDAHOVIRGINIA20.092944GEORGIAOKLAHOMA20.