多元统计分析数据

、聚类分析例1、为深入了解我国人口的文化程度状况，现利用1990年全国人口普查数据对全国30个省市自治区进行聚类分析。分析选用了三个指标：（1）大学以上文化程度的人口占全部人口的比例QXBZ）；（2）初中文化程度的人口占全部人口的比例（CZBZ）；（3）文盲半文盲人口占全部人口的比例（WMBZ）,分别用来反映较高、中等、较低文化程度人口的状况，原始数据如下表：（%）地区DXBZCZBZWMBZ北京9.3030.558.70天津4.6729.388.92河北0.9624.6915.21山西1.3829.2411.30内蒙1.4825.4715.39辽宁2.6032.328.81吉林2.1526.3117.23黑龙江2.1428.4610.87上海6.5331.5911.04江苏1.4726.4317.23浙江1.1723.7417.46安徽0.8819.9724.43福建1.2316.8715.63江西0.9918.8416.22山东0.9825.1816.87河南0.8526.5516.15湖北1.5723.1615.79湖南1.1422.5712.10广东1.3423.0410.45广西0.7919.1410.61海南1.2422.5313.97四川0.9621.6516.24贵州0.7814.6524.27云南0.8113.8525.44西藏0.573.8544.43陕西1.6724.3617.62甘肃1.1016.8527.93青海1.4917.7627.70宁夏1.6120.2722.06新疆1.8520.6612.75例2、根据信息基础设施的发展状况，对世界20个国家和地区进行分类。这里选取了发达国家、新兴工业化国家、拉美国家、亚洲发展中国家、转型国家等不同类型的20个国家作聚类分析。描述信息基础设施的变量主要的有六个：call――千人拥有电话号码，movecall――每千户居民蜂窝移动电话，fee高峰时期每三分钟国际电话成本，computer每千人拥有的计算机数，mips每千人中计算机功率，net——每千人互联网络户主数。序号countrycallmovecallfeecomputermipsnet1美国631.60161.900.36403.0026073.0035.342日本498.40143.203.57176.0010223.006.26

3德国557.6070.602.18199.0011571.009.484瑞典648.10281.801.40286.0016660.0029.395瑞士644.0093.501.98234.0013621.0022.686丹麦620.30248.602.56296.0017210.0021.847新加坡498.40147.502.50284.0013578.0013.498中国台北469.4056.103.68119.006911.001.729韩国434.5073.003.3699.005795.001.6610巴西81.9016.303.0219.00876.000.5211智利138.608.201.4031.001411.001.2812墨西哥92.209.802.6131.001751.000.3513俄罗斯174.905.005.1224.001101.000.4814波兰169.006.503.6840.001796.001.4515凶牙利262.2049.402.6668.003067.003.0916马来西亚195.5088.404.1953.002734.001.2517泰国78.6027.804.9522.001662.000.1118印度13.600.306.282.00101.000.0119法国559.1042.901.27201.0011702.004.7620英国521.10122.500.98248.0014461.0011.91例3、为了研究1982年全国各地区农民家庭收支的分布规律，根据抽样调查资料进行分类处理，共抽取28个省、市、自治区的样本，每个样本有六个指标，这六个指标反映了平均每人生活消费的支出情况，其原始数据见表3。表31982年各地区农民生活消费支出抽样调查资料表单位：元序号地区食品衣着燃料住房生活用品及其它文化生活服务支出1北京190.3343.779.7360.5449.019.042天津135.2036.4010.4744.1636.493.943河北95.2122.839.3022.4422.812.804山西104.7825.116.469.8918.173.255内蒙128.4127.638.9412.5823.993.276辽宁145.6832.8317.7927.2939.093.477吉林159.3733.3818.3711.8125.295.228黑龙江116.2229.5713.2413.7621.756.049上海221.1138.6412.53115.6550.825.8910江苏144.9829.1211.6742.6027.305.7411浙江169.9232.7512.7247.1234.355.0012安徽153.0023.0915.6223.5418.186.3913福建144.9221.2616.9619.5221.756.7314江西140.5421.5917.6419.1915.974.9415山东115.8430.7612.2033.6133.773.8516河南101.1823.268.4620.2020.504.3017湖北140.6428.2612.3518.5320.956.2318湖南164.0224.7413.6322.2018.066.0419广东182.5520.5218.3242.4036.9711.6820广西139.0818.4714.6813.4120.663.8521四川137.8020.7411.0717.7416.494.39

22贵州121.6721.5312.5814.4912.184.5723云南124.2719.818.8914.2215.533.0324陕西106.0220.5610.9410.1118.003.2925甘肃95.6516.825.706.0312.364.4926青海107.1216.458.985.408.785.9327宁夏113.7424.116.469.6122.922.5328新疆123.2438.0013.724.6417.775.75例4为了研究世界各国森林、草原资源的分布规律，共抽取了21个国家的数据，每个国家4项指标，原始数据见表4，试用该数据对别国进行聚类分析。序号国别森林面积（万公顷）森林覆盖率（％）林木积畜量（亿立方米）草原面积（万公顷）1中国1197812.593.5319082美国2844630.4202.0237543日本250167.224.8584德国102828.414.05995英国2108.61.511476法国145826.716.012887意大利63521.13.65148加拿大3261332.7192.823859澳大利亚1070013.910.54519010前苏联9200041.1841.53737011捷克45835.88.916812波兰86824.811.440513匈牙利16117.42.512914南斯拉夫92936.311.464015罗马尼亚63426.711.344716保加利亚38534.72.520017印度674820.529.0120018印度尼西亚218084.033.7120019尼日利亚149016.10.8209020墨西哥485024.632.6745021巴西5750067.6238.015900例5若要从沪市的蒲发银行、齐鲁石化、东北高速、武钢股份、东风汽车等53家上市公司中优选适合开放式基金组合投资的10只股票，我们以总股本和流通股本为分类标志，根据这53家公司的总股本和A股流通股本数据（见表5.3），用聚类分析法将它们分成若干类，再从各类公司中选出比较活跃的股票建立股票池。表5.353家上市公司股本资料单位：十万股编号公司名称总股本流通量编号公司名称总股本流通量1蒲发银仃24000400028长征电器17005202齐鲁石化19500350029浙江东日12004003东北高速11000300030三峡水利17505804武钢股份20900320031中国泛旅27008005东风汽车10000300032太极集团25308306中国国贸8000160033重庆啤酒1700520

7首创股份11000300034东湖高新27608308上港集箱9000210035道博股份10404109宁波联合300085436长江包装67017410黄山旅游300052037青旅控股2700117011中技贸易130039038鼎天科技76029412古越龙山200082039兴发集团160040013皖维咼新250099040大兀股份200060014南京咼科34001554541离合器140042015上海梅林3200120042邢台轧辊170045016南京中达140052243维科精华2900111017新疆天业230097044天坛生物192048018青鸟华光220096045益金泰4400136019人福科技160064046山东临工1800107520明天科技226596247莲花味精6800280021精密股份2610133048辽宁时代106030022禾嘉股份130051049苏福马83030023云天化3700100050海鸟电子87239824明星电力150073051先锋股份92030025永鼎光缆250075052轻工机械210024026重庆路桥310090053宏盛科技82511227长春热缩1200405例6沪市上市公司2001年末总股本在10000—12000万股、流通股本在3600—5050万股之间共有23家（对于股本结构在其它范围内的上市公司，用雷同的方法，可以建立相应的每股收益预测模型），各公司2000年及2001年有关的财务数据见表。表23家上市公司2000年及2001年财务资料公司名称平均每股财务指标（元）净资产收益率（％）收益(2001)X8收益(2000)X1净资产X2现金流量X3主营收入X4资产X5(2001)X6(2000)X7万东医疗0.290.243.100.112.954.539.338.06浙江东日0.020.133.000.020.563.650.694.3道博股份0.240.104.030.051.688.265.915.1金宇集团0.130.184.73-0.321.916.792.765.65铜峰电子0.400.214.540.572.156.608.874.91景谷林业0.220.202.94-0.591.775.387.332.29国电南自0.240.123.89-0.194.637.606.210.83铃锐股份0.250.214.000.031.725.836.256.09国光瓷业0.290.273.490.453.158.058.428.43亿阳信通0.690.548.392.215.8612.818.276.87美罗股份0.370.254.600.075.337.747.995.71冰山橡塑0.150.162.970.042.125.055.129.17华微电子0.220.274.830.101.917.784.5514.86金瑞科技0.290.256.44-0.312.128.094.533.95大西洋0.210.293.820.023.755.515.5916.9洪城股份0.170.224.230.071.075.483.9410.39成量股份0.020.021.120.031.193.222.111.71

新宇软件0.190.401.850.591.863.6010.1713.91云维股份0.420.203.350.392.334.5212.46.3金荔科技0.310.142.170.091.095.3414.217.56西藏金珠0.210.212.89-0.621.552.897.346.6保税科技0.120.162.650.611.134.834.6711.48界龙实业0.050.091.810.224.556.482.744.95二、判别分析例1、人文发展指数是联合国开发计划署于1990年5月发表的第一份《人类发展报告》中公布的。该报告建议，目前对人文发展的衡量应当以人生的三大要素的指标指示分别采用出生时的预期寿命、成人识字率和实际人均GTP,将以上三个指标指示数值合成为一个复合指数，即人文发展指数。今从1995年世界各国人文发展指数的排序中，选取高发展水平、中等发展水平的国家各五个作为两组样本，另选四个国家作为待判样本作距离判别分析、逐步判别分析。类别序号国家出生时期预期寿命（岁）1992X,成人识字率（％）1992£调整后人均GDPX31992第一类1美国76995374（高发展2日本79.5995359水平国3瑞士78995372家）4阿根廷72.195.952425阿联酋73.877.75370第二类6保加利亚71.2934250（中等发7古巴75.394.93412展水平国8巴拉圭7091.23390家）9格鲁吉亚72.899230010南非62.980.6379911中国68.579.31950待判样本12罗马尼亚69.996.9284013希腊77.693.8523314哥伦比亚69.390.3515811V二(S+S)二一Sn+n—212812(15.3821.713—555.875\21.71366.6125—1446.0975、—555.875—1446.0975262546.515.3821.713-555.87521.71366.6125-1446.0975-555.875-1446.0975262546.5X⑴X⑵75.8870.4494.0891.745343.43430.2

（0.6523\a=V-i（X⑴-X⑵）=0.0122、0.00873丿a中国罗马尼亚希腊哥伦比亚0.652368.569.977.669.30.012279.396.993.890.30.0087319502840523315158例2、对全国30个省、市自治区1994年影响各地区经济增长差异的制度变量：X]——经济增长率（％）、X2——非国有化水平（％）、X3——开放度（％）、X4——市场化程度（％）作判别分析。类别序号地区X1X2X3X4第组1辽宁11.257.2513.4773.412河北14.967.197.8973.093天津14.364.7419.4172.334北京13.555.6320.5977.335山东16.275.5111.0672.086上海14.357.6322.5177.357浙江2083.9415.9989.58福建21.868.0339.4271.99广东1978.3183.0380.7510广西1657.1112.5760.9111海南11.949.9730.769.2第组12黑龙江8.730.7215.4160.2513吉林14.337.6512.9566.4214内家古10.134.637.6862.9615山西9.156.3310.366.0116河南13.865.234.6964.2417湖北15.355.626.0654.7418湖南1155.558.0267.4719江西1862.856.458.8320甘肃10.430.014.6160.2621宁夏8.229.286.1150.7122四川11.462.885.3161.4923云南11.628.579.0868.4724贵州8.430.236.0355.5525青海8.215.968.0440.2626新疆10.924.758.3446.0127西藏15.621.4428.6246.01待判样本28江苏16.580.058.8173.0429安徽20.681.245.3760.4330陕西8.642.068.8856.37例3研究某年全国各地区农民家庭收支分布规律，根据抽样调查资料进行分类处理，抽取28个省、市、自治区的样本，每个样本有六个指标。先采用聚类分析将28个样本分为3类，其中有3个样本（北京、上海、广州）属于孤立样本，未归属于已分的三类中，现采用多组判别分析判定这28个样本的所属类别。原始数

据见表3。表3原始数据表类别序号地区食品X1衣着X2燃料X3住房X4生活用品及其它兀文化生活服务支出X6组1天津135.2036.4010.4744.1636.403.942辽宁145.6832.8317.7927.2639.093.473吉林159.3733.3818.3711.8125.295.224江苏144.9829.1211.6742.6027.305.745浙江169.9232.7512.7247.1234.355.006山东115.8430.7612.2033.6133.773.85组7黑龙江116.2229.5713.2413.7621.756.048安徽153.1123.0915.6223.5418.186.399福建144.9221.2616.9619.5221.756.7310江西140.5421.5917.6419.1915.974.9411湖北140.6428.2612.3518.5320.956.2312湖南164.0224.7413.6322.2018.066.0413广西139.0818.4714.6813.4120.663.8514四川137.8020.7411.0717.7416.494.3915贵州121.6721.5312.5814.4912.184.5716新疆123.2438.0013.724.6417.775.75组17河北95.2122.839.3022.4422.812.8018山西104.7825.116.469.8918.173.2519内蒙128.4127.638.9412.5823.993.2720河南101.1823.268.4620.2020.504.3021云南124.2719.818.8914.2215.533.0322陕西106.0220.5610.9410.1118.003.2923甘肃95.6516.825.706.0312.364.4924青海107.1216.458.985.408.785.9325宁夏113.7424.116.469.6122.922.53待判样本26北京190.3343.779.7360.5449.019.0427上海221.1138.6412.53115.6550.825.8928广州182.5520.5218.3242.4036.9711.68试对3个待判样本进行判别分析。因子分析及主成分分析例1（因子分析）我国山区某大型化工厂，在厂区及邻近地区挑选有代表性的8个取样点，每日四次同时抽取大气样本，测定其中含有的6种气体的浓度，前后4天，每个取样点每种气体实测16次。计算每个取样点每种气体的平均浓度，数据如下表所示。气体氯硫化氢SO2碳4环氧氯丙烷环已烷10.0560.0840.0310.0380.00810.02220.0490.0550.1000.1100.02200.007330.0380.1300.0790.1700.05800.04340.0340.0950.0580.1600.2000.02950.0840.0660.0290.3200.0120.04160.0640.0720.1000.2100.0281.380

70.0480.0890.0620.2600.0380.03680.0690.0870.0270.2500.0450.021因子得分表-.89378-1.36256-.98459-.08608.38162-1.35185-.03992-1.25792.26303-.33036-.208842.12013-.26157-.131142.34591-.10347-.768791.44274-.53662-.787662.15684.53711-.37098-.33777-.05786.36966.03073.41017-.81949.82641-.23570.04260例2（因子分析）对我国30个省市自治区的农业生产情况作因子分析。从农业生产条件和生产结果及效益出发，选取六项指标分别为：X]—乡村劳动力人口（万人）、x2—人均经营耕地面积（亩）x3—户均生产性固定资产原值（元）x4—家庭基本纯收入（元）x5—人均农业总产值（千元人）、x6—增加值占总产值比重（%），原始资料数据见下表。序号地区x1x2x3x4X5x61北京66.90.932972.413290.732.52549.42天津80.21.644803.542871.621.77449.63河北1621.82.035146.351965.810.8004544山西635.42.762257.661499.140.55556.25内蒙514.110.175834.941550.150.905166.46辽宁605.12.963108.862059.351.475253.17吉林534.24.734767.511940.461.115463.18黑龙江494.88.245573.022075.421.628357.89上海661.021660.034571.813.044835.610江苏1530.21.262826.862868.331.192150.611浙江1123.10.945494.233289.070.856563.312安徽1953.61.443573.621508.240.575659.213福建775.80.822410.052295.191.149662.814江西1103.21.32310.981804.930.664959.915山东2475.11.443109.111989.530.88095516河南2815.81.53782.261508.360.582358.517湖北1296.51.62291.61854.130.879962.818湖南2089.31.422348.721719.180.58764.719广东1439.80.883249.612928.241.09659.720广西1579.91.433090.171590.90.569464.521海南165.91.354454.771575.490.353565.222四川3903.71.082870.451340.610.444364.123贵州1376.61.182282.271206.250.289265.424云南1642.22.424025.061096.730.345664.225西藏88.62.5111559.831257.710.434970.426陕西1046.12.62228.551091.960.438359.727甘肃6725.862897.361037.120.488357.228青海137.12.626725.111133.060.409670.3

29宁夏139.14.015607.971346.890.497362.530新疆288.53.967438.131161.711.493957.8例3（主成分分析）对全国30个省市自治区经济发展情况的八项指标做主成分分析，原始资料如下：省份GDPX1居民消费水平X。固定资产投资X3职工平均工资X4货物周转量X5居民消费价格指数X6商品零售价格指数X7工业总产值X8北京1394.892505519.018144373.9117.3112.6843.43天津920.112720345.466501342.8115.2110.6582.51河北2849.521258704.8748392033.3115.2115.81234.85山西1092.481250290.94721717.3116.9115.6697.25内蒙832.881387250.234134781.7117.5116.8419.39辽宁2793.372397387.9949111371.1116.11141840.55吉林1129.21872320.454430497.4115.2114.2762.47黑龙江2014.532334435.734145824.8116.1114.31240.37上海2462.575343996.489279207.4118.71131642.95江苏5155.2519261434.9559431025.5115.8114.32026.64浙江3524.7922491006.396619754.4116.6113.5916.59安徽2003.5812544744609908.3114.8112.7824.14福建2160.522320553.975857609.3115.2114.4433.67江西1205.111182282.844211411.7116.9115.9571.84山东5002.3415271229.5551451196.6117.6114.22207.69河南3002.741034670.3543441574.4116.5114.91367.92湖北2391.421527571.684685849120116.61220.72湖南2195.71408422.6147971011.8119115.5843.83广东5381.7226991639.838250656.5114111.61396.35广西1606.151314382.595105556118.4116.4554.97海南364.171814198.355340232.1113.5111.364.33四川35341261822.544645902.3118.51171431.81贵州630.07942150.844475301.1121.4117.2324.72云南1206.6812613345149310.4121.3118.1716.65西藏55.98111017.8773824.2117.3114.95.57陕西1000.031208300.274396500.9119117600.98甘肃553.351007114.815493507119.8116.5468.79青海165.31144547.76575361.6118116.3105.8宁夏169.75135561.985079121.8117.1115.3114.4新疆834.571469376.955348339119.7116.7428.76数据来源：1996年《中国统计年鉴》。典型相关分析例1对某高中一年级男生38人进行体力测试（共有七项指标）及运动能力测试（共有五项指标），试对两组指标作典型相关分析。体力测试指标：X]—反复横向跳（次），X2—纵向跳（cm）,X3—背力（kg）,X4—握力（kg）,X5—台阶测试（指数），X6—立定体前屈（cm）,X7—俯卧上体后仰（cm）。运动能力测试指标：X8—50米跑（秒），X9—跳远（cm），X]0—投球（m）,X^—引体向上（次），X]2—耐力跑（秒）。

原始数据表序号体力测试指标运动能力测试指标