多元统计分析因子分析案例

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,多元统计分析因子分析案例,1,、,求相关系数矩阵,R,2,、,计算,R,的特征值,主成分,Y,1,Y,2,Y,3,特征根,贡献率（,%,）,累计贡献率,2.741,45.69,45.69,2.428,40.46,86.15,0.438,7.30,93.45,3,、,求特征根所对应的单位,特征向量,特征向量,Y,1,Y,2,X,1,X,2,X,3,X,4,X,5,X,6,0.276,0.313,0.202,0.518,0.538,0.477,0.538,0.500,0.492,-0.270,-0.212,-0.318,教学水平,教学态度,4,、,由,特征向量,写出主成分的表达式,5,、主成分的含义解释,6,、初始因子载荷矩阵,载荷,Y,1,Y,2,X,1,X,2,X,3,X,4,X,5,X,6,0.459,0.517,0.335,0.858,0.890,0.790,0. 837,0.780,0.767,-0.420,-0.329,-0.495,7,、旋转后的因子载荷阵矩阵,载荷,F,1,F,2,X,1,X,2,X,3,X,4,X,5,X,6,0.007,0.080,-0.030,0.949,0.945,0.931,0. 932,0.958,0.469,0.089,0.085,-0.068,教学水平,教学态度,8,、因子得分,例,2,：,In a job interview , 48 applicants were each judged on 15 variables. The variables were,Form of letter of application,Appearance,Academic ability,Likeability,Self-confidence,Lucidity,Honesty,Salesmanship,Experience,Drive,Ambition,Grasp,Potential,Keenness to join,Suitability,1,、,求相关系数矩阵,R,2,、,计算,R,的特征值,Y,1,Y,2,Y,3,Y,4,特征根,贡献率（,%,）,累计贡献率,7.50,50,50,2.06,13.73,63.73,1.46,9.73,73.46,1.21,8.07,81.53,0.74,y,1,y,2,y,3,y,4,X,1,X,2,X,3,X,4,X,5,X,6,X,7,X,8,X,9,X,10,X,11,X,12,X,13,X,14,X,15,0.162,0.213,0.040,0.221,0.292,0.316,0.158,0.322,0.133,0.315,0.319,0.332,0.333,0.259,0.236,0.431,-0.033,0.237,-0.125,-0.249,-0.131,-0.400,-0.039,0.553,0.046,-0.068,-0.022,0.024,-0.079,0.421,0.308,-0.014,-0.414,0.476,-0.244,-0.151,0.298,-0.202,0.082,-0.083,-0.212,-0.111,-0.065,0.463,0.085,特征向量,申请书,外貌,学术,讨人喜欢,自信,精明,老实,推销,经历,积极性,抱负,理解,潜力,交际能力,适应性,y,1,y,2,y,3,y,4,X,1,X,2,X,3,X,4,X,5,X,6,X,7,X,8,X,9,X,10,X,11,X,12,X,13,X,14,X,15,0.445,0.583,0.109,0.606,0.799,0.865,0.433,0.881,0.365,0.864,0.873,0.908,0.912,0.710,0.646,0.618,-0.048,0.340,-0.180,-0.358,-0.188,-0.576,-0.056,0.795,0.066,-0.098,-0.031,0.035,-0.114,0.605,0.372,-0.017,-0.500,0.575,-0.295,-0.182,0.361,-0.245,0.099,-0.100,-0.256,-0.134,-0.078,0.560,0.103,-0.119,0.289,0.710,0.361,-0.178,-0.070,0.448,-0.230,0.070,-0.165,-0.206,0.092,0.213,-0.234,-0.028,初始因子载荷矩阵,f,1,f,2,f,3,f,4,X,1,X,2,X,3,X,4,X,5,X,6,X,7,X,8,X,9,X,10,X,11,X,12,X,13,X,14,X,15,0.918,0.863,0.917,0.798,0.917,0.806,0.741,0.83,0.852,0.797,-0.872,-0.863,-0.538,0.928,-0.522,旋转后的因子载荷矩阵,申请书,外貌,学术,讨人喜欢,自信,精明,老实,推销,经历,积极性,抱负,理解,潜力,交际能力,适应性,第一公共因子 f1 : 申请者外露的能力,第二公共因子 f2 : 经历,第三公共因子 f3 : 讨人喜欢,第四公共因子 f4 : 学术能力,“外貌和“交际能力在任何一个因子上都没有大的载荷值。,将上章例子对全国 31个地区的社会经济开展的17 项指标作因子分析。,数据见,反映地区社会经济开展的指标体系,X1：国内生产总值GDP X2：人均GDP,X3：第三产业产值占GDP比重 X4：人均出口额,X5：工业企业劳动生产率 X6：人均社会消费品零售额,X7：每万人拥有卫生技术人员数 X8：每万人高等学校在校生数,X9：教育经费投入占GDP比重 X10：人均货运总量,X11：人均邮电业务总量 X12：每万人 机装机数,X13：人均固定资产投资 X14：人均实际利用外资,X15：地方财政收入占GDP比重 X16：每万人科研机构数,X17：科研经费占GDP比重,1,、,求相关系数矩阵,R,2,、,计算,R,的特征值,主成分,Y,1,Y,2,Y,3,Y,4,特征根,贡献率（,%,）,累计贡献率,11.1134,65.37,65.37,2.6656,15.68,81.05,0.9126,5.37,86.42,0.7052,4.15,90.57,y,1,y,2,y,3,y,4,X,1,X,2,X,3,X,4,X,5,X,6,X,7,X,8,X,9,X,10,X,11,X,12,X,13,X,14,X,15,X,16,X,17,0.12823,0 .92016,0.81227,0.87838,0.60188,0.96955,0.86623,0.93517,0.31414,0.71990,0.97349,0.96099,0.94015,0.86344,0.72272,0.86663,0.70772,0.83792,0.33162,-0.29855,0.31611,0.35476,0.18554,-0.26862,-0.18716,-0.38142,-0.24218,0.13628,0.21648,0.17209,0.32557,-0.29605,-0.42673,-0.48287,-0.08600,-0.05689,-0.00600,0.16405,0.59498,-0.09472,-0.26184,-0.18498,0.31302,-0.33831,0.02439,-0.06414,0.02189,0.08623,0.40794,-0.10586,-0.08101,0.32628,-0.04976,0.18584,0.07920,-0.11212,0.03643,-0.17976,0.12837,0.10554,-0.50281,0.08648,-0.01679,-0.04075,-0.01538,-0.25396,0.08748,0.38341,3,、用,主成分法,得到,初始因子载荷矩阵,y,1,y,2,y,3,y,4,X,1,X,2,X,3,X,4,X,5,X,6,X,7,X,8,X,9,X,10,X,11,X,12,X,13,X,14,X,15,X,16,X,17,0.36476,0.69104,0.36105,0.78837,0.92226,0.62703,0.27491,0.37746,0.02543,0.25966,0.67988,0.65907,0.68347,0.74125,0.60631,0.28362,0.15066,-0.01356,0.41494,0.73168,0.42280,0.00720,0.56659,0.58194,0.77170,0.50168,0.21634,0.59021,0.50739,0.47467,0.36873,0.28811,0.77616,0.88549,-0.09974,0.51072,0.26591,0.27899,0.03069,0.49666,0.68189,0.46591,-0.10558,0.87360,0.39706,0.51118,0.46804,0.34934,0.28303,0.41315,0.12400,-0.83020,-0.22770,0.21693,-0.16291,0.05607,-0.15459,0.24019,0.07210,0.79724,0.09953,-0.07801,-0.14711,-0.06432,-0.17291,0.55692,0.31378,0.25580,4,、,旋转后的,因子载荷矩阵,5,、将,17,项指标,按高载荷,分成四类，并给,各公共因子命名,如下：,高载荷指标,因子命名,公共因子,F,1,x,2,:,人均,GDP,x,4,:,人均出口额,x,5,:,工业企业劳动生产率,x,6,:,人均社会消费品零售额,x,11,:,人均邮电业务总量,x,12,:,每万人电话装机数,x,13,:,人均固定资产投资,x,14,:,人均实际利用外资,X,15,： 地方财政收入占,GDP,比重,发展实力,公共因子,F,2,X,3,：第三产业占,GDP,比重,X,7,：每万人拥有卫生技术人员数,X,8,：每万人高等学校在校生数,X,9,：教育经费投入占,GDP,比重,X,16,：每万人科研机构数,X,17,：科研经费占,GDP,比重,人文发展,公共因子,F,3,X,10,：,人均货运总量,交通运输,公共因子,F,4,X,1,：,GDP,总量,6,、,因子得分,地区,F,1,得分,F,2,得分,地区,F,1,得分,F,2,得分,北京,天津,河北,山西,内蒙古,辽宁,吉林,黑龙江,上海,江苏,浙江,安徽,福建,江西,山东,河南,0.7155,0.4212,-0.2370,-1.1269,-0.7406,-0.5088,-0.8362,-0.3889,3.1695,0.1618,0.1741,-0.3588,0.9353,-0.9027,0.1243,-0.3990,4.5448,0.2392,-0.4544,-0.8717,-0.8819,-0.1261,0.2413,-0.6099,0.3311,0.3413,-0.2304,-0.3616,-0.3808,0.0831,-0.0658,-0.0984,湖北,湖南,广东,广西,海南,重庆,四川,贵州,云南,西藏,陕西,甘肃,青海,宁夏,新疆,-0.2463,-0.6029,2.5415,-0.1316,0.7151,-0.9363,-0.5405,0.0669,1.9646,-0.4841,-0.7702,-0.6141,-0.5599,-0.4392,-0.1057,0.1963,0.1450,-0.1925,-0.2635,-0.5340,0.1916,0.1041,-0.6585,-1.8751,0.9150,0.9528,-0.0166,0.0616,-0.1895,-0.5367,“生活质量的概念最先是由美国的经济学家加尔布雷思在1958年提出的。所谓生活质量，就是用来反映居民生活需要满足程度的一个概念。 “生活水平是指社会提供给广阔居民用于生活消费的商品数量和质量的状况，主要反映居民在物质需求方面的满足程度。生活质量既反映人们的物质生活状况，又反映社会和心理特征，是一个内容广泛的概念。具体包括：经济条件、物质生活、生活环境、精神生活和居民素质。其具体内容决定了其最根本特点是它具有综合性，是各个方面相互制约、共同作用的综合结果。,考虑选择以下,12,项指标。,X1,：人均国内生产总值,X2,：人均可支配收入,X3,：人均消费支出,X4,：人均居住面积,X5,：自来水普及率,X6,；液化气普及率,X7,：每万人拥有公共汽车数,X8,；人均公共绿地面积,X9,；工业废水处理率,X10,：文化教育娱乐消费占总消费支出比重,X11,：城市就业率,X12,：每万人拥有医生数,数据见,旋转后的因子载荷矩阵,(R=Q),F1,F2,F3,F4,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,0.75098,0.95902,0.95165,0.79535,0.38256,0.64071,0.73659,0.48544,0.48062,0.37119,0.27914,0.32819,0.40920,0.12015,0.05989,-0.04001,0.81957,0.66229,0.04002,0.00575,0.66203,-0.33973,0.06969,0.33287,0.30044,0.05279,0.08195,-0.41120,0.03029,-0.04779,0.32641,-0.46648,0.03070,0.63693,0. 01093,0.75497,0.11906,-0.00192,-0.06935,0.10837,0.15663,0.12555,0.11523,0.40284,-0.33660,-0.27116,0.87038,0.30609,公共因子,方差贡献,4.911408,1.968393,1.572913,1.284663,高载荷指标,命名,公共因子,F,1,X,1:,人均,GDP,X,2:,人均可支配收入,X,3:,人均消费支出,X,4:,人均居住面积,X,7:,每万人拥有公共汽车数,物质生活条件因子,公共因子,F,2,X,5:,自来水普及率,X,6:,液化气普及率,X,9:,工业废水处理率,生活设施和,环境因子,公共因子,F,3,X,10:,文化教育娱乐消费占,总消费支出比重,X,12:,每万人拥有医生数,文化生活和,卫生条件因子,公共因子,F,4,X,11:,就业率,社会保障因子,城镇居民生活质量评估指标体系,X1:人均国内生产总值 X2:人均可支配收入,X3:人均消费支出 X4:城市就业率,X5:人均居住面积 X6:每百户电脑拥有量,X7:每百户移动 拥有量 X8:每百户空调拥有量,X9:每百户排油烟机拥有量 X10:每百户淋浴热水器拥有量,X11:每百户家用汽车拥有量 X12:每人文娱效劳支出,X13:每万人拥有医生数 X14:恩格尔系数,X15:人均公共绿地面积 X16:大专以上人口所占比例,X17:人均教育经费 X18:人均图书拥有量,X19:平均预期寿命,第一主成分的表达式,PCR1,XXXXXX,6,XXX,9,XXX,12,XXX,15,XXX,18,X,19,对旋转后的因子载荷矩阵进展因子命名,F1,：,经济,教育,因子,变量名,F1,F2,F3,F4,F5,X1,人均国内生产总值,0.87523,0.3031,0.2222,0.15528,-0.18857,X2,人均可支配收入,0.89176,0.33784,0.27132,0.0497,-0.03647,X3,人均消费支出,0.86287,0.38729,0.28659,0.11079,-0.02129,X6,每百户电脑拥有量,0.66048,0.59956,0.37525,-0.03276,0.14581,X16,大专以上人口所占比例,0.88993,0.02428,0.21977,0.12575,0.20447,X17,人均教育经费,0.88239,0.12221,0.29812,-0.04599,0.21931,X18,人均图书拥有量,0.87712,0.3311,0.09834,0.14173,0.13559,F2,：,物质,生活,因子,X5,人均居住面积,0.2371,0.83355,-0.04812,0.0198,-0.16962,X7,每百户移动电话拥有量,0.18235,0.55745,0.61609,-0.32227,-0.10919,X8,每百户空调拥有量,0.45192,0.81243,0.05042,0.09489,0.19627,X10,每百户淋浴热水器拥有量,0.22876,0.77878,0.14875,0.00139,0.14735,X12,每人文娱服务支出,0.50391,0.52816,0.50800,-0.15105,0.26693,F3,：生活环境因子,X9,每百户排油烟机拥有量,0.38874,-0.14085,0.55381,0.52991,-0.06564,X11,每百户家用汽车拥有量,0.25325,0.12318,0.77102,-0.03948,0.3939,X15,人均拥有绿化面积,0.31905,0.04187,0.74269,0.15618,0.1326,F4,：医疗保健因子,X13,每万人拥有医生数,-0.26639,0.50624,0.14811,0.67216,-0.1475,X14,1-,恩格尔系数,0.26673,-0.15137,-0.08608,0.84763,0.17644,X19,平均预期寿命,0.60478,0.4611,0.02692,0.52272,-0.04882,F5,：社会保障因子,X4,城市就业率,0.07487,0.05229,0.23948,0.06604,0.92574,浙江省县域经济综合实力的评价指标体系,X1：GDP,X2：人均GDP,X3：社会消费品零售总额 (TRSCG),X4：全社会固定资产投资 (TIFA,X5：财政总收入 (TFR),X6：农村居民人均纯收入 (PNIRR),X7：人均居民年末储蓄余额 (PSDR),X8：农林牧渔业总产值 (TOVA),X9：工业总产值 (TOI),X10：每万人拥有医生数 (PD),X11：每万人拥有专业技术人员数 (PSTP),X12：人均社会消费品零售额 (PRSCG),X13：人均固定资产投资 (PIFA),X14：人均财政收入 (PFR),X15：人均农林牧渔业产值 (POVA),X16：人均工业产值 (POI),特征值,Component,特征值,方差贡献率,累积方差贡献率,PCR1,9.6387,0.6024,0.6024,PCR2,1.8911,0.1182,0.7206,PCR3,1.4616,0.0914,0.8120,PCR4,0.9247,0.0578,0.8698,PCR5,0.5947,0.0372,0.9069,Variable,PCR1,PCR2,PCR3,GDP,0.2937,-0.2338,0.0670,PGDP,0.2968,0.1840,-0.1026,TRSCG,0.2544,-0.2913,0.1821,TIFA,0.3053,-0.0752,-0.0794,TFR,0.2960,-0.2146,0.0370,PNIRR,0.2925,-0.0499,0.0851,PSDR,0.2798,0.0700,-0.2254,TOVA,0.1237,0.2156,0.6568,TOI,0.2888,-0.1136,0.0167,PD,0.0948,0.4189,-0.3310,PSTP,0.1998,0.0577,0.2858,PRSCG,0.2536,0.0779,0.0732,PIFA,0.1881,0.4142,-0.3073,PFR,0.2977,0.0970,-0.0967,POVA,-0.0275,0.5830,0.3877,POI,0.2823,0.0497,-0.0611,特征向量,旋转后的因子载荷阵及因子命名,FACTOR1,FACTOR2,FACTOR3,FACTOR4,因子命名,X,1,：,GDP,0.93617,-0.21431,-0.09754,0.09661,经济发展,X,2,：人均,GDP,0.89395,0.33664,0.11926,-0.04851,X,3,：社会消费品零售总额,0.83745,-0.44468,0.00937,-0.14648,X,4,：全社会固定资产投资,0.95406,0.04754,-0.08185,-0.01746,X,5,：财政总收入,0.94350,-0.18570,-0.09765,0.03420,X,6,：农村居民人均纯收入,0.90727,-0.02625,0.07259,0.11066,X,7:,人均居民年末储蓄余额,0.86532,0.25338,-0.05915,-0.25219,X,9,：工业总产值,0.89328,0.01029,-0.08764,0.29858,X,14,：人均财政收入,0.90755,0.24305,0.04778,-0.02940,X,3:,人均社会消费品零售额,0.79346,-0.00918,0.25390,-0.33895,X,16,：人均工业产值,0.85038,0.24472,-0.02417,0.28418,X,10,：每万人拥有医生数,0.22466,0.77324,0.02375,0.11089,卫生事业和投资,X,13,：人均固定资产投资,0.53740,0.65315,0.14846,-0.32013,X,8,：农林牧渔业总产值,0.35447,-0.21366,0.80772,0.20789,农业发展,X,15,人均农林牧渔业产值,-0.15277,0.29056,0.88437,-0.07606,X,11,每万人拥有专业技术人员数,0.58025,0.05631,0.23088,0.66178,技术发展,谢谢观赏,