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,例,1,某大学挑出,20,名教师进行了教学质量评分。评比的主要 工作之一如下：“请按下面几个方面对被评教师打分”,语言表达,D.,知识内容,师生交流,E.,教案质量,逻辑性,F.,板书质量,ABCDEF,1,2,3,20,879786,988676,667555,978776,要求：根据上面的评比结果对教师进行综合评价并分类。,例1 某大学挑出20名教师进行了教学质量评分。评比的主要,1,、,求相关系数矩阵,R,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,2.741,45.69,45.69,2.428,40.46,86.15,0.438,7.30,93.45,2、 计算R的特征值主成分Y1Y2Y3特征根2.7412.,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,3、 求特征根所对应的单位特征向量特征向量Y1Y2X10.,4,、,由,特征向量,写出主成分的表达式,5,、主成分的含义解释,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,-0.495,6、初始因子载荷矩阵载荷Y1Y2X10.4590. 837,7,、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,7、旋转后的因子载荷阵矩阵载荷F1F2X10.0070. 9,8,、因子得分,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,例2：In a job intervi,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,7.50,50,50,2.06,13.73,63.73,1.46,9.73,73.46,1.21,8.07,81.53,0.74,1、 求相关系数矩阵RY1Y2Y3Y4特征根7.502.0,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,诚实,推销,经验,积极性,抱负,理解,潜力,交际能力,适应性,y1y2y3y4X10.1620.4310.308特征向量,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,y1y2y3y4X10.4450.6180.372-0.11,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,诚实,推销,经验,积极性,抱负,理解,潜力,交际能力,适应性,f1f2f3f4X10.83旋转后的因子载荷矩阵申请书,第一公共因子,f,1,:,申请者,外露,的能力,第二公共因子,f,2,:,经验,第三公共因子,f,3,:,讨人喜欢,第四公共因子,f,4,:,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。,第一公共因子 f1 : 申请者外露的能力 “外貌”,将上章例子对全国,31,个地区的社会经济发展的,17,项指标作因子分析。,数据见,cd.pcrex01,将上章例子对全国 31个地区的社会经济发展的17 项指标作因,反映地区社会经济发展的指标体系,X,1,：国内生产总值（,GDP,）,X,2,：人均,GDP,X,3,：第三产业产值占,GDP,比重,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,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,10,：人均货运总量,X,11,：人均邮电业务总量,X,12,：每万人电话机装机数,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,X,16,：每万人科研机构数,X,17,：科研经费占,GDP,比重,反映地区社会经济发展的指标体系,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,11.1134,65.37,65.37,2.6656,15.68,81.05,0.9126,5.37,86.42,0.7052,4.15,90.57,1、 求相关系数矩阵R主成分Y1Y2Y3Y4特征根11.1,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,y1y2y3y4X10.128230.83792-0.086,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,y1y2y3y4X10.36476-0.01356-0.09,5,、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,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,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,-0.5367,6、因子得分地区F1得分F2得分地区F1得分F2得分北京0.,“,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,”是指社会提供给广大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基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。,“生活质量”的概念最先是由美国的经济学家加尔布雷思在195,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,cd.citlife,考虑选择以下12项指标。数据见cd.citlife,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,旋转后的因子载荷矩阵 (R=Q)F1F2F3F4X10.7,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,高载荷指标命名公共因子F1X1: 人均GDP物质生活条件因子,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:,每百户移动电话拥有量,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:,每人文娱服务支出,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,城镇居民生活质量评估指标体系 X1:人均国内生产总值,第一主成分的表达式,PCR1,=0.28561,X,1+0.302701,X,2+0.308213,X,3+0.095231,X,4+0.173657,X,5+0.303004,X,6,+0.187225,X,7+0.252521,X,8+0.159696,X,9,+0.199146,X,10+0.188606,X,11+0.27006,X,12,+0.05236,X,13+0.073222,X,14+0.186296,X,15,+0.260721,X,16+0.276966,X,17+0.287724,X,18,+0.24083,X,19,第一主成分的表达式PCR1=0.28561X1+0.3027,对旋转后的因子载荷矩阵进行因子命名,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,对旋转后的因子载荷矩阵进行因子命名变量名F1F2F3F4F5,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),浙江省县域经济综合实力的评价指标体系 X1：GDP,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,特征值Component特征值方差贡献率累积方差贡献率PCR,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,VariablePCR1PCR2PCR3GDP0.2937-,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,旋转后的因子载荷阵及因子命名FACTOR1FACTOR2FA,知识回顾,Knowledge 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