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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。,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,诚实,推销,经验,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,诚实,推销,经验,积极性,抱负,理解,潜力,交际能力,适应性,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。,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,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,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,
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