多元统计分析实验4.doc

安徽财经大学统计与数学模型分析实验中心多元统计分析实验报告班级： 09统计 班 学号： 姓名： 实验时间 第13周 实验地点 广学楼 实验名称：主成分分析的应用 使用软件： SPSS实验目的（1）掌握主成分分析方法；（2）能够利用SPSS进行主成分分析；（3）能够对分析结果进行合理的解释.实验内容1、对某市15个大中型工业企业进行经济效益分析，经研究确定，从有关经济效益指标中选取7个指标作分析，即固定资产产值率(X1)，固定资产利税率(X2)，资金利润率(X3)，资金利税率(X4)，流动资金周转天数(X5)，销售收入利税率(X6)和全员劳动生产率(X7)。数据资料如下：企业及编号固定资产率X1固定资产利税率(X2)资金利润率(X3)资金利税率(X4)流动资金周转天数(X5)销售收入利税率(X6)全员劳动生产率(X7)康佳电子1茂名石化2华空空调3三星集团4数源科技5中华电子6南方制药7中国长城8白云制药9五羊自行10广发卷烟11岭南通信12华南冰箱13潮州二轻14稀土高科1553.2559.8246.7834.3975.3266.4668.1856.1359.2552.4755.7661.1950.4167.9551.0716.6819.7015.207.2929.4532.9325.3915.0519.8221.1316.7515.8316,5322.2412.9218.419.216.244.7643.6833.8727.5614.2120.1726.5219.2317.4320.6337.0012.5426.7527.5623.408.9756.4942.7837.8519.4928.7835.2028.7228.0329.7354.5920.8255556562695063767162586169636631.8432.9432.9821.3040.7447.9833.7627.2133.4139.4129.6226.4032.4931.0525.121.752.871.531.632.142.602.431.751.831.731.521.601.311.571.对数据资料进行主成分分析：(1)前两个最大特征根为_4.635_、_1.285_，其对应的特征向量为_0.238 0.191 0.265 0.270 0.173 0.135 -0.046_，_-0.087 0.096 -0.126 -0.159 -0.628 0.167 0.477_。(2)第一主成分的表达式为_F1=_0.238x1+0.191x2+0.265x3+0.270x4+0.173x5+0.135X6-0.046x7_，该主成分包含了原始信息的66.219_%，第二主成分的表达式为_F2= -0.087x1+0.096x2-0.126x3-0.159 x4-0.628x5+0.167x6+0.477x7，该主成分的方差贡献率为_18.358%_。(3)如果舍弃第二主成分，则哪个原始变量的损失信息最大：_流动资金周转天数_。(4)第一个主成分与第二个变量间的相关系数为_0.355_。(5)第一个主成分主要反映盈利能力，现对第一主成分计算得分为_ _，对得分进行排序(降序)，各企业的得分排名顺序依次为：_ _ _(依企业顺序写出排名)。若利用第一、二主成分构造综合评价函数，则两主成分的权数分别为_、_。2、下表是我国2003年各地区农村居民家庭平均每人主要食品消费量,其中粮食(X1)、蔬菜(X2)、食油(X3)、猪牛羊肉(X4)、家禽(X5)、蛋类及其制品(X6)、水产品(X7)、食糖(X8)、酒(X9);试用主成分方法对各主要食品和地区进行分析.地区X1X2X3X4X5X6X7X8X9北京134.0592.789.1514.602.1710.134.252.9214.42天津150.2069.9910.0011.07.8410.808.35.7210.14河北216.7255.976.597.10.546.362.25.657.29山西218.9180.875.725.36.246.15.471.152.59内蒙古207.3070.772.7921.181.413.821.451.3410.77辽宁194.39178.595.9016.452.519.594.49.7310.80吉林255.99115.206.2711.423.238.643.60.7513.64黑龙江195.08111.707.627.852.616.263.35.9015.09上海189.4476.608.5916.377.407.5116.112.1216.77江苏251.98109.128.2712.054.506.729.091.308.82浙江208.4683.915.8116.426.035.3314.642.1324.15安徽228.3580.976.879.074.275.045.431.4210.61福建198.2799.925.1916.515.143.5513.302.3516.84江西264.80144.228.7713.243.313.505.191.137.31山东229.06118.196.968.092.7011.614.011.0010.81河南236.97100.114.226.481.238.011.351.134.23湖南227.39159.769.4019.862.743.868.10.927.29湖北247.21149.448.3517.513.893.286.891.134.02广东233.75130.226.7322.2710.402.8313.302.163.33广西205.65108.944.9214.447.331.123.571.186.14海南236.3186.615.7015.409.771.3114.751.243.88实验结果分析Total Variance ExplainedComponentInitial EigenvaluesExtraction Sums of Squared LoadingsRotation Sums of Squared LoadingsTotal% of VarianceCumulative %Total% of VarianceCumulative %Total% of VarianceCumulative %12.92732.52132.5212.92732.52132.5212.71930.20930.20922.22024.67157.1922.22024.67157.1921.42615.84146.04931.34414.93672.1281.34414.93672.1281.28114.23360.2824.8018.90581.033.8018.90581.0331.27614.17474.4575.6547.26388.296.6547.26388.2961.24513.83988.2966.3964.39992.6947.3353.72796.4228.2222.47298.8949.1001.106100.000Extraction Method: Principal Component Analysis.由此表得，前五个累计方差贡献率大于85%，故选取前五个作主成分分析！Component Score Coefficient MatrixComponent12345粮食.143-.749.220-.020-.062蔬菜-.130-.119.157.764.044食油.095.030-.202-.042.831猪牛羊肉.066.376-.093.531-.187家禽.386-.170-.015-.122.054蛋类及其制品-.214-.056.399.041.212水产品.398-.200.190-.163.255食糖.155.392-.007-.023-.076酒.023-.207.881.097-.184Undefined error #11401 - Cannot open text file C:PROGRA1IBMSPSSSTATIS119langenspss.err: Undefined error #11408 - Cannot open text file C:PROGRA1IBMSPSSSTATIS119langenspss.err: Undefined error #11418 - Cannot open text file C:PROGRA1IBMSPSSSTATIS119langenspss.err: 由此可得因子得分系数矩阵Rotated Component MatrixaComponent12345粮食.155-.878-.223.154-.178蔬菜-.036-.278-.067.906.178食油.048.088.003.112.961猪牛羊肉.592.341-.046.627-.160家禽.921-.085-.062.073-.063蛋类及其制品-.601.142.506-.115.414水产品.894.058.246.001.230食糖.559.599.250-.053-.068酒.140.251.917-.055-.023Undefined error #11401 - Cannot open text file C:PROGRA1IBMSPSSSTATIS119langenspss.err: Undefined error #11408 - Cannot open text file C:PROGRA1I