实 验 报 告主成分分析（综合性实验）(Principal component analysis)实验原理：主成分分析利用指标之间的相关性，将多个指标转化为少数几个综合指标，从而达到降维和数据结构简化的目的。这些综合指标反映了原始指标的绝大部分信息，通常表示为原始指标的某种线性组合，且综合指标间不相关。利用矩阵代数的知识可求解主成分。实验题目一：将彩色胶卷在显影液下处理后在不同情形下曝光，然后通过红、绿、蓝三种滤色片并在高、中、低三种密度下进行测量，每个胶卷有高红、高绿、高蓝、中红、…、低蓝等九个指标（分别记为 X1－X9 九个变量）。试验了 108 个胶卷，由数据已算得如下协差阵： (S2a1)177 179 95 96 53 32 -7 -4 -3 419 245 131 181 127 -2 1 4 302 60 109 142 4 4 11 158 102 42 4 3 2 137 96 4 5 6 128 2 2 8 34 31 33 39 39 48实验要求：（1）试从协差阵出发进行主成分分析；（2）计算方差累积贡献率；（3）作 Scree 图，并结合（2）的结果确定主成分的个数；（4）试对结果进行解释。实验题目二：下表中给出了不同国家及地区的男子径赛记录： (t8a6)Country100m (s)200m (s)400m (s)800m (min)1500m (min)5000m (min)10,000m (min)Marathon (mins)Argentina10.3920.8146.841.813.714.0429.36137.72Australia10.3120.0644.841.743.5713.2827.66128.3Austria10.4420.8146.821.793.613.2627.72135.9Belgium10.3420.6845.041.733.613.2227.45129.95Bermuda10.2820.5845.911.83.7514.6830.55146.62Brazil10.2220.4345.211.733.6613.6228.62133.13Burma10.6421.5248.31.83.8514.4530.28139.95Canada10.1720.2245.681.763.6313.5528.09130.15Chile10.3420.846.21.793.7113.6129.3134.03China10.5121.0447.31.813.7313.929.13133.53Columbia10.4321.0546.11.823.7413.4927.88131.35Cook Islands12.1823.252.942.024.2416.735.38164.7Costa Rica10.9421.948.661.873.8414.0328.81136.58Czechoslovakia10.3520.6545.641.763.5813.4228.19134.32Denmark10.5620.5245.891.783.6113.528.11130.78Dominican Republic10.1420.6546.81.823.8214.9131.45154.12Finland10.4320.6945.491.743.6113.2727.52130.87France10.1120.3845.281.733.5713.3427.97132.3German (D.R.)10.1220.3344.871.733.5613.1727.42129.92German (F.R.)10.1620.3744.51.733.5313.2127.61132.23Great Br...
