matlab与对应分析.doc

第九章对应分析安庆师范学院 胡云峰习题 用对应分析法，对我国16个地区农民1982年支出情况的6项指标进行分类。16个地区农民生活水平的调查数据（单位:元）地区食品衣着燃料住房生活用品及其他文化生活服务支出x1x2x3x4 x5x6北京190.3343.779.7360.5449.019.04天津135.236.410.4744.1613.493.94河北95.2122.839.322.4422.812.8山西104.7825.116.49.8918.173.25内蒙128.4127.638.9412.5823.993.27辽宁145.6832.8317.7927.2939.093.47吉林159.3733.3818.3711.8125.295.22黑龙江116.2229.5713.2413.7621.756.04上海221.1138.6412.53115.6550.825.89江苏144.9829.1211.6742.627.35.74浙江169.9232.7512.7247.1234.355安徽153.1123.0915.6223.5418.186.39福建144.9221.2616.9619.5221.756.73江西140.5421.517.6419.1915.974.94山东115.8430.2612.233.6133.773.85河南101.1823.268.4620.220.54.3解 第一步求出协方差矩阵A=ZZ程序：x=190.33 43.77 9.73 60.54 49.01 9.04;135.20 36.40 10.47 44.16 13.49 3.94;. 95.21 22.83 9.30 22.44 22.81 2.80;104.78 25.11 6.40 9.89 18.17 3.25;. 128.41 27.63 8.94 12.58 23.99 3.27;145.68 32.83 17.79 27.29 39.09 3.47;. 159.37 33.38 18.37 11.81 25.29 5.22;116.22 29.57 13.24 13.76 21.75 6.04;. 221.11 38.64 12.53 115.65 50.82 5.89;144.98 29.12 11.67 42.60 27.30 5.74;. 169.92 32.75 12.72 47.12 34.35 5.00;153.11 23.09 15.62 23.54 18.18 6.39;. 144.92 21.26 16.96 19.52 21.75 6.73;140.54 21.5 17.64 19.19 15.97 4.94;. 115.84 30.26 12.20 33.61 33.77 3.85;101.18 23.26 8.46 20.2 20.5 4.3;n p=size(x);T=sum(sum(x);xliehe=zeros(1,p);xhanghe=zeros(1,n);for k=1:p xliehe(k)=sum(x(:,k);endfor l=1:n xhanghe(l)=sum(x(l,:);endZ=zeros(p,p);for i=1:1:n for j=1:1:p Z(i,j)=(x(i,j)-xhanghe(i)*xliehe(j)/T)/(xhanghe(i)*xliehe(j)(1/2); endendA=Z*Z输出结果A = 0.0042 0.0003 0.0032 -0.0090 -0.0026 0.0012 0.0003 0.0034 0.0001 -0.0044 0.0004 0.0000 0.0032 0.0001 0.0055 -0.0091 -0.0016 0.0010 -0.0090 -0.0044 -0.0091 0.0284 0.0014 -0.0029 -0.0026 0.0004 -0.0016 0.0014 0.0055 -0.00080.0012 0.0000 0.0010 -0.0029 -0.0008 0.0014然后求A的特征值及特征向量程序X B=eig(A)输出结果X = 0.7547 -0.3203 0.3733 0.0438 0.3135 0.2972 0.3441 0.1587 -0.4490 0.7199 -0.3485 0.1227 0.2253 0.1520 -0.7095 -0.5207 0.2386 0.3078 0.3628 0.0685 -0.1587 -0.0255 0.2293 -0.8861 0.3311 -0.0066 0.1281 -0.4555 -0.8120 -0.0850 0.1417 0.9189 0.3377 -0.0243 0.1071 0.0970B = 0.0000 0 0 0 0 0 0 0.0010 0 0 0 0 0 0 0.0016 0 0 0 0 0 0 0.0033 0 0 0 0 0 0 0.0069 0 0 0 0 0 0 0.0357（0.0357+0.0069）/（0.0357+0.0069+0.0033+0.0016+0.0010）*100%=87.83%前两个方差的累计贡献率已达87%，因此，选前两个特征值分别计算R型与Q型的因子载荷阵如下程序F=zeros(p,2);for t=1:1:p F(t,1)=(0.03570.5)*(X(t,6); F(t,2)=(0.00690.5)*(X(t,5);endFG=Z*F输出结果F = 0.0562 0.0260 0.0232 -0.0289 0.0582 0.0198 -0.1674 0.0191 -0.0161 -0.0674 0.0183 0.0089G = -0.0079 -0.0021 -0.0054 0.0024 -0.0001 -0.0013 0.0075 -0.0011 0.0080 -0.0012 0.0035 -0.0024 0.0128 0.0001 0.0083 -0.0007 -0.0246 0.0012 -0.0044 0.0006 -0.0042 0.0000 0.0062 0.0027 0.0077 0.0018 0.0080 0.0028 -0.00