1、2、变量y1-y2的相关系数矩阵 Correlations Among the WITH Variables y1 y2 y1 1.0000 0.4200 y2 0.4200 1.00003、变量x1-x2与y1-y2的相关系数矩阵 Correlations Between the VAR Variables and the WITH Variables x1 0.2400 0.0600 x2 -0.0600 0.0700变量间高度相关。05 Thursday, November 18, 2013 24 典型相关分析的一般结果 Canonical Correlation Analysis Ad
2、justed Approximate Squared Canonical Canonical Standard Canonical Correlation Correlation Error Correlation典型相关系数 校正的典型相关系数 近似的标准误 典型相关系数平方 1 0.397112 0.396910 0.008423 0.157698 2 0.072889 . 0.009947 0.0053135、检验各对典型变量是否显著相关 Test of H0: The canonical correlations in the Eigenvalues of Inv(E)*H curre
3、nt row and all that follow are zero = CanRsq/(1-CanRsq) Likelihood ApproximateEigenvalue Difference Proportion Cumulative Ratio F Value Num DF Den DF Pr F各对相关系 相邻两特 特征值占 特征值占方差 似然比值 数特征值 征值之差 方差比例 比例累计值 1 0.1872 0.1819 0.9723 0.9723 0.83782737 462.33 4 19992 .0001 2 0.0053 0.0277 1.0000 0.99468712 5
4、3.40 1 9997 Wilks Lambda 0.83782737 462.33 4 19992 Pillais Trace 0.16301046 443.56 4 19994 Hotelling-Lawley Trace 0.19256330 481.20 4 11994 Roys Greatest Root 0.18722205 935.83 2 9997 R11=1 0.63;0.63 1; R12=0.24 0.06;-0.06 0.07; R21=0.24 -0.06;0.06 0.07; R22=1 0.42;0.42 1; v1,d1=eig(R11); v2,d2=eig(
5、R22); p1=inv(v1*sqrt(d1)*v1); p2=inv(v2*sqrt(d2)*v2 T1=p1*R12*inv(R22)*R21*p1; T2=p2*R21*inv(R11)*R12*p2;结果:有上求出的结果可以得到:典型相关系数为:r1=0.0729 r2=0.3971典型变量:(2)检验各对典型变量的显著相关 p=2; q=2; n=140; k=1:2; d1k=(p-k+1).*(q-k+1); d=0.0729 0.3971; D=1-d.2; Ak=D(1)*D(2),D(2); Tk=-n-0.5*(p+q+3).*log(Ak); pk=1-chi2cdf
6、(Tk,d1k)可以看出,第一、第二典型变量都是显著性相关的。即一名学生的阅读速度和阅读理解能力越强,他的技术速度和计算正确程度就越好。4.9 SAS实现data examp4_9;input x1-x2 y1-y2; 1 191 155 179 145 2 195 149 201 152 3 181 148 185 149 4 183 153 188 149 5 176 144 171 142 6 208 157 192 152 7 189 150 190 149 8 197 159 189 152 9 188 152 197 15910 192 150 187 15111 179 158
7、186 14812 183 147 174 14713 174 150 185 15214 190 159 195 15715 188 151 187 15816 163 137 161 13017 195 155 183 15818 186 153 173 14819 181 145 182 14620 175 140 165 13721 192 154 185 15222 174 143 178 14723 176 139 176 14324 197 167 200 15825 190 163 187 150proc cancorr data=examp4_9 corr;由SAS proc
8、 cancorr过程求得样本相关系数矩阵20 Thursday, November 18, 2013 1 Correlations Among the VAR Variables x1 1.0000 -0.2094 x2 -0.2094 1.0000 Correlations Among the WITH Variables y1 y2 y1 1.0000 0.6932 y2 0.6932 1.0000 x1 -0.0108 -0.2318 x2 0.7346 0.7108 The SAS System 14:21 Saturday, October 30, 2012 4 Adjusted A
9、pproximate Squared Canonical Canonical Standard Canonical 1 0.787478 0.772383 0.077543 0.620121 2 0.292947 . 0.186607 0.085818 Test of H0: = CanRsq/(1-CanRsq) Likelihood Approximate Eigenvalue Difference Proportion Cumulative Ratio F Value Num DF Den DF Pr 1 1.6324 1.5385 0.9456 0.9456 0.34727867 7.
10、32 4 42 0.0001 2 0.0939 0.0544 1.0000 0.91418197 2.07 1 22 0.1648第一对典型变量贡献率94.56%。进行分析求得特征值在方差占比例的累计值(贡献率)为0.9141也可看出,只需要两对变量即可。以下输出用wilksLambda 等四种方法对典型相关系数为零的假设检验。 S=2 M=-0.5 N=9.5 Lambda 0.34727867 7.32 4 42 0.0001 Pillais Trace 0.70593888 6.00 4 44 0.0006 Hotelling-Lawley Trace 1.72629023 8.94 4
11、 24.198 0.0001s Greatest Root 1.63241610 17.96 2 22 The CANCORR Procedure x1 0.0091725722 0.1386496154 x2 0.1036642178 0.0151230041 y1 0.0845052096 0.168128993 y2 0.0459765801 -0.130308033 The SAS System 20:20 Thursday, November 18, 2013 4第一组变量x1-x3的典型变量的系数(原始变量标准化后) x1 0.0675 1.0204 x2 1.0120 0.147
12、6 第二组变量y1-y3的典型变量的系数(原始变量标准化后) Standardized Canonical Coefficients for the WITH Variables y1 0.6231 1.2396 y2 0.4616 -1.3083第一对典型变量主要成年长子的头长、头宽加权主要次子头宽影响第一对典型变量主要表现头宽和头长的相关性。 Canonical Structure 第一组变量x1-x3和典型变量 x1 -0.1444 0.9895 x2 0.9978 -0.0660 第二组变量y1-y3和典型变量 Correlations Between the WITH Variabl
13、es and Their Canonical Variables y1 0.9430 0.3327 y2 0.8935 -0.4491 第一组变量x1-x3和第二组典型变量 Correlations Between the VAR Variables and the Canonical Variables of the WITH Variables x1 -0.1137 0.2899 x2 0.7858 -0.0193 第二组变量y1-y3和第一组典型变量 Correlations Between the WITH Variables and the Canonical Variables o
14、f the VAR Variables y1 0.7426 0.0975 y2 0.7036 -0.13164.9 MATLAB实现建立data.txt,并导入数据。 a=data;n,m=size(a);b=a./(ones(n,1)*std(a);R=cov(b);X=b(:,1:2);Y=b(:,3:4);A,B,r,U,V,ststs=canoncorr(X,Y)A = 0.0675 -1.0204 1.0120 -0.1476B = 0.6231 -1.2396 0.4616 1.3083r = 0.7875 0.2929U = 0.4373 1.5839 0.8611 1.3848
15、 -0.5810 1.4579 -0.3645 1.2890 -1.0810 1.2562 2.2454 0.6336 0.2850 0.7823 1.1235 0.5227 0.1997 0.5201 0.6235 0.3210 -0.7150 0.3789 -0.2911 0.1798 -1.2149 0.1772 0.4529 -0.2034 0.2547 -0.3118 -2.3277 -0.0724 0.9987 -0.6949 0.0749 -0.6975 -0.4343 -0.7605 -1.0471 -0.8084 0.7244 -1.2042 -1.1324 -1.0706 -0.9159 -1.2395 1.2702 -1.6957 0.5538 -1.7285V = 0.1054 -1.2830 0.6098 2.5925 -0.2103 0.6757 0.3501 0.2260 -1.1920 -0.4761
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