实验报告9典型相关分析.doc

1、.实验九典型相关分析实验目的和要求能利用原始数据与相关矩阵、协主差矩阵作相关分析,能根据 SAS 输出结果选出满足要求的几个典型变量实验要求 :编写程序，结果分析实验容：4.8SAS 实现dataexamp4_8(type=corr);input_name_$ x1-x2 y1-y2;_type_= corr;cards ;x11.000.630.24 0.06x20.631.00 -0.06 0.07y10.24 -0.061.00 0.42y20.060.070.42 1.00;run ;proccancorrdata =examp4_8corr ;var x1-x2;withy1-y2;

2、run ;The SAS System20:05 Thursday, November 18, 20131专业资料.The CANCORR ProcedureCorrelations Among the Original Variables1 、变量 x1-x2 的相关系数矩阵R11 ：Correlations Among the VAR Variablesx1x2x11.00000.6300x20.63001.00002 、变量 y1-y2的相关系数矩阵R22 ：Correlations Among the WITH Variablesy1y2y11.00000.4200y20.42001.

3、00003 、变量 x1-x2与 y1-y2的相关系数矩阵R12 ：Correlations Between the VAR Variables and the WITH Variables专业资料.y1y2x10.24000.0600x2-0.06000.0700变量间高度相关。The SAS System20:05 Thursday, November 18, 20132The CANCORR Procedure4 典型相关分析的一般结果Canonical Correlation AnalysisAdjustedApproximateSquaredCanonicalCanonicalSta

4、ndardCanonicalCorrelationCorrelationErrorCorrelation典型相关系数k校正的典型相关系数近似的标准误典型相关系数平方10.3971120.3969100.0084230.15769820.072889.0.0099470.0053135 、检验各对典型变量是否显著相关专业资料Eigenvalues of Inv(E)*H= CanRsq/(1-CanRsq).Test of H0: The canonical correlations in thecurrent row and all that follow are zeroLikelihood

5、 ApproximateEigenvalue Difference Proportion CumulativeRatioF Value Num DF DenDF Pr F各对相关系相邻两特特征值占特征值占方差似然比kFk 值d1kd2kpk数特征值征值之差方差比例比例累计值10.18720.18190.97230.97230.83782737462.33419992.000120.00530.02771.00000.9946871253.4019997 FWilks Lambda0.83782737462.33419992.0001Pillais Trace0.16301046443.5641

6、9994.0001Hotelling-Lawley Trace0.19256330481.20411994.0001Roys Greatest Root08329997 R11=1 0.63;0.63 1;专业资料. 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(R22); p1=inv(v1*sqrt(d1)*v1); p2=inv(v2*sqrt(d2)*v2); T1=p1*R12*inv(R22)*R21*p1;

7、T2=p2*R21*inv(R11)*R12*p2;结果：专业资料.有上求出的结果可以得到：典型相关系数为： r1=0.0729r2=0.3971典型变量： U 10.3180x10.7687 x2 ， V11.1019 x10.4564x2U 21.2478 x11.0330x2 ， V20.0071x11.0030x2（ 2 ）检验各对典型变量的显著相关程序如下：专业资料. 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).

8、*log(Ak); pk=1-chi2cdf(Tk,d1k)结果：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。4.9SAS 实现dataexamp4_9;inputx1-x2 y1-y2;cards ;1191 155 179 145专业资料.2 195 149 201 1523 181 148 185 1494 183 153 188 1495 176 144 171 1426 208 157 192 1527 189 150 190 1498 197 159 189 1529 188 152 197 15910 1

9、92 150 187 15111179 15814812 183 147 174 14713 174 150 185 15214 190 159 195 15715 188 151 187 15816 163 137 161 13017 195 155 183 15818 153 173 14819 181 145 182 14620 175 140 165 13721 192 154 185 15222 174 143 178 14723 176 176 143专业资料.24 197 167 200 15825 190 163 187 150;run;proc cancorr data =e

10、xamp4_9 corr ;varx1-x2;withy1-y2;run;由 SAS proc cancorr过程求得 ( X 1, X 2, Y1,Y2 )TR11R12样本相关系数矩阵 RR22R21The SAS System20:20 Thursday, November 18, 20131The CANCORR ProcedureCorrelations Among the Original Variables1 、变量 x1-x2 的相关系数矩阵R11 ：Correlations Among the VAR Variablesx1x2x11.0000-0.2094x2-0.2094

11、1.00002 、变量 y1-y2 的相关系数矩阵R22 ：Correlations Among the WITH Variablesy1y2y11.00000.6932y20.69321.00003 、变量 x1-x2 与 y1-y2 的相关系数矩阵R12 ：Correlations Between the VAR Variables and the WITH Variablesy1y2专业资料.x1-0.0108-0.2318x20.73460.7108变量间高度相关。The SAS System14:21 Saturday, October 30, 20124The CANCORR Pr

12、ocedure4 典型相关分析的一般结果Canonical Correlation AnalysisAdjustedApproximateSquaredCanonicalCanonicalStandardCanonicalCorrelationCorrelationErrorCorrelation典型相关系数k校正的典型相关系数近似的标准误典型相关系数平方10.7874780.7723830.0775430.62012120.292947.0.1866070.0858185 、检验各对典型变量是否显著相关Test of H0: The canonical correlations in the

13、Eigenvalues of Inv(E)*Hcurrent row and all that follow are zero= CanRsq/(1-CanRsq)Likelihood ApproximateEigenvalue Difference Proportion CumulativeRatioF Value Num DF Den DFPr F各对相关系相邻两特特征值占特征值占方差似然比kFk 值d1kd 2kpk数特征值征值之差方差比例比例累计值11.63241.53850.94560.9456 0.347278677.324420.000120.09390.05441.0000 0

14、.914181972.071220.1648第一对典型变量贡献率94.56% 。充分反映了两组变量的相互关系。检验假设 H 0(k) :k0d检验统计量Fkd2 k 11/ t H( k)真k0 F (d1k , d2 k ) ， d1k , d2k 为第一、 第二自由度 由检验1 / k1kk专业资料.结果可知，p10.05,p20.05 ，故两对典型变量显著相关取两对进行分析即可另外，从对典型变量(U k ,Vk ) 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 wilks Lambda等四种方法对典型相关系数为零的假设检验。6

15、、求出典型变量及典型相关系数，并解释典型变量的系数和典型结构Multivariate Statistics and F ApproximationsS=2M=-0.5N=9.5StatisticValueF ValueNum DFDen DFPr FWilks Lambda0.347278677.324420.0001Pillais Trace0.705938886.004440.0006Hotelling-Lawley Trace1.726290238.94424.1980.0001Roys Greatest Root1.6324161017.96222 a=data;n,m=size(a)

16、;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 =0.0675-1.02041.0120-0.1476B =专业资料.0.6231-1.23960.46161.3083r =0.78750.2929U =0.43731.58390.86111.3848-0.58101.4579-0.36451.2890-1.08101.25622.24540.63360.28500.78231.12350.52270.19970.52010.62350.3210专业资料.-0.7150

17、0.3789-0.29110.1798-1.21490.17720.4529-0.20340.2547-0.3118-2.3277-0.07240.9987-0.69490.0749-0.6975-0.4343-0.7605-1.0471-0.80840.7244-1.2042-1.1324-1.0706-0.9159-1.23951.2702-1.69570.5538-1.7285V =0.1054-1.28300.60982.5925-0.21030.6757专业资料.0.35010.2260-1.1920-0.47610.87210.07470.18860.99100.9031-0.65250.67941.56690.05060.60010.6807-0.8753-0.8006-0.5895-0.04130.33951.17900.12940.13510.4319-2.2433-0.60230.2893-0.7618