实验报告材料9典型相关分析报告

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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：4.8 SAS实现data examp4_8(type=corr);in put _n ame_ $ x1-x2 y1-y2;_type_= corr;cards;x1 1.000.63 0.24 0.06x2 0.631.00 -0.06 0.07y1 0.24 -0.061.00 0.42y2 0.060.07 0.42 1.00Jrun ;proc cancorr data=examp4_8 corr;var x1-x2;w

2、ith y1-y2;run ;The SAS System 20:05 Thursday, November 18, 20131The CANCORR ProcedureCorrelati ons Among the Origi nal Variables1、变量x1-x2的相关系数矩阵R11 :Correlations Among the V AR Variablesx1x2x1x21.00000.63000.63001.00002、变量y1-y2的相关系数矩阵Correlatio ns Among the WITH Variablesy1y2y11.00000.4200y20.42001.

3、00003、变量x1-x2与y1-y2的相关系数矩阵 R12 :Correlatio ns Betwee n the VAR Variables and the WITH Variablesy1y20.06000.0700x10.2400x2-0.0600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Canoni cal Correlati on An alysisAdjusted ApproximateSquaredCanon icalCanon icalSt

4、an dardCanonicalError Correlati onCorrelati on Correlati on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0.0084230.0099470.1576980.0053131 0.3971120.3969102 0.072889.5、检验各对典型变量是否显著相关Test of H0: The canonical correlations in theEige nvalues of In v(E)*Hcurre nt row and all that follow are zero=Ca nRsq/(1-Ca nRsq)L

5、ikelihood ApproximateEige nvalue Differe nee 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k Fk值d1kd 2kpk数特征值征值之差方差比例比例累计值10.18720.18190.97230.97230.83782737462.334 19992 .000120.00530.02771.00000.9946871253.4019997 FWilks Lambda0.83782737462.33419992.0001Pillais Trace

6、0.16301046443.56419994.0001Hotell in g-Lawley Trace0.19256330481.20411994.0001Roys Greatest Root0.18722205935.8329997 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(R22); p1=i nv(v1*sqrt(d1)*v1); p2=i nv(v2*sqrt(d2)*v2); T1= p1*R12

7、*i nv(R22)*R21*p1; T2=p2*R21*i nv(R11)*R12*p2;结果： p% da i J T Dva 二-0 33080.5566da =0” 00530a 0. 1&77 vbj dbj=erg(T2)vb -0. 97800. 2087-0* 2087O.9780 db =Q. 1577000.0033 Al=p l*vaAl =-0.3180 -L 2478-0.75?1.0330 Bl=p2*vbBl =L 1019-0.0071-Q.45341.0030 r=sqrt (suraCda1)0,07290- 3&7有上求出的结果可以得到：典型相关系数为：r

8、1=0.0729r2=0.39710.4564X21.0030 x2典型变量： Ui0.3180xi 0.7687X2，V1.1019xiU21.2478x1 1.0330x2，V20.0071x1(2 )检验各对典型变量的显著相关 程序如下： p=2； q=2； n=140; k=1:2; d1k=(p-k+1).*(q-k+1); d=0.0729 0.3971; D=1-d.A2; Ak=D(1)*D(2),D(2); Tk=- n-0.5*(p+q+3).*log(Ak); pk=1-chi2cdf(Tk,d1k)结果：? pk=l-chi2cdf (Tk.dlk)1. 0t-04 *

9、0. 74480. 0130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;in put x1-x2 y1-y2;cards;1191 155 179 1452149 201 1523181 148 185 1494183 153 188 1495176 144 171 1426208 157 192 1527150 190 14981591529188 15215910192 150 187 15111179 158 14812183 147 174 14713174 15

10、0 185 15214190 159 1571518815118715816137 161 13017155 183 15818153 173 14819181 145 182 14620175 140 165 13721192 154 185 15222174 143 178 14723176 176 14324167 200 15825190 187 150run ;proc cancorr data=examp4_9 corr;var x1-x2;with y1-y2;Rl1R12run ;由SAS proc cancorr过程求得（XX2 ,丫勺，丫2）丁样本相关系数矩阵 RThe S

11、AS 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 Variablesx1x2x11.0000-0.2094x2-0.20941.00002、 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y

12、1-y2的相关系数矩阵R12 :Correlations Between the VAR Variables and the WITH Variablesy1y2x1-0.0108-0.2318x20.73460.7108变量间高度相关。The SAS System14:21 Saturday, October 30, 20124The CANCORR Procedure4 典型相关分析的一般结果Canonical Correlation AnalysisAdjusted ApproximateSquaredCanonical CanonicalStandard CanonicalCorrel

13、ation CorrelationError Correlation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1 0.7874780.7723830.0775430.6201212 0.292947.0.1866070.0858185、检验各对典型变量是否显著相关Test of H0: The canonical correlations in theEigenvalues of lnv(E)*Hcurrent row and all that follow are zero=CanRsq/(1-CanRsq)Likelihood ApproximateEigenvalu

14、e Difference Proportion CumulativeRatioF 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Fk值d1kd2kPk数特征值征值之差方差比例比例累计值11.63241.53850.94560.9456 0.347278677.3242 0.000120.09390.05441.0000 0.914181972.0722 0.1648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。检验统计量Fkd 2k 11/t H0k)真kd1k1/kkF (d1k,d2k)d1k , d2k 为第第二自由度.由检

15、验结果可知，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(Uk,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、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=9.5StatisticValue F Value Num DFDen DF Pr FWilks Lambda0.347278677.324

16、420.0001Pillais Trace0.705938886.004440.0006Hotelling-Lawley Trace1.726290238.94424.0.0001Roys Greatest Root1.6324161017.96222 a=data;n ,m=size(a);b=a./(o nes( n,1)*std(a);R=cov(b);X=b(:,1:2);Y=b(:,3:4);A,B,r,U,V,ststs=ca non corr(X,Y)0.06751.0120-1.0204-0.14760.62310.4616-1.23961.30830.78750.29290.

17、43731.58390.86111.3848-0.58101.4579-0.36451.2890-1.08101.25622.24540.63360.28500.78231.12350.52270.19970.52010.62350.3210-0.71500.3789-0.29110.1798-1.21490.17720.4529-0.20340.2547-0.3118-2.3277-0.07240.9987-0.69490.0749-0.6975-0.4343-0.7605-1.0471-0.80840.7244-1.2042-1.1324-1.0706-0.9159-1.23951.270

18、2-1.69570.5538-1.72850.1054-1.28300.60982.5925-0.21030.67570.35010.2260-1.1920-0.47610.87210.07470.18860.99100.9031-0.65250.67941.56690.05060.60010.6807-0.8753-0.8006-0.5895-0.04130.33951.17900.12940.13510.4319-2.2433-0.60230.2893-0.7618-0.3395-1.7286-0.60180.7892-1.8059-0.58540.2967-0.3331-0.95470.6042-1.38471.01612.0849-0.56411.1492-1.5856ststs =Wilks: 0.3473 0.9142dfl: 4 1df2: 42 22F: 7.3176 2.0652pF: 1.4471e-004 0.1648chisq: 22.7390 1.9841 pChisq: 1.4277e-004 0.1590dfe: 4 1p: 1.4277e-004 0.1590