實(shí)驗(yàn)報(bào)告材料9典型相關(guān)分析報(bào)告

實(shí)用實(shí)驗(yàn)九 典型相關(guān)分析實(shí)驗(yàn)?zāi)康暮鸵竽芾迷紨?shù)據(jù)與相關(guān)矩陣、協(xié)主差矩陣作相關(guān)分析 ,能根據(jù)SAS輸出結(jié)果選出滿足要求的幾個(gè)典型變量．實(shí)驗(yàn)要求:編寫程序，結(jié)果分析．實(shí)驗(yàn)內(nèi)容：4.8 SAS 實(shí)現(xiàn)dataexamp4_8(type=corr) ;input _name_$x1-x2y1-y2;_type_=’corr’;cards;x11.000.630.240.06x20.631.00-0.060.07y10.24-0.061.000.42y20.060.070.421.00;run;proc cancorr data=examp4_8corr;varx1-x2;with y1-y2;run;TheSASSystem 20:05Thursday,November18,2013 1TheCANCORRProcedureCorrelationsAmongtheOriginalVariables1、變量x1-x2的相關(guān)系數(shù)矩陣 R11：CorrelationsAmongtheVARVariablesx1 x2x11.00000.6300x20.63001.00002、變量y1-y2的相關(guān)系數(shù)矩陣R22：CorrelationsAmongtheWITHVariables文檔實(shí)用y1 y2y1 1.0000 0.4200y2 0.4200 1.00003、變量x1-x2與y1-y2的相關(guān)系數(shù)矩陣 R12：CorrelationsBetweentheVARVariablesandtheWITHVariablesy1y2x10.24000.0600x2-0.06000.0700變量間高度相關(guān)。TheSASSystem20:05Thursday,November18,20132TheCANCORRProcedure典型相關(guān)分析的一般結(jié)果CanonicalCorrelationAnalysisAdjustedApproximateSquaredCanonicalCanonicalStandardCanonicalCorrelationCorrelationErrorCorrelation典型相關(guān)系數(shù)k校正的典型相關(guān)系數(shù)近似的標(biāo)準(zhǔn)誤典型相關(guān)系數(shù)平方10.3971120.3969100.0084230.15769820.072889.0.0099470.0053135、檢驗(yàn)各對典型變量是否顯著相關(guān)TestofH0:ThecanonicalcorrelationsintheEigenvaluesofInv(E)*Hcurrentrowandallthatfollowarezero=CanRsq/(1-CanRsq)LikelihoodApproximateEigenvalueDifferenceProportionCumulativeRatioFValueNumDFDenDFPr>F各對相關(guān)系相鄰兩特特征值占特征值占方差似然比kFk值d1kd2kpk數(shù)特征值征值之差方差比例比例累計(jì)值10.18720.18190.97230.97230.83782737462.33419992<.00012 0.0053 0.0277 1.0000 0.99468712 53.40 1 9997文檔實(shí)用<.0001第一對典型變量貢獻(xiàn)率 97.23%。充分反映了兩組變量的相互關(guān)系。檢驗(yàn)假設(shè)H0(k):k0d2k11/tH0(k)真Fkk~F(d1k,d2k)d1k1/kd1k,d2k檢驗(yàn)統(tǒng)計(jì)量k，為第一、第二自由度．由檢驗(yàn)結(jié)果可知，p10.05,p20.05，．故兩對典型變量顯著相關(guān)．取兩對進(jìn)行分析即可．另外，從對典型變量(Uk,Vk)進(jìn)行分析求得特征值在方差占比例的累計(jì)值（貢獻(xiàn)率）為0.9947也可看出，兩對變量即可。以下輸出用 wilks’Lambda等四種方法對典型相關(guān)系數(shù)為零的假設(shè)檢驗(yàn)6、求出典型變量及典型相關(guān)系數(shù)，并解釋典型變量的系數(shù)和典型結(jié)構(gòu)MultivariateStatisticsandFApproximationsS=2 M=-0.5 N=4997StatisticValueFValueNumDFDenDFPr>FWilks'Lambda0.83782737462.33419992<.0001Pillai'sTrace0.16301046443.56419994<.0001Hotelling-LawleyTrace0.19256330481.20411994<.0001Roy'sGreatestRoot08329997<.0001NOTE:FStatisticforRoy'sGreatestRootisanupperbound.NOTE:FStatisticforWilks'Lambdaisexact.TheSASSystem 20:05Thursday,November18,2013 3TheCANCORRProcedureCanonicalCorrelationAnalysisRawCanonicalCoefficientsfortheVARVariables第一組變量x1-x3的典型變量的系數(shù)（原始變量未標(biāo)準(zhǔn)化）第一典型變量?第二典型變量?U1U2V1 V2x11.2477984840.3179603133x2-1.0330394770.7687192318文檔實(shí)用RawCanonicalCoefficientsfortheWITHVariables第二組變量y1-y3的典型變量的系數(shù)（原始變量為標(biāo)準(zhǔn)化）?第一典型變量 V? 第二典型變量 V21W1 W2y1 1.1018762969 -0.007089979y2 -0.456353717 1.0029570909數(shù)據(jù)未標(biāo)準(zhǔn)化結(jié)果，即利用協(xié)方差矩陣分析的結(jié)果。U1=1.2478x1-1.033x2V1=1.1019y10.4564y2TheSASSystem20:05Thursday,November18,20134TheCANCORRProcedureCanonicalCorrelationAnalysis第一組變量 x1-x2的典型變量的系數(shù)（原始變量標(biāo)準(zhǔn)化后）StandardizedCanonicalCoefficientsfortheVARVariables第一典型變量*第二典型變量*U1U2V1 V2x11.24780.3180x2-1.03300.7687第二組變量 y1-y2的典型變量的系數(shù)（原始變量標(biāo)準(zhǔn)化后）StandardizedCanonicalCoefficientsfortheWITHVariables第一典型變量V1* 第一典型變量 V2*W1 W2y11.1019-0.0071y2-0.45641.0030?*11給出AR11R12R22R21的三個(gè)特征值?20.157698,ρ?20.005313ρ12第一對典型變量?***U11.2478x1-1.0330x2主要閱讀速度，閱讀理解力的影響。V?1*=1.1019y1*0.4564y2*主要計(jì)算速度，計(jì)算正確程度影響。第一對典型變量主要表現(xiàn)閱讀和計(jì)算的相關(guān)性。第一對典型相關(guān)系數(shù)為 ρ1 0.3971第二對典型變量及典型相關(guān)系數(shù)文檔實(shí)用?*=0.318*0.7687x*U20x12V?2*=（0.0071）y1*-1.0030y2*ρ?2 0.07289輸出原變量和典型變量間的相關(guān)系數(shù)TheSASSystem 20:05Thursday,November18,2013 5TheCANCORRProcedureCanonicalStructure第一組變量x1-x2和典型變量U1*,U2*的相關(guān)系數(shù)CorrelationsBetweentheVARVariablesandTheirCanonicalVariablesV1 V2x10.59700.8023x2-0.24690.9690第二組變量y1-y2和典型變量V*,V*的相關(guān)系數(shù)12CorrelationsBetweentheWITHVariablesandTheirCanonicalVariablesW1W2y10.91020.4142y20.00641.0000第一組變量x1-x2和第二組典型變量V1*,V2*的相關(guān)系數(shù)CorrelationsBetweentheVARVariablesandtheCanonicalVariablesoftheWITHVariablesW1W2x10.23710.0585x2-0.09810.0706第二組變量y1-y2和第一組典型變量U1*,U2*的相關(guān)系數(shù)CorrelationsBetweentheWITHVariablesandtheCanonicalVariablesoftheVARVariablesV1V2y10.36150.0302y20.00260.0729由數(shù)據(jù)分析得：原變量和第一對變量相關(guān)程度高，第二組提取的信息很少，與典型對系數(shù)一文檔實(shí)用致。4.8 Matlab實(shí)現(xiàn)1）可以用matlab求出各樣本典型相關(guān)變量和樣本的典型相關(guān)系數(shù)程序如下：R11=[10.63;0.631];R12=[0.240.06;-0.060.07];R21=[0.24-0.06;0.060.07];R22=[10.42;0.421];[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;T2=p2*R21*inv(R11)*R12*p2;結(jié)果：文檔實(shí)用有上求出的結(jié)果可以得到：典型相關(guān)系數(shù)為： r1=0.0729 r2=0.3971典型變量：U10.3180x10.7687x2，V11.1019x10.4564x2U21.2478x11.0330x2，V20.0071x11.0030x22）檢驗(yàn)各對典型變量的顯著相關(guān)程序如下：p=2;q=2;n=140;k=1:2;d1k=(p-k+1).*(q-k+1);d=[0.07290.3971];D=1-d.^2;Ak=[D(1)*D(2),D(2)];Tk=-[n-0.5*(p+q+3)].*log(Ak);pk=1-chi2cdf(Tk,d1k)結(jié)果：文檔實(shí)用可以看出，第一、第二典型變量都是顯著性相關(guān)的。即一名學(xué)生的閱讀速度和閱讀理解能力越強(qiáng)，他的技術(shù)速度和計(jì)算正確程度就越好。4.9SAS實(shí)現(xiàn)dataexamp4_9;input x1-x2y1-y2;cards;191155179145195149201152181148185149183153188149176144171142208157192152189150190149197159189152188152197159101921501871511117915818614812183147174147131741501851521419015919515715188151187158163137161130195155183158186153173148181145182146175140165137192154185152174143178147176139176143197167200158190163187150;run;proc cancorr data=examp4_9corr;varx1-x2;文檔實(shí)用with y1-y2;run;由SASproccancorr過程求得(X1,X2,Y1,Y2)T樣本相關(guān)系數(shù)矩陣RR11R12R21R22TheSASSystem 20:20Thursday,November18,2013 1TheCANCORRProcedureCorrelationsAmongtheOriginalVariables1、變量x1-x2的相關(guān)系數(shù)矩陣 R11：CorrelationsAmongtheVARVariablesx1 x2x11.0000-0.2094x2-0.20941.00002、變量y1-y2的相關(guān)系數(shù)矩陣R22：CorrelationsAmongtheWITHVariablesy1y2y11.00000.6932y20.69321.00003、變量x1-x2與y1-y2的相關(guān)系數(shù)矩陣R12：CorrelationsBetweentheVARVariablesandtheWITHVariablesy1y2x1-0.0108-0.2318x20.73460.7108變量間高度相關(guān)。TheSASSystem 14:21Saturday,October30,2012 4TheCANCORRProcedure典型相關(guān)分析的一般結(jié)果CanonicalCorrelationAnalysisAdjusted Approximate SquaredCanonical Canonical Standard CanonicalCorrelation Correlation Error Correlation文檔實(shí)用典型相關(guān)系數(shù)k校正的典型相關(guān)系數(shù)近似的標(biāo)準(zhǔn)誤典型相關(guān)系數(shù)平方10.7874780.7723830.0775430.62012120.292947.0.1866070.0858185、檢驗(yàn)各對典型變量是否顯著相關(guān)TestofH0:ThecanonicalcorrelationsintheEigenvaluesofInv(E)*Hcurrentrowandallthatfollowarezero=CanRsq/(1-CanRsq)LikelihoodApproximateEigenvalueDifferenceProportionCumulativeRatioFValueNumDFDenDFPr>F各對相關(guān)系相鄰兩特特征值占特征值占方差似然比kFk值d1kd2kpk數(shù)特征值征值之差方差比例比例累計(jì)值11.63241.53850.94560.94560.347278677.324420.000120.09390.05441.00000.914181972.071220.1648第一對典型變量貢獻(xiàn)率94.56%。充分反映了兩組變量的相互關(guān)系。檢驗(yàn)假設(shè)H0(k):k0d檢驗(yàn)統(tǒng)計(jì)量 Fkd

2k11/tH0(k)真k~F(d1k,d2k)，d1k,d2k為第一、第二自由度．由檢驗(yàn)1/k1kk結(jié)果可知， p1 0.05, p2 0.05，．故兩對典型變量顯著相關(guān)．取兩對進(jìn)行分析即可．另外，從對典型變量 (Uk,Vk)進(jìn)行分析求得特征值在方差占比例的累計(jì)值（貢獻(xiàn)率）為0.9141也可看出，只需要兩對變量即可。以下輸出用wilks’Lambda等四種方法對典型相關(guān)系數(shù)為零的假設(shè)檢驗(yàn)。6、求出典型變量及典型相關(guān)系數(shù)，并解釋典型變量的系數(shù)和典型結(jié)構(gòu)MultivariateStatisticsandFApproximationsS=2 M=-0.5 N=9.5Statistic Value FValue NumDF DenDF Pr>FWilks'Lambda0.347278677.324420.0001Pillai'sTrace0.705938886.004440.0006Hotelling-LawleyTrace1.726290238.94424.1980.0001Roy'sGreatestRoot1.6324161017.96222<.0001NOTE:FStatisticforRoy'sGreatestRootisanupperbound.NOTE:FStatisticforWilks'Lambdaisexact.文檔實(shí)用TheCANCORRProcedureCanonicalCorrelationAnalysisRawCanonicalCoefficientsfortheVARVariables第一組變量x1-x3的典型變量的系數(shù)（原始變量未標(biāo)準(zhǔn)化）第一典型變量?第二典型變量?U1U2V1V2x10.00917257220.1386496154x20.10366421780.0151230041第二組變量y1-y3的典型變量的系數(shù)（原始變量為標(biāo)準(zhǔn)化）RawCanonicalCoefficientsfortheWITHVariables第一典型變量??第二典型變量V2V1W1 W2y10.08450520960.168128993y20.0459765801-0.130308033數(shù)據(jù)未標(biāo)準(zhǔn)化結(jié)果，即利用協(xié)方差矩陣分析的結(jié)果。U10.0092x10.1037x2V10.0845y10.0459y2TheSASSystem20:20Thursday,November18,20134TheCANCORRProcedureCanonicalCorrelationAnalysis第一組變量x1-x3的典型變量的系數(shù)（原始變量標(biāo)準(zhǔn)化后）StandardizedCanonicalCoefficientsfortheVARVariables第一典型變量*第二典型變量*U1U2V1 V2x10.06751.0204x21.01200.1476第二組變量y1-y3的典型變量的系數(shù)（原始變量標(biāo)準(zhǔn)化后）StandardizedCanonicalCoefficientsfortheWITHVariables第一典型變量V1* 第一典型變量 V2*文檔實(shí)用W1 W2y10.62311.2396y20.4616-1.3083?*11的三個(gè)特征值給出AR11R12R22R21?20.620121,ρ?20.085818ρ12第一對典型變量?***U10.0675x11.0120x2主要成年長子的頭長、頭寬加權(quán)V?*0.6231y*0.4616y*主要次子頭寬影響112第一對典型變量主要表現(xiàn)頭寬和頭長的相關(guān)性。第一對典型相關(guān)系數(shù)為 ρ1 0.787478第二對典型變量及典型相關(guān)系數(shù)?*1.*0.1476x*U20204x12V?*1.2396y*1.3083y*212ρ?2 0.292947輸出原變量和典型變量間的相關(guān)系數(shù)TheCANCORRProcedureCanonicalStructure第一組變量x1-x3和典型變量U1*,U2*的相關(guān)系數(shù)CorrelationsBetweentheVARVariablesandTheirCanonicalVariablesV1V2x1-0.14440.9895x20.9978-0.0660第二組變量y1-y3和典型變量V1*,V2*的相關(guān)系數(shù)CorrelationsBetweentheWITHVariablesandTheirCanonicalVariablesW1 W2y10.94300.3327y20.8935-0.4491第一組變量x1-x3和第二組典型變量V1*,V2*的相關(guān)系數(shù)CorrelationsBetweentheVARVariablesandtheCanonicalVariablesoftheWITHVariablesW1 W2文檔實(shí)用x1 -0.1137 0.2899x2 0.7858 -0.0193第二組變量y1-y3和第一組典型變量 U1*,U*2的相關(guān)系數(shù)CorrelationsBetweentheWITHVariablesandtheCanonicalVariablesoftheVARVariablesV1 V2y10.74260.0975y20.7036-0.1316由數(shù)據(jù)分析得：原變量和第一對變量相關(guān)程度高，第二組提取的信息很少，與典型對系數(shù)一致。4.9MATLAB實(shí)現(xiàn)建立data.txt ，并導(dǎo)入數(shù)據(jù)。a=[data];[n,m]=size(a);b=a./(ones(n,1)*std(a));R=cov(b);X=b(:,1:2);Y=b(:,3:4)