十項(xiàng)全能運(yùn)動(dòng)員得分相關(guān)矩陣X1X2X3X4X5X6

X7X8X9X10X1X2X3X4X5X6

X7X8X9X101.000.591.000.350.421.000.340.510.381.000.630.490.190.291.000.400.520.360.460.341.000.280.310.730.270.170.321.000.200.360.240.390.230.330.241.000.110.210.440.170.130.180.340.241.00-0.770.09-0.080.180.390.00-0.020.17-0.001.00第一頁(yè)，共七十九頁(yè)。例

為了評(píng)價(jià)即將進(jìn)大學(xué)的高中生的學(xué)習(xí)能力，抽了200名高中生進(jìn)行問(wèn)卷調(diào)查，共50個(gè)問(wèn)題。素有這些問(wèn)題可以歸結(jié)為閱讀理解、數(shù)學(xué)水平和藝術(shù)素養(yǎng)三個(gè)方面。例

公司老板對(duì)48名應(yīng)聘者進(jìn)行面試，并給出他們?cè)?5個(gè)方面的得分，這15個(gè)方面是：申請(qǐng)書的形式(x1)、外貌(x2)、專業(yè)能力(x3)、討人喜歡(x4)、自信心(x5)、精明(x6)、誠(chéng)實(shí)(x7)、推銷能力(x8)、經(jīng)驗(yàn)(x9)、積極性(x10)、抱負(fù)(x11)、理解能力(x12)、潛力(x13)、交際能力(x14)、適應(yīng)性(x15)。通過(guò)因子分析，這15個(gè)方面可歸結(jié)為應(yīng)聘者的外露能力、討人喜歡的程度、經(jīng)驗(yàn)、專業(yè)能力和外貌。第二頁(yè)，共七十九頁(yè)?！?.2因子模型一、數(shù)學(xué)模型第三頁(yè)，共七十九頁(yè)。

假設(shè)條件第四頁(yè)，共七十九頁(yè)。二、因子模型的性質(zhì)第五頁(yè)，共七十九頁(yè)。例8.2.1設(shè)隨機(jī)向量(x1,x2,x3,x4)’的協(xié)方差矩陣為第六頁(yè)，共七十九頁(yè)。2、模型不受單位影響第七頁(yè)，共七十九頁(yè)。3、因子載荷不唯一（相差一個(gè)正交變換）注：在實(shí)際中，利用因子載荷陣的不唯一性對(duì)因子進(jìn)行旋轉(zhuǎn)，使得新的因子有更好的實(shí)際意義。第八頁(yè)，共七十九頁(yè)。三、因子載荷矩陣的統(tǒng)計(jì)意義2、A的行元素平方和——公因子對(duì)原始變量的方差貢獻(xiàn)1、A的元素aij——原始變量xi與公因子fj之間的協(xié)方差函數(shù)第九頁(yè)，共七十九頁(yè)。3、A的列平方和——公共因子fj對(duì)x的貢獻(xiàn)率第十頁(yè)，共七十九頁(yè)。Principalcomponents:主成分法Unweightedleastsquare:不加權(quán)最小平方法Generalizedleastsquares:普通最小平方法Maximumlikelihood:最大似然法Principalaxisfactoring:主因子法Alphafactoring:α因子提取法Imagefactoring:映象因子提取法常用確定q的方法是按特征根由大至小的次序抽取，直到與接近為止?！?.3參數(shù)估計(jì)第十一頁(yè)，共七十九頁(yè)。一、主成分法：

第十二頁(yè)，共七十九頁(yè)。例

在例中，分別取m=1,m=2,用主成分法估計(jì)的因子載荷和共性方差如下表：

變量m=1m=2ai1(f1)

ai1f1ai2f2

0.8170.8670.9150.9490.9590.9380.9440.880

0.6680.7520.8380.9000.9200.8790.8910.774

0.8170.5310.8670.4320.9150.2330.9490.0120.959-0.1310.938-0.2920.944-0.2870.880-0.411

0.9500.9390.8920.9000.9380.9650.9730.943所解釋的總方差的累計(jì)比例0.828

0.8280.938第十三頁(yè)，共七十九頁(yè)。相應(yīng)于m=2的解的殘差矩陣為：

第十四頁(yè)，共七十九頁(yè)。dataexamp733(type=corr);inputx1-x8;cards;1.000.......0.9231.000......0.8410.8511.000.....0.7560.8070.8701.000....0.7000.7750.8350.9181.000...0.6190.6950.7790.8640.9281.000..0.6330.6970.7870.8690.9350.9751.000.0.5200.5960.7050.8060.8660.9320.9431.000;proc

factordata=examp733(type=corr);varx1-x8;proc

factordata=examp733(type=corr)n=2;varx1-x8;run;第十五頁(yè)，共七十九頁(yè)。proc

iml;x={1.000

0.923

0.841

0.756

0.700

0.619

0.633

0.520,

0.923

1.000

0.851

0.807

0.775

0.695

0.697

0.596,

0.841

0.851

1.000

0.870

0.835

0.779

0.787

0.705,

0.756

0.807

0.870

1.000

0.918

0.864

0.869

0.806,

0.700

0.775

0.835

0.918

1.000

0.928

0.935

0.866,

0.619

0.695

0.779

0.864

0.928

1.000

0.975

0.932,

0.633

0.697

0.787

0.869

0.935

0.975

1.000

0.943,

0.520

0.596

0.705

0.806

0.866

0.932

0.943

1.000};C={0.81717

0.53110,0.86729

0.43271,0.91517

0.23251,

0.94874

0.01185,0.95938-0.13148,0.93766-0.29268,

0.94397-0.28708,0.87981-0.41117};a={0.877

0.888

0.845

0.884

0.927

0.995

0.967

0.905};y=x-i(8)+diag(a);b=eigval(y);e={0.050

0.061

0.108

0.100

0.062

0.035

0.027

0.057};D=x-c*t(c)-diag(e);printybd;第十六頁(yè)，共七十九頁(yè)。1、給出共同度hi2的初步估計(jì)值hi*2

以第i個(gè)變量xi*與其它所有變量x1*,x2*,…,xi1*,xi+1*,…,xp*回歸的復(fù)相關(guān)系數(shù)的平方作為初始估計(jì)值2、求出約化相關(guān)陣計(jì)算Di*=1-hi*2,再計(jì)算出R*=R-D*3、求出特征根和特征向量由方程︱R*-λI︱=0求出，并利用特征根、特征向量求出因子載荷陣A14、求出D的估計(jì)，用估計(jì)值代替第二步的D*D的估計(jì)：D*（1）=R-A1A1′5、繼續(xù)第三步，直到A，

D的估計(jì)達(dá)到穩(wěn)定為止二、主因子法第十七頁(yè)，共七十九頁(yè)。例8.3.2在例中取m=2,選用xi與其他7個(gè)變量的復(fù)相關(guān)系數(shù)平方作為的初始估計(jì)值。計(jì)算得:第十八頁(yè)，共七十九頁(yè)。約相關(guān)矩陣為第十九頁(yè)，共七十九頁(yè)。ai1f1ai2f2

0.8070.4960.8580.4120.8900.2160.9390.0240.956-0.1140.938-0.2820.946-0.2810.874-0.378

0.8970.9060.8560.8810.9260.9600.9740.907所解釋的總方差的累計(jì)比例0.8160.914第二十頁(yè)，共七十九頁(yè)。相應(yīng)于m=2的解的殘差矩陣為：

第二十一頁(yè)，共七十九頁(yè)。dataexamp733(type=corr);inputx1-x8;cards;1.000.......0.9231.000......0.8410.8511.000.....0.7560.8070.8701.000....0.7000.7750.8350.9181.000...0.6190.6950.7790.8640.9281.000..0.6330.6970.7870.8690.9350.9751.000.0.5200.5960.7050.8060.8660.9320.9431.000;proc

factorm=prinitpriors=smc;varx1-x8;proc

factorm=prinitpriors=smcn=2;varx1-x8;run;第二十二頁(yè)，共七十九頁(yè)。

proc

factor

data=sasuser.exec65n=2method=prinitheywood;varx1-x8;run;proc

iml;x={1.00000

0.92264

0.84115

0.75603

0.70024

0.61946

0.63254

0.51995,0.92264

1.00000

0.85073

0.80663

0.77495

0.69538

0.69654

0.59618,0.84115

0.85073

1.00000

0.87017

0.83527

0.77861

0.78720

0.70499,

0.75603

0.80663

0.87017

1.00000

0.91804

0.86359

0.86905

0.80648,0.70024

0.77495

0.83527

0.91804

1.00000

0.92811

0.93470

0.86555,0.61946

0.69538

0.77861

0.86359

0.92811

1.00000

0.97464

0.93219,

0.63254

0.69654

0.78720

0.86905

0.93470

0.97464

1.00000

0.94318,0.51995

0.59618

0.70499

0.80648

0.86555

0.93219

0.94318

1.00000};y={0.81202

0.51251,0.86094

0.41594,0.90061

0.21099,0.93708

0.01791,0.95452-0.11798,

0.93843-0.28554,0.94696-0.28620,0.87304

-0.37739};z={1,1,1,1,1,1,1,1}-{0.92204479,0.91422910,0.85561058,0.87844540,0.92502009,0.96217654,0.97865293,0.90462155};a=diag(z);b=x-y*t(y)-a;printab;run;第二十三頁(yè)，共七十九頁(yè)。三、極大似然法用迭代法求上述方程組的解。第二十四頁(yè)，共七十九頁(yè)。第二十五頁(yè)，共七十九頁(yè)。第二十六頁(yè)，共七十九頁(yè)。第二十七頁(yè)，共七十九頁(yè)。第二十八頁(yè)，共七十九頁(yè)。第二十九頁(yè)，共七十九頁(yè)。第三十頁(yè)，共七十九頁(yè)。

載荷矩陣A是不唯一的，有人建議添加一個(gè)計(jì)算上方便的的唯一性條件：第三十一頁(yè)，共七十九頁(yè)。第三十二頁(yè)，共七十九頁(yè)。第三十三頁(yè)，共七十九頁(yè)。第三十四頁(yè)，共七十九頁(yè)。第三十五頁(yè)，共七十九頁(yè)。ai1f1ai2f2

0.731-0.6200.792-0.5450.855-0.3430.916-0.1610.958-0.0260.9720.1440.981-0.1430.923-0.249

0.9190.9240.8490.8650.9180.9660.9820.914所解釋的總方差的累計(jì)比例0.8010.917例8.3.3在例中，取m=2，同,極大似然法的計(jì)算結(jié)果如下表：的初始估計(jì)值與例第三十六頁(yè)，共七十九頁(yè)。極大似然解的殘差矩陣為：

第三十七頁(yè)，共七十九頁(yè)。dataexamp733(type=corr);inputx1-x8;cards;1.000.......0.9231.000......0.8410.8511.000.....0.7560.8070.8701.000....0.7000.7750.8350.9181.000...0.6190.6950.7790.8640.9281.000..0.6330.6970.7870.8690.9350.9751.000.0.5200.5960.7050.8060.8660.9320.9431.000;proc

factorm=ml;varx1-x8;proc

factorm=mln=2;varx1-x8;run;第三十八頁(yè)，共七十九頁(yè)。TheFACTORProcedureInitialFactorMethod:MaximumLikelihoodPriorCommunalityEstimates:SMCx1x2x3x4

0.877839350.888722470.844686300.88357282x5x6x7x80.927120960.955454730.967228140.90408487第三十九頁(yè)，共七十九頁(yè)。PreliminaryEigenvalues:Total=101.310432Average=12.6638039EigenvalueDifferenceProportionCumulative

193.788831185.53188880.92580.9258

28.25694237.70562430.08151.0073

30.55131810.49621880.00541.0127

40.05509930.21273650.00051.0132

5-0.15763720.1387816-0.00161.0117

6-0.29641880.0631990-0.00291.0088

7-0.35961780.1684675-0.00351.0052

8-0.5280854-0.00521.00002factorswillberetainedbythePROPORTIONcriterion.第四十頁(yè)，共七十九頁(yè)。

IterationCriterionRidgeChangeCommunalities

10.33712300.00000.03300.910880.919410.854320.872500.921540.96588

0.981680.91119

20.33200700.00000.00650.917410.923640.849470.866060.919070.96667

0.982090.91339

30.33178100.00000.00130.918530.924910.848480.864860.918460.96664

0.982260.91341

40.33177200.00000.00030.918850.925070.848230.864600.918360.96665

0.982270.91345Convergencecriterionsatisfied.第四十一頁(yè)，共七十九頁(yè)。SignificanceTestsBasedon10000ObservationsPr>TestDFChi-SquareChiSqH0:Nocommonfactors28142472.086<.0001HA:AtleastonecommonfactorH0:2Factorsaresufficient133315.7842<.0001HA:Morefactorsareneeded第四十二頁(yè)，共七十九頁(yè)。TheFACTORProcedureInitialFactorMethod:MaximumLikelihoodChi-SquarewithoutBartlett'sCorrection3317.3878Akaike'sInformationCriterion3291.3878Schwarz'sBayesianCriterion3197.6534TuckerandLewis'sReliabilityCoefficient0.9501SquaredCanonicalCorrelationsFactor1Factor20.992346680.92414870第四十三頁(yè)，共七十九頁(yè)。EigenvaluesoftheWeightedReducedCorrelationMatrix:Total=141.845985Average=17.7307481EigenvalueDifferenceProportionCumulative

1129.662297117.4786080.91410.9141

212.18368911.5974400.08591.0000

30.5862490.4011620.00411.0041

40.1850870.1759800.00131.0054

50.0091070.0612700.00011.0055

6-0.0521630.239994-0.00041.0051

7-0.2921570.143967-0.00211.0031

8-0.436124-0.00311.0000T129.64951012.18376200.587805900.183956100.00909540-0.0535390-0.2925640-0.4354380第四十四頁(yè)，共七十九頁(yè)。FactorPatternFactor1Factor2x10.73040-0.62079x20.79140-0.54661x30.85454-0.34348x40.91565-0.16171x50.95795-0.02600x60.972630.14371x70.980890.14189x80.922860.24854VarianceExplainedbyEachFactorFactorWeightedUnweightedFactor1129.6622976.40592383Factor212.1836890.93152570第四十五頁(yè)，共七十九頁(yè)。TheFACTORProcedureInitialFactorMethod:MaximumLikelihoodFinalCommunalityEstimatesandVariableWeightsTotalCommunality:Weighted=141.84599Unweighted=7.337450VariableCommunalityWeightx10.9188651412.3222163x20.9250959313.3456046x30.848210716.5890175x40.864559767.3855720x50.9183397412.2487688x60.9666533029.9870945x70.9822744556.4139209x80.9134505211.5537899第四十六頁(yè)，共七十九頁(yè)。proc

iml;x={0.87783935

0.88872247

0.84468630

0.88357282

0.92712096

0.95545473

0.96722814

0.90408487};y={1.000

0.923

0.841

0.756

0.700

0.619

0.633

0.520,0.923

1.000

0.851

0.807

0.775

0.695

0.697

0.596,0.841

0.851

1.000

0.870

0.836

0.779

0.787

0.705,0.756

0.807

0.870

1.000

0.918

0.864

0.869

0.806,0.700

0.775

0.835

0.918

1.000

0.928

0.935

0.866,0.619

0.695

0.779

0.864

0.928

1.000

0.975

0.932,0.633

0.697

0.787

0.869

0.935

0.975

1.000

0.943,0.520

0.596

0.705

0.806

0.866

0.932

0.943

1.000};z=sqrt(inv(i(8)-diag(x)));s=z*y*z;t=eigval(s-i(8));printt;第四十七頁(yè)，共七十九頁(yè)。prociml;h={0.918850.925070.848230.86460

0.91836

0.96665

0.98227

0.91345};r={1.000

0.923

0.841

0.756

0.700

0.619

0.633

0.520,0.923

1.000

0.851

0.807

0.775

0.695

0.697

0.596,0.841

0.851

1.000

0.870

0.836

0.779

0.787

0.705,0.756

0.807

0.870

1.000

0.918

0.864

0.869

0.806,0.700

0.775

0.835

0.918

1.000

0.928

0.935

0.866,0.619

0.695

0.779

0.864

0.928

1.000

0.975

0.932,0.633

0.697

0.787

0.869

0.935

0.975

1.000

0.943,0.520

0.596

0.705

0.806

0.866

0.932

0.943

1.000

};d1=sqrt(inv(i(8)-diag(h)));S=d1*r*d1;t=eigval(s-i(8));t1=eigvec(s-i(8))[,1:5];d=diag(t[1:5,1]);a=inv(d1)*t1*sqrt(d);b1=a[,1:2];b=b1[,##];c=a[##,];d1=1/(j(8,1)-b);printtt1dabcd1;特殊方差的倒數(shù)weight共性方差h2第四十八頁(yè)，共七十九頁(yè)。T

129.649510

12.1837620

0.58780590

0.18395610

0.00909540

-0.0535390

-0.2925640

-0.4354380第四十九頁(yè)，共七十九頁(yè)。

proc

factor

data=sasuser.exec65n=2method=mlheywood;varx1-x8;run;proc

iml;x={1.00000

0.92264

0.84115

0.75603

0.70024

0.61946

0.63254

0.51995,0.92264

1.00000

0.85073

0.80663

0.77495

0.69538

0.69654

0.59618,

0.84115

0.85073

1.00000

0.87017

0.83527

0.77861

0.78720

0.70499,

0.75603

0.80663

0.87017

1.00000

0.91804

0.86359

0.86905

0.80648,0.70024

0.77495

0.83527

0.91804

1.00000

0.92811

0.93470

0.86555,0.61946

0.69538

0.77861

0.86359

0.92811

1.00000

0.97464

0.93219,

0.63254

0.69654

0.78720

0.86905

0.93470

0.97464

1.00000

0.94318,0.51995

0.59618

0.70499

0.80648

0.86555

0.93219

0.94318

1.00000};y={0.731-0.620,0.792-0.545,0.855-0.343,

0.916-0.161,0.958-0.026,0.972

0.144,

0.981

0.143,0.923

0.249};z={1,1,1,1,1,1,1,1}-{0.919,0.924,0.849,0.865,0.918,0.966,

0.982,0.914};a=diag(z);b=x-y*t(y)-a;printab;run;第五十頁(yè)，共七十九頁(yè)?！?.4因子旋轉(zhuǎn)因子旋轉(zhuǎn)的意義：使公因子易于解釋。方法：正交旋轉(zhuǎn)，斜交旋轉(zhuǎn)。實(shí)施：對(duì)載荷矩陣作正交（斜交）變換。正交旋轉(zhuǎn)：第五十一頁(yè)，共七十九頁(yè)。最大方差旋轉(zhuǎn)法：選擇正交矩陣T使得A*的所有m個(gè)列元素平方和的相對(duì)方差之和達(dá)到最大。第五十二頁(yè)，共七十九頁(yè)。m=2時(shí)，設(shè)元因子載荷矩陣為第五十三頁(yè)，共七十九頁(yè)。第五十四頁(yè)，共七十九頁(yè)。第五十五頁(yè)，共七十九頁(yè)。第五十六頁(yè)，共七十九頁(yè)。第五十七頁(yè)，共七十九頁(yè)。變量

f1f2f1f2f1f2

0.2740.9350.3760.8930.5430.7730.7120.6270.8130.5250.9020.3890.9030.3970.9360.2610.2870.9030.3810.8720.5410.7510.6950.6310.7990.5370.8950.3990.9000.4050.9090.2840.2880.9140.3790.8830.5410.7460.6890.6240.7970.5320.8990.3970.9060.4020.9140.281

所解釋的總方差的累計(jì)比例0.5230.9830.5100.9140.5120.917

例8.4.1在例中分別用最大方差旋轉(zhuǎn)法，旋轉(zhuǎn)后的因子載荷矩陣如下表

主成分

主因子

極大似然第五十八頁(yè)，共七十九頁(yè)。dataexamp733(type=corr);inputx1-x8;cards;1.000.......0.9231.000......0.8410.8511.000.....0.7560.8070.8701.000....0.7000.7750.8350.9181.000...0.6190.6950.7790.8640.9281.000..0.6330.6970.7870.8690.9350.9751.000.0.5200.5960.7050.8060.8660.9320.9431.000;proc

factordata=examp733(type=corr)rotate=varimax;varx1-x8;proc

factordata=examp733(type=corr)n=2rotate=varimax;varx1-x8;run;第五十九頁(yè)，共七十九頁(yè)。例8.4.2滬市604家上市公司2001年財(cái)務(wù)報(bào)表中有如下十個(gè)主要財(cái)務(wù)指標(biāo)：x1:主營(yíng)業(yè)務(wù)收入（元）x6：每股凈資產(chǎn)（元）x2：主營(yíng)業(yè)務(wù)利潤(rùn)（元）x7：凈資產(chǎn)收益率（%）x3：利潤(rùn)總額（元）x8：總資產(chǎn)收益率（%）x4：凈利潤(rùn)（元）x9：資產(chǎn)總計(jì)（元）x5：每股收益（元）x10：股本第六十頁(yè)，共七十九頁(yè)。X1X2X3X4X5X6X7X8X9X10X1X2X3X4X5X6

X7X8X9X101.0000.7231.0000.4270.7431.0000.4070.6970.9821.0000.1710.3250.5390.5591.0000.1490.2280.2840.2740.5851.0000.0960.1770.3620.4020.7760.2181.0000.0060.2040.4550.5000.8490.2900.8331.0000.7480.7680.5740.5670.1250.1380.0670.0581.0000.6220.6190.4850.5000.002-0.0660.0330.0510.8611.000樣本相關(guān)矩陣如下表：第六十一頁(yè)，共七十九頁(yè)。

f1f2f3

0.695-0.4720.1210.835-0.3460.0970.8860.003-0.0370.8880.037-0.0820.6660.6920.0190.3910.3670.8410.5270.670-0.3250.5810.703-0.2600.747-0.5640.0190.636-0.596-0.219

0.6720.8260.7860.7960.9340.9510.8320.8990.8770.808所解釋的總方差的累計(jì)比例0.4880.7450.838

m=3時(shí)的主成分解第六十二頁(yè)，共七十九頁(yè)。

f1f2f3

0.809-0.0290.1290.8740.1710.1820.7060.5090.1670.6880.5520.1350.1150.8490.4470.0820.1990.9510.0220.9120.0040.0450.9430.0870.936-0.0120.0280.869-0.013-0.228

0.6720.8260.7860.7950.9340.9510.8320.8990.8770.808所解釋的總方差的累計(jì)比例0.4040.7120.838

m=2,3時(shí)用最大方差旋轉(zhuǎn)法旋轉(zhuǎn)后的主成分解第六十三頁(yè)，共七十九頁(yè)。dataexamp842(type=corr);inputx1-x10;cards;1.000.........0.7231.000........0.4270.7431.000.......0.4070.6970.9821.000......0.1710.3250.5390.5591.000.....0.1490.2280.2840.2740.5851.000....0.0960.1770.3620.4020.7760.2181.000...0.0660.2040.4550.5000.8490.2900.8331.000..0.7480.7680.5740.5670.1250.1380.0670.0581.000.0.6220.6190.4850.5000.002-0.0660.0330.0510.8611.000;procfactordata=examp842method=prinn=3rotate=varimax;varx1-x10;run;第六十四頁(yè)，共七十九頁(yè)?！?.5因子得分

因子得分是對(duì)不可觀測(cè)的因子變量的估計(jì)一、加權(quán)最小二乘法

改寫因子模型為：第六十五頁(yè)，共七十九頁(yè)。第六十六頁(yè)，共七十九頁(yè)。Bartlett(1937)得分（加權(quán)最小二乘估計(jì)）：第六十七頁(yè)，共七十九頁(yè)。第六十八頁(yè)，共七十九頁(yè)。二、回歸法(Thompson因子得分)

第六十九頁(yè)，共七十九頁(yè)。第七十頁(yè)，共七十九頁(yè)。第七十一頁(yè)，共七十九頁(yè)。第七十二頁(yè)，共七十九頁(yè)。例8.5.1在例中，用回歸法得到的因子得分為：第七十三頁(yè)，共七十九頁(yè)。dataexamp842(type=corr);inputx1-x10;cards;1.000.........0.7231.000........0.4270.7431.000.......0.4070.6970.9821.000......0.1710.3250.5390.5591.000.....0.1490.2280.2840.2740.5851.000....0.0960.1770.3620.4020.7760.2181.000...0.0060.2040.4550.5000.8490.2900.8331.000..0.7480.7680.5740.5670.1250.1380.0670.0581.000.0.6220.6190.4850.5000.002-0.0660.0330.0510.8611.000;procfactordata=examp842n=3rotate=varimaxscore;varx1-x10;run;第七十四頁(yè)，共七十九頁(yè)。

TheSASSystem16:32Thursday,November11,20061TheFACTORProcedureInitialFactorMethod:PrincipalComponentsPriorCommunalityEstimates:ONEEigenvaluesoftheCorrelationMatrix:Total=10Average=1EigenvalueDifferenceProportionCumulative14.870307642.280618630.48700.487022.589689011.656127420.25900.746030.933561590.229068640.09340.839440.704492950.307384070.07040.909850.397108880.212314950.03970.949560.184793930.03