實(shí)驗(yàn)報(bào)告七-SAS典型相關(guān)分析

實(shí)驗(yàn)項(xiàng)目名稱所屬課程名稱實(shí)驗(yàn)類型實(shí)驗(yàn)日期實(shí)驗(yàn)項(xiàng)目名稱所屬課程名稱實(shí)驗(yàn)類型實(shí)驗(yàn)日期班級(jí)

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成績(jī)實(shí)驗(yàn)報(bào)告典型相關(guān)分析統(tǒng)計(jì)分析及SAS實(shí)現(xiàn)驗(yàn)證性實(shí)驗(yàn)2016-12-11數(shù)學(xué)與應(yīng)用數(shù)學(xué)實(shí)驗(yàn)概述：【實(shí)驗(yàn)?zāi)康募耙蟆空莆誗AS中進(jìn)行典型相關(guān)分析的方法，理解典型相關(guān)分析的基本思想。理解典型相關(guān)變量的性質(zhì)。理解典型相關(guān)系數(shù)的求解步驟、特征根的求解，掌握典型相關(guān)系數(shù)的假設(shè)檢驗(yàn)過(guò)程。掌握SAS系統(tǒng)中INSIGHT模塊、“分析家”模塊以及編程進(jìn)行典型相關(guān)分析?！緦?shí)驗(yàn)原理】SAS軟件的操作方法及原理【實(shí)驗(yàn)環(huán)境】（使用的軟件）SAS9.3實(shí)驗(yàn)內(nèi)容:【實(shí)驗(yàn)方案設(shè)計(jì)】一．理解典型相關(guān)分析的概念及步驟；二．掌握典型相關(guān)分析的方法；三.用INSIGHT、“分析家”計(jì)算統(tǒng)計(jì)量和編程實(shí)現(xiàn)實(shí)際問(wèn)題中的典型相關(guān)分析;【實(shí)驗(yàn)過(guò)程】（實(shí)驗(yàn)步驟、記錄、數(shù)據(jù)、分析）【練習(xí)7-1】對(duì)某高中一年級(jí)男生38人進(jìn)行體力測(cè)試及運(yùn)動(dòng)能力測(cè)試，如表所示，試對(duì)兩組指標(biāo)作典型相關(guān)分析。表體力測(cè)試、運(yùn)動(dòng)能力測(cè)試指標(biāo)Numx1x2x3x4x5x6x7y1y2y3y4y514655126517525726.848927836025255954281.218507.246430334834669107389818746.8430329386449501054897.616606.836226633154255904666.52687.2453231139164861106437825587405297389749601004990.6156074202110379848631225256.117687.1466282362945551054876156174152463861048641203860.220627.14132873981149521004253.46427.44042364001247621003461.210627.24272574071341511015362.456083722534091452551254386.35626.84963010350154552945051.420657.63942433991649571104772.31945744630113371753651124790.415756.64463012357184777954772.39646.64202544471948601204786.412626.844728113812049551134184.1156073982743872148691284247.920637.14853073502242571224654.215637.24002863882354641555171.419616.951133122982453631204256.68537.54302943532542711384465.2175574872993702646661204562.222687.4470287360274556912966.218517.93802653582850601204256.68576.8460325348294251126505013577.33982723833048501154152.96397.44152863143142521404856.315606.950027113483248671053969.223607.645028103263349741514954.2205875003012330

3447551134071.419647.64102973313549741205354.522596.950033213423644521103754.914577.54002924213752661304745.914456.850528113553848681004553.623707.2522289352其中，體力測(cè)試指標(biāo)為：X反復(fù)橫向跳（次），X縱跳（cm）,X背力（kg），X4捏力（kg），X臺(tái)階測(cè)試（指數(shù)），X356定向體前屈（cm），X俯臥上提后仰（cm）。7運(yùn)動(dòng)能力測(cè)試的指標(biāo)為y-50m跑（s），y-跳遠(yuǎn)（cm），y-投球（m），y引體1234向上（次），y-耐力跑（s）。5【解答】利用INSIGHT模塊進(jìn)行典型相關(guān)分析：Analyze"ablesGraphsCurvesV;HisSograni/ElarChart(Y}BoxPlot/MosaicPlotC￥}LinePict(YX)Analyze"ablesGraphsCurvesV;HisSograni/ElarChart(Y}BoxPlot/MosaicPlotC￥}LinePict(YX)ScatterPint[YXJContourPlot(Z￥X)RottingPlot(ZVX)Disinbution(￥}5UVX)毎CanonicalCorrelabonOption^CurvwnwiITabI日?s:VdncinicalCvre-lAtiondi-岸Coma1stiiom^(右itraat；Lir&)PSt-dSaorIhqCoefx廠RssScotl"QCcefs[RfSHkiHdonGyIFlew?Vwianc*)PRepkind>9incv(Rkrf⑷曠iwwx.)LancuDEcalFlats:FIrot2ConpDixentEiFIrst9CoiTTj^DxentsBeatty-PlotCBipl^t(Bltd￥X)

>!"Biplist(Rau￥X)PaIr-tfExePJots:UutpulScam:^■rrrrMultivanate(YX}W.ICwelI1^1DbectIpt?wStatIsRUnivoriiflitc廠SS￡P(guān)ICSSCPrcwpm1^1DbectIpt?wStatIsRUnivoriiflitc廠SS￡P(guān)ICSSCPrcwpmICOflflp*<*j?lues廠COHIIrwwTfl廠PalKUaWLOOFirinoilpailCm衛(wèi)取n自ntiHnigi]ysIPrinciipel匚EP?hi曰陽(yáng)tC?onIc：?ICarrelaitanAirialirii[CanonIcalCarn-ldbionOptionB>P7IPartlaiISiivsrlatePlots；FBcathsrPlolIHatrix-Pr&ia?I：口nf\Ellipsa廠irrijHiHudiJifukhricyHaMiouiihRBduiindhncrs/陽(yáng)七icm|CononicalDiscrimiinant^nalyCancnicaIDImvIroinant￡|ptEotia二xSxBPl4w4k5—j1―InJTGroypLabelHluiMJ^analje(YXJ|Concfl-l疲||LanceIiri^tlriod|IkilgulJRsawi±||Concfl-l纟口果:表7.1UnivariateStatisticsVariableNMeanStdDevMinimumMaximumy1387.13160.33546.60008.0000y238441.842143.2138362.0000522.0000y33827.81582.749521.000033.0000y4387.52633.83262.000021.0000

y538366.605331.2976298.0000447.0000x13847.42113.366241.000054.0000x23860.21057.451350.000077.0000x338114.473715.659890.0000155.0000x43844.63165.354629.000053.0000x53866.910514.448545.900098.0000x63815.34215.95152.000025.0000x73859.73688.142939.000075.0000由表7.1得知一些基本統(tǒng)計(jì)量，各變量下的均值、標(biāo)準(zhǔn)差、最大值、最小值。表7.2CorrelationMatrixx1x2x3x4x5x6x7y1-0.3784-0.3791-0.3498-0.3184-0.4011-0.0719-0.2552y20.32380.52700.57890.2777-0.19460.25360.1478y30.41160.39770.5538-0.0414-0.01160.33100.0388y40.25680.45500.33480.25070.12570.22650.0998y5-0.4709-0.0488-0.4802-0.1007-0.0132-0.29390.1923CanCorrAdj.CanCorrApproxStd.ErrorCanRsq0.8487080.7976840.0459820.7203050.7029630.5825560.0831600.4941570.646784.0.0956260.4183290.3542120.1778850.1437730.1254660.268706.0.1525290.07220312345表7.3CanonicalCorrelations由表7.2相關(guān)系數(shù)陣、表7.3典型相關(guān)系數(shù)得知，第一典型相關(guān)系數(shù)為0.848708，修正值為0.797684，標(biāo)準(zhǔn)誤差為0.045982，典型相關(guān)系數(shù)的平方為0.720305；第二典型相關(guān)系數(shù)為0.702963，修正值為0.582556，標(biāo)準(zhǔn)誤差為0.083160，典型相關(guān)系數(shù)的平方為0.494157；第三典型相關(guān)系數(shù)為0.646784，標(biāo)準(zhǔn)誤差為0.095626，典型相關(guān)系數(shù)的平方為0.418329；第四典型相關(guān)系數(shù)為0.354212，修正值為0.177885，標(biāo)準(zhǔn)誤差為0.143773，典型相關(guān)系數(shù)的平方為0.125466；第五典型相關(guān)系數(shù)為0.268706，標(biāo)準(zhǔn)誤差為0.152529，典型相關(guān)系數(shù)的平方為

0.072203。表7.4EigenvaluesEigenvalueDifferenceProportionCumulative12.57531.59840.57320.573220.97690.25770.21740.790730.71920.57570.16010.950740.14350.06560.03190.982750.07780.01731.0000由表7.4特征根可以得到特征根、相鄰兩特征根之差、特征根所占方差信息量的比例、累計(jì)方差信息量的比例，其中前三對(duì)典型變量所能解釋的變異占總變異的95.07%，其他兩個(gè)典型相關(guān)變量的作用很小，一共只解釋了總變異的4.93%，因此不予考慮。表7.5：TestofH0:CanCorr[j]=0,j>=KKL.RatioApproxFNumDFDenDFPr>F10.0667742.884235111.8019<.000120.2387392.01822495.40180.008930.4719621.61911577.69710.087840.8113900.7987858.00000.606150.9277970.7782330.00000.5154應(yīng)用似然比法檢驗(yàn)典型相關(guān)系數(shù)與零的差別，由表7.5檢驗(yàn)典型相關(guān)系數(shù)與零的差別得到P值依次為＜0.0001、0.0089、0.0878，因此，對(duì)于前兩組典型相關(guān)變量，拒絕小于此對(duì)典型變量典型相關(guān)系數(shù)的所有典型相關(guān)系數(shù)為0的原假設(shè)，因此，前兩組變量的相關(guān)性的研究可轉(zhuǎn)化為研究前兩對(duì)典型相關(guān)變量的相關(guān)性。表7.6Correlations(Strueture)VariableCY1CY2CX1CX2y1-0.71220.1036-0.60440.0728y20.72120.56270.61210.3955y30.76370.23260.64820.1635y40.57650.16610.48930.1167

y5-0.68030.2445-0.57740.1719x10.5707-0.16840.6725-0.2395x20.41780.45670.49230.6496x30.64170.17420.75610.2479x40.23020.00030.27120.0004x50.1830-0.47690.2156-0.6784x60.29870.09080.35190.1292x70.08930.19440.10520.2765由表7.6典型相關(guān)結(jié)構(gòu)，從相關(guān)系數(shù)判斷，體力測(cè)試指標(biāo)除x(0.2712)、4x(0.2156)、x(0.1052)外各變量與第一典型相關(guān)變量間的相關(guān)性比較高，57運(yùn)動(dòng)能力測(cè)試的指標(biāo)與第一典型相關(guān)變量間的相關(guān)性都比較高；x與第二典型相5關(guān)變量間的相關(guān)性比較高，說(shuō)明第一對(duì)典型相關(guān)變量對(duì)臺(tái)階測(cè)試(x)的解釋作用不大。5從體力測(cè)試指標(biāo)組的變量與運(yùn)動(dòng)能力測(cè)試的指標(biāo)組的典型變量之間，運(yùn)動(dòng)能力測(cè)試的指標(biāo)組的變量與體力測(cè)試指標(biāo)組的典型變量之間的相關(guān)系數(shù)可見(jiàn)，各組變量與前兩對(duì)典型變量之間均有較強(qiáng)的相關(guān)性。表7.7StdCanonicalYCoefficientsVariableCY1CY2y1-0.5340160.655116y20.1474291.070199y30.3331930.371059y4-0.0323250.085995y5-0.4079430.938190表7.8StdCanonicalXCoefficientsVariableCX1CX2x10.449775-0.150127x20.1651090.582368x30.6594610.013959x40.067975-0.131520x50.267853-0.723637x60.113355-0.130192

x70.0147380.391286由表7.7、表7.8標(biāo)準(zhǔn)化變量的典型變量的系數(shù)可知，來(lái)自運(yùn)動(dòng)能力測(cè)試的指標(biāo)的第一典型變量CY1為：CY1=—0.534016y+0.147529y*+O.333193y*—0.032325y*-0.407943y*12345CY1在y*上的系數(shù)近似為0,在y*、y*、y*上的系數(shù)為負(fù)值，在y*上的系數(shù)較大，因此此CY1主要代表了投球等指標(biāo)。53來(lái)自體力測(cè)試指標(biāo)的第一典型變量CX1為：CX1=0.449775x*+0.165109x*+0.659461x*123+0.067975x*+0.267853x*+0.113355x*+0.014738x*

4567CX1在X*上的系數(shù)最大，在X*上的系數(shù)較大，在其余變量上的系數(shù)均較小，因31此，CX1主要代表了反復(fù)橫向跳、背力等指標(biāo)。表7.9StdVariance（YVariables）ExplainedbyCY'sExplainedbyCX'sProportionCumulativeCanRsqProportionCumulative0.48120.48120.7203050.34660.34660.09380.57490.4941570.04630.3929表7.10StdVariance(XVariables)ExplainedbyCY'sExplainedbyCX'sExplainedbyCY'sExplainedbyCX'sProportionCumulativeCanRsqProportionCumulative10.15650.15650.7203050.21730.217320.07720.23380.4941570.15630.3736ProportionCumulativeCanRsqProportionCumulative10.15650.15650.7203050.21730.217320.07720.23380.4941570.15630.3736由表7.9、表7.10典型冗余分析（CanonicalRedundancyAnalysis）表明，兩對(duì)典型變量仍不能全面預(yù)測(cè)配對(duì)的那組變量。來(lái)自運(yùn)動(dòng)能力測(cè)試的指標(biāo)被對(duì)方兩個(gè)典型變量（CX1、CX2）解釋的累積方差比例為39.29%，來(lái)自體力測(cè)試指標(biāo)被對(duì)方兩個(gè)典型變量（CY1、CY2）解釋的累計(jì)方差比例為37.36%?！揪毩?xí)7-2】用典型相關(guān)分析研究我國(guó)農(nóng)業(yè)投入與產(chǎn)出的關(guān)系（見(jiàn)表）。農(nóng)業(yè)產(chǎn)出水平選取如下三個(gè)指標(biāo)作為“產(chǎn)出組”指標(biāo)：農(nóng)業(yè)總產(chǎn)出（億元），用農(nóng)林牧漁業(yè)總產(chǎn)值表示，記為y；農(nóng)業(yè)勞動(dòng)生產(chǎn)率（元/人），用人均農(nóng)業(yè)牧漁業(yè)總產(chǎn)值表示，記為y。農(nóng)業(yè)總產(chǎn)出增長(zhǎng)速度（％），用農(nóng)林牧漁業(yè)總產(chǎn)值的增2長(zhǎng)速度表示，記為y。3農(nóng)業(yè)投入水平選取如下7個(gè)指標(biāo)作為”投入組”指標(biāo)：農(nóng)業(yè)勞動(dòng)投入（人）用從業(yè)人數(shù)表示，記為X：農(nóng)業(yè)物質(zhì)消耗（億元），用農(nóng)業(yè)牧漁業(yè)中間消耗價(jià)值表示，記為X：農(nóng)民受教育程度（年），用農(nóng)民家庭的平均文化程度表示，記為2

X3：農(nóng)業(yè)機(jī)械化程度（萬(wàn)kw），用農(nóng)業(yè)機(jī)械總動(dòng)力表示，記為X；農(nóng)業(yè)電力文化程度（億kw.h），用農(nóng)村電量表示，記為X：農(nóng)業(yè)土地投入（khm2），用有效灌5溉面積表示，記為X：化肥用量（10kt）用農(nóng)牧漁業(yè)化肥施用量來(lái)表示，記為6X。77表我國(guó)農(nóng)業(yè)投入與產(chǎn)出yeary1y2y3x1x2x3x4x5x6x719801965684.1.4028696064.311474321448812698626819812091716.6.4129186364.561568370448713355610419822327779.11.229837044.8216613974417151393964719832508811.7.7830917515.091802428446416592072419842816902.12.231208325.3619494644445174030897319852912933.3.4131188915.612091509440317767273619863010961.3.3731319235.712295587442219313210619873185999.5.8131869995.82248365944401999593631988331010263.92322410695.93265771244372141.409561989341310273.11332211036.05280679047912357.205771990367210767.59341111926.21287084447402590.307731991380810893.70349512696.58293896347822805.406821992405211646.41347914116.653030110748592930.505801993436812867.80339616216.783181124548643150.006661994474414218.61333828886.883380147448753318.0062919955261159310.9330122767.023611165649283594.4008811996575617499.41329126197.283854181350383828.000711997613518536.58330927617.414210198051233981.805681998650319566.003323292645212042522940867.55.80206

【解答】利用“分析家”實(shí)現(xiàn)典型相關(guān)分析:Des.cr!ptiveTableAnalysis...Hypoth-esisTesEANOVARegressionMultivariate-SurvivalMultivariate-SampleSize[ndex...結(jié)果:TheCANCORRProcedureCanonicalCorrelationAnalysis表7.11典型相關(guān)系數(shù)CanonicalCorrelationAdjustedCanonicalCorrelationApproximateStandardErrorSquaredCanonicalCorrelation10.998993.0.0004740.99798720.994616.0.0025310.98926130.6153120.5141670.1464630.378609由表7.11得知本題提取了3個(gè)典型相關(guān)系數(shù)，第一個(gè)典型相關(guān)系數(shù)CanR]=0.998993，為第一對(duì)典型相關(guān)變量之間的相關(guān)性。第二典型相關(guān)系數(shù)為0.994616，第三典型相關(guān)系數(shù)為0.615312。表7.12特征根及典型相關(guān)系數(shù)的檢驗(yàn)

EigenvaluesofTestofHO:ThecanonicalcorrelationsInv(E)*H=CanRsq/(1-CanRsq)inthecurrentrowareandallzerothatfollowEigeDiffPropCumuLikelihoApproximNumDenPr>FnvalerenortilatiodateDFDFueceonveRatioFValue495.403.0.840.840.00001361.252126.39<.000186277450252543392.191.50.150.990.00667318.741220<.00011770846590170.600.001.000.6213901.345110.317593100084由表7.12可以得到特征根、相鄰兩特征根之差、特征根所占方差信息量的比例、累計(jì)方差信息量的比例，其中前兩對(duì)典型變量所能解釋的變異占總變異的99.9%，其他兩個(gè)典型相關(guān)變量的作用很小，一共只解釋了總變異的0.1%，因此不予考慮。應(yīng)用似然比法檢驗(yàn)典型相關(guān)系數(shù)與零的差別，由表7.12檢驗(yàn)典型相關(guān)系數(shù)與零的差別得到P值依次為＜0.0001、＜0.0001、0.3175,因此，對(duì)于前兩組典型相關(guān)變量，拒絕小于此對(duì)典型變量典型相關(guān)系數(shù)的所有典型相關(guān)系數(shù)為0的原假設(shè)，因此，前兩組變量的相關(guān)性的研究可轉(zhuǎn)化為研究前兩對(duì)典型相關(guān)變量的相關(guān)性。表7.13MultivariateStatisticsandFApproximationsS=3M=1.5N=3.5StatisticValueFValueNumDFDenDFPr>FWilks'Lambda0.0000134361.252126.393<.0001Pillai'sTrace2.365857445.862133<.0001Hotelling-Lawley588.58976097231.232113.2<.0001TraceRoy'sGreatestRoot495.86272728779.21711<.0001NOTE:FStatisticforRoy'sGreatestRootisanupperbound.由表7.13對(duì)典型相關(guān)系數(shù)均為0的F檢驗(yàn)，本題中Wilk'Lambda檢驗(yàn)結(jié)果與表7.12一致，因此表明至少有一個(gè)典型相關(guān)系數(shù)在a＜0.0001的顯著性水平下非0。表7.14RawCanonicalCoefficientsfortheVARVariables

x1x10.0001161552-0.00114241-0.000133841x2x2-0.0000549482.481698E-60.0005683876x3x30.16057894891.4385417297-2.845012836x4x40.00002555710.0001081585-0.000405964x5x50.0006043675-0.002086845-0.005582127x6x60.0000365196-1.041965E-6-0.000751765x7x70.00006987030.00053724690.0120878105VIV2V3表7.15RawCanonicalCoefficientsfortheWITHVariablesW1W2W3y1y10.0025192649-0.0073647640.000206527y2y2-0.0064122440.0268791995-0.001248478y3y3-0.004515265-0.0377417370.3409407567由表7.14、表7.15可知，表中數(shù)據(jù)為原始表達(dá)的典型變量的系數(shù)，沒(méi)有使用相同的單位進(jìn)行測(cè)量，造成出現(xiàn)數(shù)據(jù)十分小的結(jié)果，因此對(duì)原始變量進(jìn)行標(biāo)準(zhǔn)化處理。7.16StandardizedCanonicalCoefficientsfortheVARVariablesV1V2V3x1x10.2087-2.0524-0.2404x2x2-0.04490.00200.4642x3x30.15581.3961-2.7610x4x40.22870.9679-3.6330x5x50.3469-1.1977-3.2037x6x60.0988-0.0028-2.0337x7x70.06470.497211.1857表7.17StandardizedCanonicalCoefficientsfortheWITHVariablesW1W2W3

W1W2W3y1y13.4256-10.01440.2808y2y2-2.462110.3209-0.4794y3y3-0.0137-0.11431.0321由表7.16、表7.17標(biāo)準(zhǔn)化變量的典型相關(guān)系數(shù)知，來(lái)自“投入組”指標(biāo)的第一典型變量VI為：V1=0.2087x*-0.0449x*+0.1558x*123+0.2287x*+0.3469x*+0.0988x*+0.0647x*

4567VI在x*上的系數(shù)最大，在其余變量上的系數(shù)均較小，因此，VI主要代表了3農(nóng)業(yè)機(jī)械化程度等指標(biāo)。來(lái)自“產(chǎn)出組”指標(biāo)的第一典型變量W1為：W1=3.4256y*-2.4621y*一0.0137y*123W1在y*上的系數(shù)較大，因此W1主要代表了農(nóng)業(yè)總產(chǎn)出等指標(biāo)。1表7.18CorrelationsBetweentheVARVariablesandTheirCanonicalVariablesV1V2V3x1x10.8170-0.5549-0.0544x2x20.90620.30790.1440x3x30.9889-0.01330.0064x4x40.98740.1315-0.0682x5x50.96130.24930.0804x6x60.93900.0866-0.0083x7x70.99080.10190.0832表7.19CorrelationsBetweentheWITHVariablesandTheirCanonicalVariablesW1W2W3y1y10.97160.23360.0387y2y20.94460.32450.0484y3y30.17440.08720.9808由表7.18、7.19典型相關(guān)結(jié)構(gòu)，在原始變量與本組典型變量的相關(guān)關(guān)系中，“投入組”指標(biāo)的第一典型變量VI與農(nóng)業(yè)勞動(dòng)投入、農(nóng)業(yè)物質(zhì)消耗、農(nóng)民受教育程度、農(nóng)業(yè)機(jī)械化程度、農(nóng)業(yè)電力文化程度、農(nóng)業(yè)土地投入、化肥用量的相關(guān)系數(shù)都較大，說(shuō)明這個(gè)典型變量主要反映整個(gè)投入指標(biāo)；“產(chǎn)出組”指標(biāo)的第一

典型變量W1與農(nóng)業(yè)總產(chǎn)出、農(nóng)業(yè)勞動(dòng)生產(chǎn)率的相關(guān)系數(shù)都較大（0.9716、0.9446），說(shuō)明這個(gè)典型變量主要反映農(nóng)業(yè)勞動(dòng)產(chǎn)出。表7.20CorrelationsBetweentheVARVariablesandtheCanonicalVariablesoftheWITHVariablesW1W2W3x1x10.8162-0.5519-0.0335x2x20.90530.30630.0886x3x30.9879-0.01320.0039x4x40.98640.1308-0.0420x5x50.96030.24790.0494x6x60.93810.0861-0.0051x7x70.98980.10130.0512表7.21CorrelationsBetweentheWITHVariablesandtheCanonicalVariablesoftheVARVariablesV1V2V3y1y10.97060.23230.0238y2y20.94370.32270.0298y3y30.17420.08670.6035由表7.20、表7.21典型相關(guān)結(jié)構(gòu)知，在原始變量與兩組配對(duì)組的典型變量的相關(guān)關(guān)系結(jié)果，化肥用量與“投入組”指標(biāo)的第一典型變量VI的相關(guān)系數(shù)最大，說(shuō)明用農(nóng)牧漁業(yè)化肥施用量大則“投入”高；農(nóng)業(yè)總產(chǎn)出與“產(chǎn)出組”指標(biāo)的第一典型變量W1的相關(guān)系數(shù)最大（0.9706），說(shuō)明農(nóng)業(yè)總產(chǎn)出越高，產(chǎn)出量越大。表7.22RawVarianceoftheVARVariablesExplainedbyCanonicalTheirOwnCanonicalTheOppositeVariableCanonicalVariablesR-SquareCanonicalVariablesNumberProportionCumulativeProportionCumulativeProportionProportion10.95560.95560.99800.95360.953620.02730.98290.98930.02700.980730.00440.98730.37860.00170.9823

表7.23RawVarianceoftheWITHVariablesExplainedbyCanonica