實(shí)驗(yàn)五 主成份分析與因子分析

課程名稱：數(shù)據(jù)分析與sas實(shí)驗(yàn)實(shí)驗(yàn)編號及實(shí)驗(yàn)名稱實(shí)驗(yàn)五主成份分析與因子分析實(shí)驗(yàn)六典型相關(guān)分析系另U姓名學(xué)號班級實(shí)驗(yàn)地點(diǎn)實(shí)驗(yàn)日期實(shí)驗(yàn)時(shí)數(shù)4指導(dǎo)教師同組其他成員成績一、實(shí)驗(yàn)?zāi)康募耙竽康模壕椭鞒煞莘治龊鸵蜃臃治龅幕居梅ㄟM(jìn)行練習(xí)，鍛煉學(xué)生動手用這些方法解決實(shí)際問題。用驗(yàn)證典型相關(guān)分析尋找郵電業(yè)和經(jīng)濟(jì)發(fā)展的深層次關(guān)系的實(shí)驗(yàn)來向?qū)W生引入如何運(yùn)用典型相關(guān)分析來解決實(shí)際問題。二、實(shí)驗(yàn)環(huán)境及相關(guān)情況（包含使用軟件、實(shí)驗(yàn)設(shè)備、主要儀器及材料等）裝有sas系統(tǒng)的個(gè)人電腦三、實(shí)驗(yàn)內(nèi)容及步驟（包含簡要的實(shí)驗(yàn)步驟流程）內(nèi)容：運(yùn)用princomp和factor過程進(jìn)行主成份分析與因子分析。步驟：1.導(dǎo)入整理主成份分析的數(shù)據(jù)。dataclh;inputnumberx1-x4@@;cards;148417278139347176160497786149366779159458086142316676153437683150437779151427780139316874140296474161477884158497883140336777137316673152357379149478279145357077160477487156447885151427382147387378157396880147306575157488088151367480144366876141306776139326873148387078run;2.進(jìn)行主成份分析。procprincompdata=clhpredix=zout=lwh;varx1-x4;run;optionsps=32ls=85;procplotdata=lwh;plotz2*z1$number='*'/href=-1href=2vref=0;run;procsortdata=lwh;byz1;run;procprintdata=lwh;varnumberz1z2x1-x4;run;dataliuku;inputx1-x7;n=_n_;cards;11.8350.4814.3625.2125.210.810.9845.5960.52613.8524.0426.010.910.963.5250.08624.4049.311.36.820.853.6810.3713.5725.1226.00.821.0148.2870.38614.525.923.322.180.9317.9560.289.7517.0537.20.4640.987.370.50613.634.2810.698.80.564.2230.343.87.188.21.110.976.4420.194.79.173.20.741.03TOC\o"1-5"\h\z16.2340.393.15.4121.50.421.010.5850.422.44.7135.60.870.9823.5350.232.64.6151.80.311.025.3980.122.86.2111.21.141.07283.1490.1481.7632.968215.860.140.98316.6040.3171.4532.432263.410.2490.98307.310.1731.6272.729235.70.2140.99322.5150.3121.3822.32282.210.0241.00254.580.2970.8991.476410.30.2390.93304.0920.2830.7891.357438.360.1931.01202.4460.0420.7411.266309.770.290.99；run;procfactordata=liukuout=lwhNfactor=3method=prinpriors=onerotate=varimaxsimplep=0.8scoreoutstat=zhouhm;varx1-x7;run;procscoredata=liuku;score=zhouhmout=nihao;varx1-x7;run;內(nèi)容：運(yùn)用cancorr過程對郵電業(yè)和國民經(jīng)濟(jì)之間做典型相關(guān)分析導(dǎo)入整理數(shù)據(jù)。datalwh;inputyearlettersexpressagemobilestationaryindustryagriculturearchitectureservice;cards;79.555562.7362.94070.612135.824950.63728.819978.578.687096.6685.35494.714015.429447.64387.423326.268.556878.91323.37031.014441.932921.44621.626988.165.517331.82386.38742.114817.634018.44985.830580.560.529091.34329.610871.614770.035861.55172.133873.477.7111031.48453.314482.914944.740033.65522.338714.086.9312652.714522.218036.815781.343580.65931.744361.6106.0114036.220600.521422.216537.047431.36465.549898.9103.8417237.826995.326274.717381.754945.57490.856004.782.8119771.933482.431175.621412.765210.08694.364561.373.5122880.339340.635044.522420.077230.810133.873432.971.3126988.046105.836778.624040.091310.911851.184721.469.50120189.654730.636563.728095.0107367.214014.1100053.5;run;典型相關(guān)分析proccancorrdata=lwhall;varlettersexpressagemobilestationary;withindustryagriculturearchitectureservice;run;四、實(shí)驗(yàn)結(jié)果（包括程序或圖表、結(jié)論陳述、數(shù)據(jù)記錄及分析等，可附頁）1.對學(xué)生身高、體重等信息分析結(jié)果相關(guān)陣的特征值和特征向量EigenvaIuesoftheCorrelationMatrix433466576679888900290395374777777777777777788878878888468876571807032348377628848666666667676777776777787777912101034656881569232374977233333333333334333444444444079912709459878217101396801433466576679888900290395374777777777777777788878878888468876571807032348377628848666666667676777776777787777912101034656881569232374977233333333333334333444444444079912709459878217101396801433344443444444555555545566111-2.78973-0.34290215-2.766190.31256329-2.363940.47796410-2.324890.35918528-2.12466-0.1350266-2.07044-0.31742724-2.02249-0.77568814-1.83494-0.0493792-1.568450.706401027-1.34958-0.021841118-1.055870.06650124-0.74720-0.792501330-0.49442-0.144871422-0.282260.35144151-0.068730.234131616-0.06286-0.2037017260.16092-0.0424518230.24728-1.2344519210.78286-0.160342080.811960.767902190.918930.574862271.397170.0595123171.529461.6757524202.10474-0.0218125132.401480.1648826192.47936-0.9563927122.56467-0.20921Eigenva1ueDifferenceProportionCumu1ative13.541098003.227714840.88530.885320.313383160.233974200.07830.963630.079408950.013299060.01990.983540.066109890.01651.0000zlEigenvectorsz2z3z4xl0.496966-.543213-.4496270.505747x20.5145710.210246-.462330-.690844x30.4809010.7246210.1751770.461488x40.506928-.3682940.743908-.232343第一主成份的貢獻(xiàn)率以高達(dá)88.53%；且前面在各主成份的累積貢獻(xiàn)率已達(dá)96.36%。因此用兩個(gè)主成份就能很好地概括這組數(shù)據(jù)。有最大的兩個(gè)特征值對應(yīng)的特征向量可以寫出第一和第二主成份：F1=0.496966x1+0.514571x2+0.480901x3+0.506928x4;F2=-0.543213x1+0.210246x2+0.724621x3-0.368294x4;30各同學(xué)在兩個(gè)主成份上的得分身高體重胸圍坐高Obsnumberzlz2xlx2x3x42852.69362-0.016891534580862932.80006-0.3830216049778630253.034100.05678157488088第一特征值對應(yīng)的第一個(gè)特征向量的各個(gè)分量均在0.5附近，且都是正值，他反映中學(xué)生的魁梧程度，從上面的得分我們也能看出這點(diǎn)，所以把第一主成分成為大小因子，第二特征向量中第一分量和第四分量為夫，第二個(gè)和第三個(gè)分量為正值，所以他反映學(xué)生的胖瘦，成為體型因子。

2.對鹽泉數(shù)據(jù)分析結(jié)果相關(guān)陣的特征值Eigenva1uesoftheCorrelationMatrix：Tota1=7Average=1EigenvalueDifferenceProportionCumu1ative14.246941672.998205610.60670.606721.248736060.328675300.17840.785130.920060760.482432690.13140.916540.437628060.323105220.06250.979150.114522840.083095630.01640.995460.031427210.030743310.00450.999970.000683400.00011.00003factorswill1DeretainedbythePROPORTIONcriterion.上表顯示，取公因子的個(gè)數(shù)為3。因子載荷矩陣及每個(gè)公共因子解釋的方差FactorPatternFactorlFactor2FactorSxl-0.714860.563770.04685x20.41262-0.134420.89228x30.90980-0.06538-0.17282x40.945090.04758-0.17530x5-0.835870.466730.04760x60.825630.49705-0.13333x7-0.68145-0.66438-0.20263VarianceExplainedbyEachFactorFactorlFactor2FactorS4.24694171.24873610.9200608FinalCommunalityEstimates：Total=6.415738xlx8x4xBx70.831060190.984491840.861880050.926188480.918775700.946505670.94683656上表顯示，F(xiàn)actor3的對應(yīng)列中X2的數(shù)值為0.89278較大外，其余較小，表明可以用X2來解釋Factor3得：X1=-0.71486Factor1+0.56377Factor2+0.04685Factor3+e1

方差最大正交旋轉(zhuǎn)后的因子載荷矩陣TheFACTORProcedureRotationMethod：VarimaxOrthogonalTransformationMatrix上表為方差最大正交旋轉(zhuǎn)后的因子載荷矩陣明顯向0或1兩極方向分化，這就大大有利于對公共因子進(jìn)行解釋。第一公共因子的載荷正向集中于上表為方差最大正交旋轉(zhuǎn)后的因子載荷矩陣明顯向0或1兩極方向分化，這就大大有利于對公共因子進(jìn)行解釋。第一公共因子的載荷正向集中于X5和XI，而負(fù)向集中于X3和X4,說明第一公共因子主要有這四個(gè)變量解釋。類似地解釋第二和第三因子。Factor23.對郵電業(yè)和國民經(jīng)濟(jì)之間做典型相關(guān)分析結(jié)果—xlU.bdblx2-0.1859/~Corre-lationsBc-twc-tnthtFactor3-0.163000.96660兩組變量之間的相關(guān)系數(shù)U?I￡400UfiRVariable-f^ndth*HITHU-sriable-sc-xpress-sq*nc>Di1estation-3h-yndustryagriculture-archite-cturtStKWjCt-0.1翊-0.067?-0.07^00.0226。.頸&0.79430.80210.7662o.：s?o30.991S0.SS01Q.茉箜0.92800.93990.93600.967?123-0.733480.649020.201920.640590.75939-0.113910.22727-0.045800.97275Cancorr過程長生的典型相關(guān)分析的一般結(jié)果Ineomoo^sieriio-doi.ueceriDeroIneomoo^sieriCanonicalCorrelationAdjustedCanonicalCorrel-ationApproxiriateStandardErrorSquaredCanonicalCorrel-ation10.9983820.9976970.0009340.99676620.9511950.9381990.0274900.90477130.4435600.0932970.2318800.19674540.3556720.2521570.126503TestofHO：ThecanonicalcorrelationfintheEigenvalue-sofInV(E)?Hcurrentrowandallthatfollowarezero=CanRsq/(1-CanRsq)LikelihoodApproxiriateFValue-NunEi-jenvalueDifferenceProportionCunulativeRatioDFDenDFPr>F308.1901298.68910.96890.96890.0002161014.761615.913<.00019.50119.25610.02990.99880.066816233.34914.7530.01960.24490.10010.00080.99950.701640890.68■1U0.61820.14480.00051.00000.873497191.16180.3131FheCANCDRRProcedureCanonicalCorrelationAnalasis1234MultiV-3KSt-atifticUi1kf'L-snbd-aPi11-ai'sIrac*Hote-11ing-Lawle-yTractRoy'sGre-ate-stRootNOTE：FStatist&=4M=-0.5N=1.5傾gFNu。NunOFDonDFiate-St-atisticsandFApproxira-ations0.00021610U.?62.224785U2.51310.0809236492.7?308.19011051616.386664.32-K-813.A-5Pr>FM.通10.0131<.0001歡0001anuppe-rbound上表顯示：第一典型相關(guān)系數(shù)為0.998382，比郵電業(yè)和國民經(jīng)濟(jì)兩組間任一個(gè)相關(guān)系數(shù)都大。再則，第二典型變量為0的原假設(shè)的概率水平為0.0196,故在a=0.05的顯著性水平下，第二典型變量的典型相關(guān)作用也是明顯的。Cancorr過程產(chǎn)生的典型變量的系數(shù)ThtSASSysteri~~13：56TutsdTheCANCDRRProcedureCanonic-slCorrel-stionAn-slysisStandard：zedCanonic-alCoefficientsfortheVfiRVari-sblesVIV2V3W-0.093?0.62350.05130.3595expre-ss-sqt0.13540.35292.3501-0.2324nobi1e0.4604-5.7453-g.47704.0053st-stion-sry0.41335.24214.7630-4.7945