实验五 主成份分析与因子分析

课程名称：数据分析与sas实验实验编号及实验名称实验五主成份分析与因子分析实验六典型相关分析系另U姓名学号班级实验地点实验日期实验时数4指导教师同组其他成员成绩一、实验目的及要求目的：就主成份分析和因子分析的基本用法进行练习，锻炼学生动手用这些方法解决实际问题。用验证典型相关分析寻找邮电业和经济发展的深层次关系的实验来向学生引入如何运用典型相关分析来解决实际问题。二、实验环境及相关情况（包含使用软件、实验设备、主要仪器及材料等）装有sas系统的个人电脑三、实验内容及步骤（包含简要的实验步骤流程）内容：运用princomp和factor过程进行主成份分析与因子分析。步骤：1.导入整理主成份分析的数据。dataclh;inputnumberx1-x4@@;cards;148417278139347176160497786149366779159458086142316676153437683150437779151427780139316874140296474161477884158497883140336777137316673152357379149478279145357077160477487156447885151427382147387378157396880147306575157488088151367480144366876141306776139326873148387078run;2.进行主成份分析。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;内容：运用cancorr过程对邮电业和国民经济之间做典型相关分析导入整理数据。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;典型相关分析proccancorrdata=lwhall;varlettersexpressagemobilestationary;withindustryagriculturearchitectureservice;run;四、实验结果（包括程序或图表、结论陈述、数据记录及分析等，可附页）1.对学生身高、体重等信息分析结果相关阵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第一主成份的贡献率以高达88.53%；且前面在各主成份的累积贡献率已达96.36%。因此用两个主成份就能很好地概括这组数据。有最大的两个特征值对应的特征向量可以写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各同学在两个主成份上的得分身高体重胸围坐高Obsnumberzlz2xlx2x3x42852.69362-0.016891534580862932.80006-0.3830216049778630253.034100.05678157488088第一特征值对应的第一个特征向量的各个分量均在0.5附近，且都是正值，他反映中学生的魁梧程度，从上面的得分我们也能看出这点，所以把第一主成分成为大小因子，第二特征向量中第一分量和第四分量为夫，第二个和第三个分量为正值，所以他反映学生的胖瘦，成为体型因子。

2.对盐泉数据分析结果相关阵的特征值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.上表显示，取公因子的个数为3。因子载荷矩阵及每个公共因子解释的方差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上表显示，Factor3的对应列中X2的数值为0.89278较大外，其余较小，表明可以用X2来解释Factor3得：X1=-0.71486Factor1+0.56377Factor2+0.04685Factor3+e1

方差最大正交旋转后的因子载荷矩阵TheFACTORProcedureRotationMethod：VarimaxOrthogonalTransformationMatrix上表为方差最大正交旋转后的因子载荷矩阵明显向0或1两极方向分化，这就大大有利于对公共因子进行解释。第一公共因子的载荷正向集中于上表为方差最大正交旋转后的因子载荷矩阵明显向0或1两极方向分化，这就大大有利于对公共因子进行解释。第一公共因子的载荷正向集中于X5和XI，而负向集中于X3和X4,说明第一公共因子主要有这四个变量解释。类似地解释第二和第三因子。Factor23.对邮电业和国民经济之间做典型相关分析结果—xlU.bdblx2-0.1859/~Corre-lationsBc-twc-tnthtFactor3-0.163000.96660两组变量之间的相关系数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。.颈&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过程长生的典型相关分析的一般结果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倾gFNu。NunOFDonDFiate-St-atisticsandFApproxira-ations0.00021610U.?62.224785U2.51310.0809236492.7?308.19011051616.386664.32-K-813.A-5Pr>FM.通10.0131<.0001欢0001anuppe-rbound上表显示：第一典型相关系数为0.998382，比邮电业和国民经济两组间任一个相关系数都大。再则，第二典型变量为0的原假设的概率水平为0.0196,故在a=0.05的显著性水平下，第二典型变量的典型相关作用也是明显的。Cancorr过程产生的典型变量的系数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