实验名称:主成分
分析
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一、实验目的和要求通过上机操作,完成SPSS软件的主成分分析二、实验内容和步骤araiTor女口图所示点击analyze-datareduction-factorAnalyzeCraphsUtilitiesAdd-onsv^ndawHelpReportsDsscriptiveStatisticsTablesX3X4CoiTipareWeans14.245.57GeneralLinearModel12051439GeneralizedLinearModels9.G317.35MixecIModels6.8310.66Correlsle陟areS3ion6.8914.89Loglinear9.3511.19NeuralNetworks9.7512.39Classity10.001000DataReductionScaleNonpsrametricTestsliiTieSeriesiiiEarfh...CorrespondenceArialysis...OptimalScaling...r773IBIT)将6个变量选入变量框中33FactorAnalysis晶地区Options...Variables:XIK2X3X4X5xeSele^onVerieble:OKPasteResetCancelHelp分别点击descriptiverotation选项,进行以下操作FactorAnalysis;Desczi...X盅IFactorAnalysis;Rotjalion区rMethodStalisllcs□Univaridedescriptive^冋InitialsoluiionrCorrelationMatrix回Coefficianrtsr~|Siflnifio^ncelevelsIIDetatminantInverseReproducedr~|朗e®NoneOyorODirectObliminD<a:[orDisplayOGuartima:xOEquamaxOPromaxK5(5pa?0RotetedsolutionQ卜抽凹曲⑻]MaAiiTiLjmtteradionstorConvergence:〔25HelpIContinueCancelHelp点击extraction进行以下分析SaFactorAnalysis:ExtractionMethoctPrinoi卩日1component:?DisplayAna阿n7iiCorrelationmartrix■1—0UnrolledfactorsoliticnCoiori^ncemstrix--EKtractii^jiEigenvaluesover:f11Numberoffactors:J、■Magnum(terertionsfcrCorvergence;25ContinueCancelHe|)点击options越FactorAnalysis:Options结果如下所示CorrelationMatrixX1X2X3X4X5X6CorrelationX1.711.420.182.081X2.711.141.275.302X3.420.141.028.353X4.182.275.028.384.042X5.081.302.384.104X6.353.042.104上
表
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为相关矩阵,给出了6个变量之间的相关系数主对角线的值均为1,绝大大部分小于,因此可以说明因子之间相关性不是特别的大。KMOandBartlett'sTestKaiser-Meyer-OlkinMeasureofSamplingAdequacy..434Bartlett'sTestofApprox.Chi-SquareSphericitydf15Sig..000上表为KM和Bartlett检验表,KM检验是对变量是否适合做因子分析的检验,根据Kaiser常用度量
标准
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,因为此时KMO=$示此事不适合做因子分析,所以我们用主成分分析。CommunalitiesInitialExtractionX1.911X2.785X3.835X4.585X5.744X6.859ExtractionMethod:PrincipalComponentAnalysis.上表额为公因子方差,给出了盖茨分析中从每个原始变量中提取的信息,从表中可以看出除了人均城市道路面积X4(平方米),主成分几乎都包含了其余各个变量至少80%勺信息。TotalVarianceExplainedComponentInitialEigenvaluesExtractionSumsofSquaredLoadingsTotal%ofVarianceCumulative%Total%ofVarianceCumulative%12.665.442.174ExtractionMethod:PrincipalComponentAnalysis.上表为特征根于方差贡献表,给出了个主成分解释原始变量总方差的情况,从表中可以看出,本例中保留了3个主成分,集中了原始变量总信息的%Dl.O^25■O-J—134ComponentNumber上图为碎石土,分析碎石土看出因子1与因子2与因子3特征值差值比较大,而其他特征值比较小,可以出保留3个因子能概括绝大部分信息。ComponentMatrixaComponent123X2.861X1.840.236X4.528.376X3.402.801.179X5.440.462X6.024.434.819ExtractionMethod:PrincipalComponentAnalysis.a.3componentsextracted.以上为因子载荷矩阵,包含了3个特征向量。可以根据这个计算主成分,例如,X1=o令Zi为第i个主成分的变量系数向量,Z1=a1/squrt,以此类推Z2,Z3a3a2z1z2z30.77D車-035086D.11-0210G4-039D.360.340.340.290.61■D.S40.28-D020.290.83-.0223.沟67.2641-5125-31.32.5235-.31.53.09.13可以对Z排序做综合排序指标,并作结果说明。Component123X1.954.027.015X2.808.364X4.171.803.109X3.481.732X5.064.916X6.165.884aRotatedComponentMatrix说明这两以上为旋转后矩阵,第一个公共因子在前两个指标上有较大载荷,个指标有较强的相关性,可以归为一类Component1231.785.616.0582.480.5713.421.819通过相加对角线元素,判断是正交矩阵ComponentScoreCoefficientMatrixComponent123X1.528X2.413.125X4.471.114X3.254.507X5.540X6.172.690ComponentTransformationMatrixExtractionMethod:PrincipalComponentoAnalysis.RotationMethod:VarimaxwithKaiserNormalization.ComponentScores.可知F1=+