主成分分析报告

实验名称：主成分分析一、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6.8女口图所示点击analyze-datareduction-factorAnalyzeGraphsUtilitiesAdd-onsWindowHelpReeiortsk移轴■DescriptiveStatistics►TablesCompareMeansCentralLinearModelGeneralizedLinearModelsMixedMod&lsCorrelateRegressionLoglinearNeuralNetworksClassifyDataReductionScaleNonparametricTestsTimeSeriesX3X414.245.5712.0514.899.5317.356.S310.666.0914.899.3511.199.7512.3910.0010.00Factor...配CorrespondenceAnalysis...jhOptimalScaling...7.731G.01将6个变量选入变量框中ContinueCancelHelp1J]kMOandBartlett'stest口于sphericity“IFactorAnalysis:Rotation分别点击descriptiverotation选项，进行以下操作呂量FactorAnalysis:Descri-StatislicsUnivariatedescriptives回Lnrtialsolution-CorrelationMatrix回CoefficientsInverseSignificancelevelsReproducedDeterminantAnti-image点击extraction进行以下分析点击options结果如下所示CorrelationMatrixX1X2X3X4X5X6CorrelationX11.000.711.420.182.081-.166X2.7111.000.141.275.302-.051X3.420.1411.000X4.182.275.028X5.081.302-.142X6-.166-.051.353.0281.000.384.042-.142.3841.000.104.353.042.1041.000上表为相关矩阵，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0.01，因此可以说明因子之间相关性不是特别的大。KMOandBartlett'sTestKaiser-Meyer-OlkinMeasureofSamplingAdequacy.Bartlett'sTestofSphericityApprox.Chi-SquaredfSig..43445.91915.000上表为KMO和Bartlett检验表，KMO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 excel标准偏差excel标准偏差函数exl标准差函数国标检验抽样标准表免费下载红头文件格式标准下载 ，因为此时KMO=0.434，表示此事不适合做因子分析，所以我们用主成分分析。CommunaltiesInitialExtractionX11.000.911X21.000.785X31.000.835X41.000.585X51.000.744X61.000.859ExtractionMethod: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%的信息。TotalVarianceExplainedComponentInitialEigenvaluesExtractionSumsofSquaredLoadingsTotal%ofVarianceCumulative%Total%ofVarianceCumulative%12.08234.69534.6952.08234.69534.69521.39223.19757.8921.39223.19757.89231.24520.75778.6491.24520.75778.6494.66511.09089.7395.4427.36297.1016.1742.899100.000ExtractionMethod: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78.649%ScreePlot2.5-1.5-1.0-oO-aComponentNumber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。ComponentMatrixaComponent123X2.861-.071-.196X1.840.236-.387X4.528-.406.376X3.402.801.179X5.440-.580.462X6.024.434.819ExtractionMethod: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，Xl=0.861al-0.071a2-0.196a3。令Zi为第i个主成分的变量系数向量，Z1=a1/squrt(2.154)，以此类推Z2，Z3a1a2a30.770.46-0.360.860.11-0210.E4-0.390.360.240.84□.290.E1-0.640.2B-0.020.29O.BBz1z2z3-.02.2373.15.67.26.4-1-.51.25.43-.31.32.36-.31.58.09-.19可以对Z排序做综合排序指标，并作结果说明。RotatedComponentMatrixaComponent123X1.954.027.015X2.808.364-.057X4.171.803.109X3.481-.290.732X5.064.916-.102|X6|-.225|.165|.884|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，说明这两个指标有较强的相关性，可以归为一类ComponentTransformationMatrixComponent1231.785.616.0582.480-.666.5713-.391.421.819通过相加对角线元素，判断是正交矩阵。ComponentScoreCoefficientMatrixComponent123X1.528-.090-.048X2.413.125-.075X4-.002.471.114X3.254-.191.507X5-.062.540-.032X6-.200.172.690ExtractionMethod:PrincipalComponentAnalysis.RotationMethod:VarimaxwithKaiserNormalization.ComponentScores.可知F1=0.528X1+0.413X2-0.002X3+0.254X4-0.062X5-0.2X6F2=-0.09X1+0.125X2-0.471X3-0.191X4-0.540X5-0.172X6F3=-0.048X1-0.075X2+0.114X3+0.507X4-0.032X5-0.690X6