因子分析报告.docx

1、因子分析报告实验名称：因子分分析一、 实验目的和要求通过上机操作，完成SPSS软件的因子分析二、 实验内容和步骤77R型聚类如图所示选择69尺 e&ortDescriptive StatisticsTablesConipare MeansGeneral Linear ModelGeneralized Linear ModelsMixed ModelsCorrelateRegressionLoqlinerNeural NetworksClassifyDd ReductionScaleNonparametric TestsTime SeriesSurvival将6个变量选入变量框中分别点击desc

2、riptive rotation选项，进行以下操作lj! Factor Analysis: Demeri.StatisticsUnivariarte descriptives|V Initial solutionBloefficienteInverseJ Reproduced| Anti-imageCorrelation MatrixSignificance IseJs|V DeterminantV KMO and Bartletts test of sphericitySijritiriuHCancelHelp点击 extract ion点击 opti onsMissinyVdkies-Ex

3、clude cases listwise. . .Exclude cases pairwiseReplace with mean-Coefficient Display Format Hported by size| Suppress absolute values Jess then:ContinueCancelHelp结果如下所示Correlation Matrix数学物理化学语文历史英语Correlation 数学物理化学语文历史英语1.000.426.527-.464-.356-.296.4261.000.345 -.307 -.285 -.235.527.3451.000-.391-

4、.290-.136-.464-.307-.3911.000.778.810-.356-.285-.290.7781.000.820-.296-.235-.136.810.8201.000Sig. (1-tailed) 数学物理化学语文历史英语.009.001.005.027.056.009.031.050.064.105.001.031.016.060.237.005.050.016.000.000.027.064.060.000.000.056.105.237.000.000a. Determinant = .037上表为相关矩阵，给出了 6个变量之间的相关系数。主对角线系数都为 1从 表中

5、我们可知，变量与变量之间有的会高度相关，有的相关性比较低，语文与历史，语文与英语，英语与历史都是高度相关的，其他的相关度较低KMO and Bartletts TestKaiser-Meyer-Olkin Measure of Sampling Adequacy.755Bartletts Test of Sphericity Approx. Chi-Square86.576df15Sig.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，由于KMO=0.755表明此时一般适合做因子分析。CommunalitiesInitia

6、lExtraction数学1.000.812物理1.000.876化学1.000.670语文1.000.886历史1.000.876英语1.000.897ExtractionComponeMethod: Pi nt Analysis.incipal上表为公因子方差，给出了该次分析中从每个原始变量中提取的信息，从表中 可以看出除了化学外，主成分几乎都包含了其余各个变量至少 80%的信息,Total Variance ExplainedComponentInitial EigenvaluesExtraction Sums of SquaredLoadingsRotation Sums of Squ

7、aredLoadingsTotal% ofVarianceCumulative%Total% ofVarianceCumulative%Total% ofVarianceCumulative%13.23853.97253.9723.23853.97253.9722.57242.86142.86121.27721.28875.2601.27721.28875.2601.94432.40075.2603.68111.34686.6074.4587.63494.2405.2123.52697.7676.1342.233100.000Extraction Method: Principal Compo

8、nent Analysis.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 2个主成分，集中了原始变量总信息的75.260%Scree PlotComponent Number上图为碎石土，分析碎石土看出因子1与因子2的特征值差值比较大，而其他特 征值比较小，可以出保留2个因子能概括绝大部分信息。Component MatrixaComponent语文 历史 英语 数学 物理 化学Extraction Method: Principal Component Analysis.a. 2 components extracted.从因子载荷矩阵表中

9、可以看出，需要对因子载荷阵进行旋转,Rotated Component Matrix aComponent12英语.953-.072历史.904-.209语文.867-.335化学-.099.815数学-.245.795物理-.152.698经过旋转后的载荷系数已经明显地两极分化了。第一个公共因子在前三个指标 上有较大载荷，说明这三个指标有较强的相关性，可以归为一类，所以把英语, 历史，语文作为属于文科学习能力的指标；第二个公共因子在后三个指标上有 较大载荷，所以化学，数学，物理属于理科学习能力的指标。Component Plot in R戦ated Space以上是因子载荷图，可以看出因子的

10、聚集性，理科的指标聚集在一起，文科的 指标也聚集在一起，分类效果非常好。Component Score CoefficientMatrixComponent12数学.064.439物理.085.400化学.137.484语文.332-.014历史.378.073英语.432.169由上表可知F1 =0.064X1 0.085X2 0.137X3 0.332X4 0.378X5 0.432X6F2 =0.439X1 0.400X2 0.484X3 0.014X4 0.073X5 0.169X6所以可以把每个学生的六门成绩分别代入 F1、F2,比较两者的大小，F1大的适合学文科，F2大的适合学理科

11、。计算结果为学号是1、16、24的学生适合学文，其余均适合学理Q型聚类如图所示进行选择，抽 Factor Analysis： DescriptiveStatlsti cs 1Univartate descriptives Initial solution-Correlation Matrtx 4s Coefficients 巫 Inverse m Significance levels Reproduced J Determinant 門 Antf-imageJ kmo and Bartletts test of sphericityContinueCanceJX H曲直 Factor Ana

12、lysis: ExtractionMethod: Principal components -Analyze Correlation matrixO Covariance matrix-Display 了 Un rotated factor solution:* XjScree ploExtrsct Based on EigenvalueEigenvalues greater than: 1 O Fixed number of factorsFactors to extract:Maximum Iteratio ns for Con verge nee: 25ContinueQ Factor

13、Analysis: Factor Scores/ Save as variablesMethod RegrGSSion BartlettAnderson-RubinS?Display factor score coefficient matrixFactor Analysis: RotationQ Factor Analysis: Options-Missing Values Exclude cases listwise O Exdude cases pairwise Replace with memnCoefficient Display Format SliSorted by sizetS

14、uppress small coefficientsAbsolute value below:Continue结果如下11 9Mj商.-IK!TW-113-flu2WZ4-SM-IUwm-412-4M5K.0Mm4VZ-jcr919*.tnIT?倔TW193号曲爼血站14M缨-dJi甜-4li-J4如U科144-EAJ4tJJH1她inI-jIMJUJ4I-JJ7W M7心划JOidra 1141-j&i凹-44J-.4X1-JliMJ:-$-JH-9S34M2M-44)IJM-OMrrfEMTit3f)flit.9捷巒-91191J9IM他i am-W冬閩srr419424II421JW-.

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20、ia-46J1-1 HIdbm-74J.714皿IftDi?13討j15irr2加U31BM3 -25-J6LJ22L.7131JM0m相关性矩阵是主对角线为 1的矩阵，可以看出因子之间相关性不是特别的大。Communalities起始擷取11.0001.00021.0001.00031.0001.00041.0001.00051.0001.00061.0001.00071.0001.00081.0001.00091.0001.000101.0001.000111.0001.000121.0001.000131.0001.000141.0001.000151.0001.000161.0001.

21、000171.0001.000181.0001.000191.0001.000201.0001.000211.0001.000221.0001.000231.0001.000241.0001.000251.0001.000261.0001.000271.0001.000281.0001.000291.0001.000301.0001.000擷取方法：主體元件分析上表反映了公因子方差，每个同学原始变量提取到达 1因子提取达到1.說明的變異數總計元起始特徵值擷取平方和載入循環平方和載入總計變異的%累加%總計變異的%累加%總計變異的%累加%15.65652.18852.18815.65652.18852.18815.01050.03250.0326.14020.46772.6556.14020.46772.6554.48714.95564.9873.60312.00984.6643.60312.00984.6644.43214.77379.7602.8999.66494.3282.8999.66494.3283.86012.86592.6251.7015.672100.0001.7015.672100.0002.2127.375100.0001.625E-155.417E-15100.000