1、. .運(yùn)用因子分析對(duì)問(wèn)題進(jìn)展分析某一新型電子產(chǎn)品有10種不同型號(hào)的5項(xiàng)指標(biāo)(用x1-x5表示)，得到如表1所示數(shù)據(jù)： 表1型號(hào)X1X2X3X4X510.7600.8641.331.437.8721.0691.1711.332.8610.24131.8950.9074.191.3715.15942.8881.0235.892.7223.48452.4131.2315.372.0219.13161.7751.3402.923.7813.72671.5911.4622.803.339.90981.4121.3522.232.749.65990.8730.7711.201.049.643100.891

2、1.1911.572.8812.212試從這些指標(biāo)中提取因子來(lái)對(duì)這10個(gè)型號(hào)的產(chǎn)品進(jìn)展評(píng)價(jià)分析把數(shù)據(jù)導(dǎo)入spss進(jìn)展因子分析得到如下結(jié)果： 表2Descriptive StatisticsMeanStd. DeviationAnalysis NX11.5567.7049810X21.13120.23094310X32.88301.7240210X42.4170.9081210X513.10344.9342410該表格2中5個(gè)原始變量的統(tǒng)計(jì)描述結(jié)果，包括平均值，標(biāo)準(zhǔn)差和分析的個(gè)案數(shù)。 表3Correlation MatrixaX1X2X3X4X5CorrelationX11.000.198.97

3、8.207.918X2.1981.000.097.861-.019X3.978.0971.000.062.927X4.207.861.0621.000.091X5.918-.019.927.0911.000Sig. (1-tailed)X1.292.000.283.000X2.292.395.001.480X3.000.395.432.000X4.283.001.432.401X5.000.480.000.401a. Determinant = .000該表格3上半局部給出的是5個(gè)原始變量的相關(guān)矩陣。下半局部那么給出了每個(gè)相關(guān)系數(shù)的單尾顯著性水平。表格下面給出了相關(guān)系數(shù)矩陣的行列式，Deter

4、minant = .000 表4Inverse of Correlation MatrixX1X2X3X4X5X149.7466.735-52.629-13.2624.492X26.7359.167-15.029-9.1568.761X3-52.629-15.02970.41021.238-19.216X4-13.262-9.15621.23811.110-8.709X54.4928.761-19.216-8.70915.654該表格4是相關(guān)系數(shù)矩陣的逆矩陣。 表5KMO and Bartlett's TestKaiser-Meyer-Olkin Measure of Sampling

5、 Adequacy.450Bartlett's Test of SphericityApprox. Chi-Square51.970df10Sig.000該表5中給出了KMO檢驗(yàn)和Bartlett球度檢驗(yàn)結(jié)果。其中KMO值為0.450，根據(jù)統(tǒng)計(jì)學(xué)家Kaiser給出的標(biāo)準(zhǔn)，KMO取值小于0.6，不太適合因子分析。Bartlett球度檢驗(yàn)給出的相伴概率為0.000，小于顯著性水平0.05，因此拒絕Bartlett球度檢驗(yàn)的零假設(shè)，認(rèn)為適合于因子分析。 表6Anti-image MatricesX1X2X3X4X5Anti-image CovarianceX1.020.015-.015-.0

6、24.006X2.015.109-.023-.090.061X3-.015-.023.014.027-.017X4-.024-.090.027.090-.050X5.006.061-.017-.050.064Anti-image CorrelationX1.604a.315-.889-.564.161X2.315.304a-.592-.907.731X3-.889-.592.471a.759-.579X4-.564-.907.759.270a-.660X5.161.731-.579-.660.562aa. Measures of Sampling Adequacy(MSA)該表6給出了反映像相

7、關(guān)矩陣檢驗(yàn)結(jié)果。從中反映出某些元素絕對(duì)值比較大，說(shuō)明這些變量可能不太適合進(jìn)展因子分析，需要對(duì)這些變量進(jìn)展進(jìn)一步的考慮。 表7munalitiesInitialExtractionX11.000.980X21.000.934X31.000.976X41.000.927X51.000.942該表格7是因子分析初始結(jié)果，第二列是根據(jù)因子分析初始解計(jì)算出的變量共同度，第三列是根據(jù)因子分析最終解計(jì)算出的變量共同度。 表8ponentPhaseInitial EigenvaluesExtraction Sums of Squared LoadingsRotation Sums of Squared Loa

8、dingsTotal% of VarianceCumulative %Total% of VarianceCumulative %Total% of VarianceCumulative %12.94658.91358.9132.94658.91358.9132.87857.56257.56221.81436.28595.1981.81436.28595.1981.88237.63695.1983.1903.80999.0074.042.83499.8415.008.159100.000該表格8是因子分析后因子提取和因子旋轉(zhuǎn)的結(jié)果。 圖9圖9所示公共因子碎石圖。它的橫坐標(biāo)為公共因子數(shù)，縱坐標(biāo)為

9、公共因子的特征值?？梢?jiàn)前面2到3個(gè)公共因子，特征值變化非常明顯，到3個(gè)后，特征值趨于平穩(wěn)。因此說(shuō)明提取2到3個(gè)公共因子可以對(duì)原變量的信息描述有顯著作用。 表10ponent Matrixaponent12X1.986-.084X2.272.927X3.965-.212X4.300.915X5.937-.256該表格10是最終的因子載荷矩陣A。根據(jù)該表格可以如下因子分析模型 X=AF+a即=0.986-0.084=0.272+0.927. . =0.937-0.256 表11Rotated ponent Matrixaponent12X1.977.159X2.037.966X3.988.030X

10、4.068.960X5.971-.019該表格11是按照前面設(shè)定的方差極大法對(duì)因子載荷矩陣旋轉(zhuǎn)后的結(jié)果。 表12ponent Transformation Matrixponent121.970.2442-.244.970該表12輸出的是因子轉(zhuǎn)換矩陣，標(biāo)明了因子提取的方法是主成分分析，旋轉(zhuǎn)的方法是方差極大法。 表13ponent Score Coefficient Matrixponent12X1.336.037X2-.035.518X3.346-.033X4-.024.514X5.343-.059該表格13是因子得分矩陣。這是根據(jù)回歸算法計(jì)算出來(lái)的因子得分函數(shù)的系數(shù)，得到如下因子得分函數(shù)=0

11、.336-0.035+0.346-0.024+0.343=0.037+0.518-0.033+0.514-0.059表14ponent Score Covariance Matrixponent1211.000.0002.0001.000該表格14是因子變量的協(xié)方差矩陣，從中可以看出，不同因子之間的數(shù)據(jù)是0，因而也證實(shí)了2個(gè)因子變量之間是不相關(guān)的。從表8中可知指標(biāo)1和2的奉獻(xiàn)率分別是58.913%，36.285%。兩個(gè)因子累計(jì)方差奉獻(xiàn)率到達(dá)95.198%，因此選取兩個(gè)公共因子。公共因子1所占比重為58.913%95.198%=61.890%，公共因子2所占比重為38.110%。再根據(jù)下表可得型

12、號(hào)x1x2 x3 x4x5 FAC1_1 FAC2_110.760.8641.331.437.87-0.98793-1.1071521.071.1711.332.8610.24-0.761160.3787231.900.9074.191.3715.160.62885-1.1277042.891.0235.892.7223.481.96794-0.1840352.411.2315.372.0219.131.32176-0.0760261.781.3402.923.7813.730.086311.2430071.591.4622.803.339.91-0.297181.3005181.411.35

13、22.232.749.66-0.481740.7245090.870.7711.201.049.64-0.81237-1.54927100.891.1911.572.8812.21-0.664490.39742在spss軟件中pute Variable中輸入公式Z1=FAC1-1*0.6189+FAC2-1*0.3811可以得到z1 再進(jìn)展排序，如下表型號(hào)x1x2 x3 x4x5 FAC1_1 FAC2_1 z1 z210.760.8641.331.437.87-0.98793-1.10715-1.03 921.071.1711.332.8610.24-0.761160.37872-0.33 831.900.9074.191.3715.160.62885-1.12770-0.04 642.891.0235.892.7223.481.96794-0.184031.15 152.411.2315.372.0219.131.32176-0.076020.79 261.781.3402.923.7813.730.086311.243000.53 371.591.4622.803.339.91-0