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因素分析
Factor Analysis
因素分析主要目的是希望將資料的共變異數結構能夠用少數的"因素(factor)"來表達。 雖然因素分析中的因素負荷(factor loading)可由主成分分析中獲取,但和主成分分析的 目的與理論仍有相當程度的差異。此類方法一般區分為探索性因素分析(Exploratory Confirmatory FA, EFA) 與驗證性因素分析(Confirmatory FA, CFA),當你對於模式中欲萃取的因素個數以及變數間的影響參數未明時稱為探索性因素分析, 可應用於大部份的研究。驗證性因素分析則是指分析人員應用資料來分析已存在的模式(如其它學者所提出的模式假設),藉以驗證模式的正確性。此處所提供的方法主要為探索性因素分析I,欲使用驗證性因素分析,可連結至結構方程模式(Structure Equation Modeling, SEM)

I:本方法使用資料的相關矩陣為分析基礎,以避變數免單位的差異過大影響分析結果。

本方法使用之R相關套件與參考文獻:
相關套件:stats、base、graphics、psych、GPArotation
參考文獻:(依套件名稱排序)
  1. R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL:http://www.R-project.org/.
  2. Revelle, W. (2013) psych: Procedures for Personality and Psychological Research, Northwestern University, Evanston, Illinois, USA. URL:http://CRAN.R-project.org/package=psych Version = 1.4.2.
  3. Bernaards, Coen A. and Jennrich, Robert I. (2005) Gradient Projection Algorithms and Software for ArbitraryRotation Criteria in Factor Analysis, Educational and Psychological Measurement: 65, 676-696. URL:http://www.stat.ucla.edu/research/gpa
範例F-5:

數學家高斯曾說過”數學為科學之母”,數學的希臘語辭源為”學問的基礎”(取自維基百科),由此可見數學的重要性。某中學老師欲了解學生的數學能力,以Holzinger & Swineford (1939)之問卷對該校七、八年級學生進行智力測驗分析。問卷含五種構念I (空間、語言、速度、記憶及數學能力)並以24道試題呈現。隨機抽取145名七、八年級學生為施測對象協助完成測驗。資料包含性別、年齡(年)、年齡(月)、24道試題成績與年級,記錄如下表,資料說明於表後。

表:智力測驗分析表
編號 性別 年齡(年) 年齡(月) t1 t2 t3 t4 t5 ... t23 t24 年級
1 1 13 0 23 19 13 4 46 ... 11 17 7
2 2 11 10 33 22 12 17 43 ... 31 32 7
3 1 12 6 34 24 14 22 36 ... 21 18 7
145 1 13 5 26 24 16 27 51 ... 31 29 8
性別:男性(1)、女性(2)
年級:七年級(7)、八年級(8)
註I:題1-4衡量空間概念、題5-9衡量語言、題10-13衡量速度、題14-19衡量記憶、題20-24衡量數學能力

Q1:該中學教師認為由於年代的差異,此世代的學生可能因為學習環境的改變對於問卷中的構念可能有所影響,而有不同的解讀方式,希望針對問卷結果分析是否有新的構念或不同的解釋,該如何分析?
問題解析欲將資料中24個試題進一步區分出不同的構念,須量測問卷中的試題特性及將具相似特性的試題歸納並產生新的構念群,且此構念群足以代表問卷中原有的試題,適合使用維度縮減的分析方法。
統計方法綜合問題解析中的說明,所使用的統計方法須包含具有量測資料特性能力及維度縮減的方法。可採用分析方法:主成份分析(PCA)或探索性因素分析(EFA)。
因素分析 - 分析結果
  • 分析方法:因素分析
  • 資料名稱:範例F-5
  • 變數名稱:t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14, t15, t16, t17, t18, t19, t20, t21, t22, t23, t24
  • 因素選取方法:主成份法(PCA)
  • 轉軸方式:不轉軸
  • 計算時間:0.402秒

  • 樣本敘述統計量I
    變數名稱
    Variable
    樣本數
    Count
    平均數
    Mean
    中位數
    Median
    最小值
    Minimum
    最大值
    Maximum
    標準差
    Std. dev.
    t114529.57933011516.9138
    t214524.8259374.445
    t314514.3034146232.8218
    t414515.9655153368.317
    t514544.848344168411.6579
    t61459.951791193.3754
    t714518.8483194284.6493
    t814528.22810435.3575
    t914517.2828162417.9475
    t1014590.1793893014923.7822
    t1114568.5931671911816.6635
    t12145109.76551106120020.995
    t13145191.779319111233337.0354
    t14145176.275917713019810.8285
    t1514589.372489731127.5424
    t16145103.4103871196.8011
    t171457.206970264.5688
    t181459.475991204.4738
    t1914515.2414164203.5964
    t2014530.344830-188719.7802
    t2114514.4552152244.8319
    t2214527.731277509.8243
    t2314518.7517191409.3605
    t2414525.82762611354.7131
    I:樣本敘述統計量皆不包含遺失值

  • 共變異數矩陣:
    t1t2t3t4t5t6t7t8t9t10t11t12t13t14t15t16t17t18t19t20t21t22t23t24
    t147.80110.01257.260525.797926.4087.97269.935712.077817.425317.131535.251244.6507124.65659.707111.616119.71815.337611.49326.643949.243312.380328.101330.32548.9061
    t210.012519.75832.387515.416714.25423.42083.29583.71396.87647.015311.17515.67540.80283.93754.51948.74030.22225.15141.763925.88196.306910.237514.19314.3125
    t37.26052.38757.96288.586910.15752.483.48395.04315.83728.618811.645211.724440.65087.63793.95575.89171.64513.31991.572111.76274.52764.44337.65231.5874
    t425.797915.41678.586969.172436.89759.206711.09216.916722.954314.763225.124841.6585114.763214.523512.87416.33335.27812.98875.390354.803616.557531.421233.32479.0982
    t526.40814.254210.157536.8975135.907424.464835.442135.843166.737687.103866.528151.4503148.264932.993519.265214.012511.330213.69088.203592.233217.979350.924247.357922.8348
    t67.97263.42082.489.206724.464811.393511.27739.412519.166516.765720.22337.356739.308710.46486.33756.61674.25312.50923.046528.91954.29312.910513.66156.8875
    t79.93573.29583.483911.09235.442111.277321.615715.759725.32128.069119.208719.311461.230211.73665.51526.34585.32333.82274.036942.16387.062618.292217.75379.6403
    t812.07783.71395.043116.916735.84319.412515.759728.702822.852837.783326.213932.658380.370814.07646.862510.88476.6256.07085.034745.59729.338919.116724.77929.8125
    t917.42536.87645.837222.954366.737619.166525.32122.852863.162533.768438.025620.212679.993421.504812.782912.754210.35087.84377.903570.978210.446838.389136.883215.6463
    t1017.13157.01538.618814.763287.103816.765728.069137.783333.7684565.5926185.2957293.1257368.435740.422426.90522.156932.740433.136317.01276.15346.174836.187556.829559.3367
    t1135.251211.17511.645225.124866.528120.223319.208726.213938.0256185.2957277.6736147.64325.312458.446429.965135.622227.188924.68817.362867.064931.915751.896739.141332.2905
    t1244.650715.67511.724441.658551.45037.356719.311432.658320.2126293.1257147.64440.7919410.822929.641525.886518.309726.673932.1618.1195104.595336.197741.853269.434440.9385
    t13124.656540.802840.6508114.7632148.264939.308761.230280.370879.9934368.4357325.3124410.82291371.617677.582138.568969.783332.254353.633533.6023181.375277.1081105.5652132.965762.3089
    t149.70713.93757.637914.523532.993510.464811.736614.076421.504840.422458.446429.641577.5821117.256731.597928.104218.40789.098.516366.18899.540226.53325.423115.0271
    t1511.61614.51943.955712.87419.26526.33755.51526.862512.782926.90529.965125.886538.568931.597956.888116.065311.936310.34244.97239.25268.461318.191117.81535.7174
    t1619.71818.74035.891716.333314.01256.61676.345810.884712.754222.156935.622218.309769.783328.104216.065346.255610.548610.78756.208352.993111.636119.455622.58618.6597
    t175.33760.22221.64515.27811.33024.25315.32336.62510.350832.740427.188926.673932.254318.407811.936310.548620.87369.09535.380325.17124.169113.278312.82957.3831
    t1811.49325.15143.319912.988713.69082.50923.82276.07087.843733.136324.68832.16153.63359.0910.342410.78759.095320.0155.787126.82787.6514.594211.02878.5687
    t196.64391.76391.57215.39038.20353.04654.03695.03477.903517.01217.36288.119533.60238.51634.9726.20835.38035.787112.934412.10375.757412.252910.03956.3336
    t2049.243325.881911.762754.803692.233228.919542.163845.597270.978276.15367.0649104.5953181.375266.188939.252652.993125.171226.827812.1037391.255338.855892.683795.384834.4071
    t2112.38036.30694.527616.557517.97934.2937.06269.338910.446846.174831.915736.197777.10819.54028.461311.63614.16917.655.757438.855823.346917.755220.231810.204
    t2228.101310.23754.443331.421250.924212.910518.292219.116738.389136.187551.896741.8532105.565226.53318.191119.455613.278314.594212.252992.683717.755296.517446.703617.495
    t2330.325414.19317.652333.324747.357913.661517.753724.779236.883256.829539.141369.4344132.965725.423117.815322.586112.829511.028710.039595.384820.231846.703687.618519.0194
    t248.90614.31251.58749.098222.83486.88759.64039.812515.646359.336732.290540.938562.308915.02715.71748.65977.38318.56876.333634.407110.20417.49519.019422.2131

  • 相關係數矩陣:
    t1t2t3t4t5t6t7t8t9t10t11t12t13t14t15t16t17t18t19t20t21t22t23t24
    t110.32580.37210.44860.32760.34160.30910.32610.31710.10420.3060.30760.48680.12970.22280.41930.1690.37160.26720.36010.37060.41370.46860.2733
    t20.325810.19030.4170.27510.2280.15950.1560.19470.06640.15090.1680.24790.08180.13480.28910.01090.2590.11030.29440.29360.23440.34110.2058
    t30.37210.190310.36590.30880.26040.26550.33360.26030.12840.24770.19790.3890.250.18590.3070.12760.2630.15490.21070.33210.16030.28970.1194
    t40.44860.4170.365910.38050.32790.28690.37970.34730.07460.18130.23860.37260.16130.20520.28880.13890.34910.18020.33310.4120.38460.42810.2321
    t50.32760.27510.30880.380510.62170.65390.57390.72030.31420.34250.21020.34340.26140.21910.17670.21270.26250.19570.40.31920.44460.4340.4156
    t60.34160.2280.26040.32790.621710.71860.52050.71450.20890.35950.10380.31440.28630.24890.28820.27580.16620.2510.43310.26320.38930.43240.4329
    t70.30910.15950.26550.28690.65390.718610.63270.68530.25390.24790.19780.35560.23310.15730.20070.25060.18380.24140.45850.31440.40050.4080.4399
    t80.32610.1560.33360.37970.57390.52050.632710.53670.29650.29360.29030.40510.24260.16980.29870.27070.25330.26130.43030.36080.36320.49410.3886
    t90.31710.19470.26030.34730.72030.71450.68530.536710.17870.28710.12110.27180.24990.21320.2360.28510.22060.27650.45150.2720.49170.49580.4177
    t100.10420.06640.12840.07460.31420.20890.25390.29650.178710.46760.58710.41830.1570.150.1370.30130.31140.19890.16190.40180.15490.25530.5294
    t110.3060.15090.24770.18130.34250.35950.24790.29360.28710.467610.4220.52710.32390.23840.31430.35710.33120.28970.20350.39640.3170.25090.4112
    t120.30760.1680.19790.23860.21020.10380.19780.29030.12110.58710.42210.52830.13040.16350.12820.27810.34240.10750.25190.35680.20290.35330.4137
    t130.48680.24790.3890.37260.34340.31440.35560.40510.27180.41830.52710.528310.19350.13810.2770.19060.32370.25230.24760.43090.29010.38360.357
    t140.12970.08180.250.16130.26140.28630.23310.24260.24990.1570.32390.13040.193510.38690.38160.37210.18760.21870.3090.18230.24940.25080.2944
    t150.22280.13480.18590.20520.21910.24890.15730.16980.21320.150.23840.16350.13810.386910.31320.34640.30650.18330.26310.23220.24550.25230.1608
    t160.41930.28910.3070.28880.17670.28820.20070.29870.2360.1370.31430.12820.2770.38160.313210.33950.35450.25380.39390.35410.29120.35480.2702
    t170.1690.01090.12760.13890.21270.27580.25060.27070.28510.30130.35710.27810.19060.37210.34640.339510.4450.32740.27850.18890.29580.30.3429
    t180.37160.2590.2630.34910.26250.16620.18380.25330.22060.31140.33120.34240.32370.18760.30650.35450.44510.35970.30320.35390.3320.26340.4064
    t190.26720.11030.15490.18020.19570.2510.24140.26130.27650.19890.28970.10750.25230.21870.18330.25380.32740.359710.17010.33130.34680.29820.3737
    t200.36010.29440.21070.33310.40.43310.45850.43030.45150.16190.20350.25190.24760.3090.26310.39390.27850.30320.170110.40650.47690.51520.3691
    t210.37060.29360.33210.4120.31920.26320.31440.36080.2720.40180.39640.35680.43090.18230.23220.35410.18890.35390.33130.406510.3740.44730.4481
    t220.41370.23440.16030.38460.44460.38930.40050.36320.49170.15490.3170.20290.29010.24940.24550.29120.29580.3320.34680.47690.37410.50790.3778
    t230.46860.34110.28970.42810.4340.43240.4080.49410.49580.25530.25090.35330.38360.25080.25230.35480.30.26340.29820.51520.44730.507910.4311
    t240.27330.20580.11940.23210.41560.43290.43990.38860.41770.52940.41120.41370.3570.29440.16080.27020.34290.40640.37370.36910.44810.37780.43111

  • 特徵值及解釋變異比例表I
    編號特徵值
    eigenvalue
    解釋變異比例
    Proportion of var.
    累積特徵值
    Cumulative eigenvalue
    累積解釋變異比例
    Cumulative proportion of var.
    18.23880.34338.23880.3433
    22.03070.084610.26950.4279
    31.65220.068811.92170.4967
    41.53280.063913.45450.5606
    51.09050.045414.5450.606
    60.94380.039315.48880.6454
    70.80130.033416.29010.6788
    80.79110.03317.08120.7117
    90.7340.030617.81520.7423
    100.69940.029118.51460.7714
    110.61420.025619.12880.797
    120.58440.024319.71320.8214
    130.52360.021820.23680.8432
    140.50450.02120.74130.8642
    150.47610.019821.21730.8841
    160.44670.018621.66410.9027
    170.35960.01522.02360.9177
    180.34960.014622.37320.9322
    190.34090.014222.71420.9464
    200.33320.013923.04740.9603
    210.28990.012123.33720.9724
    220.26580.011123.6030.9835
    230.20770.008723.81070.9921
    240.18930.0079241
    I:選取因素個數,通常建議所選之因素其特徵值大於1

  • 陡坡圖(scree plot)I

    I:選取因素個數,通常建議所選之因素其特徵值大於1

  • 因素負荷(loadings)及解釋變異表(未轉軸):
    變數因素負荷
    主成份1主成份2主成份3主成份4主成份5
    t10.6070.04960.4229-0.14790.0168
    t20.4048-0.01990.4902-0.2016-0.1862
    t30.47080.02820.3036-0.11350.5655
    t40.57-0.08280.4625-0.1912-0.0094
    t50.7009-0.3863-0.1977-0.1340.0872
    t60.6851-0.4569-0.19990.03810.1096
    t70.681-0.4569-0.2874-0.09890.0657
    t80.6882-0.248-0.1508-0.12990.1246
    t90.6939-0.5061-0.19340.026-0.0186
    t100.48180.4716-0.49-0.2247-0.0103
    t110.58360.3705-0.2237-0.00690.214
    t120.49590.5246-0.1744-0.34530.0169
    t130.62610.29680.0212-0.37520.2526
    t140.44840.0655-0.05370.53520.3374
    t150.41310.13010.12130.50170.1811
    t160.5340.1420.34980.34540.1143
    t170.49220.2473-0.21810.5077-0.0522
    t180.55120.3770.14330.1597-0.1986
    t190.46550.145-0.04070.249-0.3049
    t200.6373-0.18480.13390.116-0.1879
    t210.63280.240.1362-0.1733-0.1219
    t220.6399-0.14250.09680.1126-0.3451
    t230.7058-0.09440.1477-0.0613-0.1932
    t240.66040.162-0.3269-0.0299-0.2907
    解釋變異8.23882.03071.65221.53281.0905
    解釋變異比例0.34330.08460.06880.06390.0454
    累積解釋變異比例0.34330.42790.49670.56060.606

  • 變數共通性(communality)表:
    變數取1個因素取2個因素取3個因素取4個因素取5個因素
    t10.36840.37090.54970.57160.5719
    t20.16380.16420.40450.44510.4798
    t30.22170.22250.31470.32760.6474
    t40.32490.33180.54570.58220.5823
    t50.49130.64050.67950.69750.7051
    t60.46930.6780.7180.71950.7315
    t70.46370.67250.75510.76490.7692
    t80.47360.53510.55790.57480.5903
    t90.48150.73760.7750.77570.776
    t100.23210.45450.69460.74510.7452
    t110.34060.47780.52790.52790.5737
    t120.24590.52110.55160.67080.6711
    t130.3920.48010.48050.62130.6851
    t140.2010.20530.20820.49470.6085
    t150.17070.18760.20230.4540.4868
    t160.28520.30540.42770.5470.5601
    t170.24230.30340.3510.60880.6115
    t180.30380.44590.46640.4920.5314
    t190.21670.23770.23940.30140.3943
    t200.40610.44020.45820.47160.5069
    t210.40050.45810.47660.50660.5215
    t220.40950.42980.43910.45180.5709
    t230.49810.5070.52880.53260.5699
    t240.43610.46230.56920.57010.6546

  • 模式適合度分析III
    卡方檢定統計量
    Chi-squared statistic
    自由度
    d.f.
    p-值
    p-value
    259.57481660
    I:使用主成份法(PCA)
    II:虛無假設:所選的因素其獨特性皆為0


    殘差矩陣

    變數t1t2t3t4t5t6t7t8t9t10t11t12t13t14t15t16t17t18t19t20t21t22t23t24
    t10.4281-0.1529-0.0698-0.117-0.01630.03680.0242-0.03690.007-0.03750.02340.0030.0233-0.0495-0.0146-0.01060.0261-0.01530.0366-0.0539-0.10660.0139-0.02340.0032
    t2-0.15290.5202-0.0661-0.08240.06980.06770.0079-0.05660.00030.07370.0702-0.0033-0.03870.09870.0456-0.00480.0161-0.0316-0.0618-0.0445-0.0821-0.1164-0.06710.0419
    t3-0.0698-0.06610.3526-0.057-0.0148-0.0462-0.0033-0.02280.020.0173-0.0915-0.0462-0.1061-0.0767-0.0946-0.08010.04220.07970.1447-0.00530.03520.04160.01750.0641
    t4-0.117-0.0824-0.0570.41770.01570.0004-0.02450.01290.00410.0226-0.01650.0142-0.03890.04150.022-0.09860.07620.0285-0.0096-0.0869-0.0261-0.0185-0.06390.0119
    t5-0.01630.0698-0.01480.01570.2949-0.0789-0.0757-0.06240.00530.03260.0127-0.0169-0.04890.00410.0552-0.0373-0.00730.0889-0.0227-0.0597-0.01730.0054-0.0593-0.028
    t60.03680.0677-0.04620.0004-0.07890.2685-0.0175-0.1031-0.02970.0060.0611-0.01980.012-0.0590.01060.0315-0.00570.00510.0141-0.0449-0.0135-0.0613-0.04120.0222
    t70.02420.0079-0.0033-0.0245-0.0757-0.01750.2308-0.0137-0.0703-0.0211-0.05930.01450.0173-0.02690.0080.02910.01930.05070.02360.00240.0231-0.0387-0.0667-0.0136
    t8-0.0369-0.0566-0.02280.0129-0.0624-0.1031-0.01370.4097-0.0898-0.0199-0.07740.0059-0.0292-0.0303-0.02130.04980.03280.03460.04110.0046-0.002-0.04030.0234-0.0427
    t90.0070.00030.020.00410.0053-0.0297-0.0703-0.08980.224-0.00610.03050.01810.0061-0.04610.0062-0.0020.01230.04880.0069-0.0648-0.017-0.0151-0.0152-0.0264
    t10-0.03750.07370.01730.02260.03260.006-0.0211-0.0199-0.00610.2548-0.0973-0.0621-0.09460.00750.06360.0629-0.0457-0.0278-0.06090.03170.0103-0.0170.0164-0.0351
    t110.02340.0702-0.0915-0.01650.01270.0611-0.0593-0.07740.0305-0.09730.4263-0.1067-0.0001-0.0426-0.05910.0062-0.0559-0.05450.0222-0.029-0.00650.0926-0.052-0.0454
    t120.003-0.0033-0.04620.0142-0.0169-0.01980.01450.00590.0181-0.0621-0.10670.3289-0.06790.04340.0817-0.03270.0424-0.0452-0.11540.0993-0.11690.02190.0607-0.0612
    t130.0233-0.0387-0.1061-0.0389-0.04890.0120.0173-0.02920.0061-0.0946-0.0001-0.06790.31490.01-0.0193-0.00610.0174-0.02620.0891-0.0084-0.07370.0591-0.0076-0.0354
    t14-0.04950.0987-0.07670.04150.0041-0.059-0.0269-0.0303-0.04610.0075-0.04260.04340.010.3915-0.13-0.0718-0.1307-0.095-0.03210.04390.02410.03320.04650.0842
    t15-0.01460.0456-0.09460.0220.05520.01060.008-0.02130.00620.0636-0.05910.0817-0.0193-0.130.5132-0.1623-0.108-0.0318-0.0927-0.01650.032-0.00610.0209-0.0258
    t16-0.0106-0.0048-0.0801-0.0986-0.03730.03150.02910.0498-0.0020.06290.0062-0.0327-0.0061-0.0718-0.16230.4399-0.0516-0.0759-0.05230.01440.0082-0.0636-0.01710.0524
    t170.02610.01610.04220.0762-0.0073-0.00570.01930.03280.0123-0.0457-0.05590.04240.0174-0.1307-0.108-0.05160.38850.0203-0.0887-0.0289-0.0707-0.0380.0292-0.0935
    t18-0.0153-0.03160.07970.02850.08890.00510.05070.03460.0488-0.0278-0.0545-0.0452-0.0262-0.095-0.0318-0.07590.02030.4686-0.046-0.0534-0.1014-0.0673-0.1398-0.0247
    t190.0366-0.06180.1447-0.0096-0.02270.01410.02360.04110.0069-0.06090.0222-0.11540.0891-0.0321-0.0927-0.0523-0.0887-0.0460.6057-0.18040.0135-0.0598-0.0542-0.0517
    t20-0.0539-0.0445-0.0053-0.0869-0.0597-0.04490.00240.0046-0.06480.0317-0.0290.0993-0.00840.0439-0.01650.0144-0.0289-0.0534-0.18040.49310.0266-0.048-0.001-0.0292
    t21-0.1066-0.08210.0352-0.0261-0.0173-0.01350.0231-0.002-0.0170.0103-0.0065-0.1169-0.07370.02410.0320.0082-0.0707-0.10140.01350.02660.4785-0.0324-0.0309-0.0048
    t220.0139-0.11640.0416-0.01850.0054-0.0613-0.0387-0.0403-0.0151-0.0170.09260.02190.05910.0332-0.0061-0.0636-0.038-0.0673-0.0598-0.048-0.03240.4291-0.0313-0.087
    t23-0.0234-0.06710.0175-0.0639-0.0593-0.0412-0.06670.0234-0.01520.0164-0.0520.0607-0.00760.04650.0209-0.01710.0292-0.1398-0.0542-0.001-0.0309-0.03130.4301-0.0294
    t240.00320.04190.06410.0119-0.0280.0222-0.0136-0.0427-0.0264-0.0351-0.0454-0.0612-0.03540.0842-0.02580.0524-0.0935-0.0247-0.0517-0.0292-0.0048-0.087-0.02940.3454

  • 分數表(下載完整CSV檔):
    觀察值主成份1主成份2主成份3主成份4主成份5
    1-1.319-0.7665-0.61350.62051.2332
    2-0.06720.23990.34540.2581-1.3819
    3-0.3419-1.50651.5778-0.5131-0.4854
    4-0.50040.6217-0.4445-1.1765-2.7142
    50.0229-0.3853-1.46940.7684-0.847
    141-0.8342-0.08110.1349-2.07561.1226
    142-1.04460.7997-0.0254-1.13820.4377
    1431.04050.6338-1.0395-0.69180.9042
    144-0.37030.0449-1.1789-0.33340.6587
    1451.40780.2834-0.581.3278-0.2639

  • 變數及資料與前三個主成份分數散佈圖I,II
    第一、二個主成份:

    第一、三個主成份:

    第二、三個主成份:

    I:圖中黑色數字表示樣本點
    II:圖中紅色數字及箭頭表示變數位置及方向

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