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主成份分析
Principal Component Analysis, PCA
主成份分析方法是由英國統計學家皮爾生(Karl Pearson, 1857-1936)所提出,後經由美國統計學家( Harold Hotelling, 1895-1973)加以發展而成為一個社會科學領域(如心理學、教育學)中常使用的統計方法,最近則在基因的研究中經常被應用。此方法主要目的是縮減資料中使用的變數個數,利用尋找變數間不同的線性組合,萃取出具代表性的主成份I,再進一步進行其他統計分析。

I:本方法使用資料的相關矩陣為分析基礎,以避免變數單位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
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/.
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)。
主成份分析 - 分析結果
  • 分析方法:主成份分析
  • 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
  • 計算時間:0.366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:選擇主成份個數,通常建議所選之主成份其特徵值大於1

  • 陡坡圖(scree plot)I

    I:選擇主成份個數,通常建議所選之主成份其特徵值大於1

  • 主成份特徵向量表(eigen vectors):
    變數主成份1主成份2主成份3主成份4主成份5主成份6主成份7主成份8主成份9主成份10主成份11主成份12主成份13主成份14主成份15主成份16主成份17主成份18主成份19主成份20主成份21主成份22主成份23主成份24
    t1-0.21150.0348-0.3290.1195-0.0161-0.1857-0.0550.16890.3936-0.1572-0.2260.1160.28060.1983-0.2335-0.00830.1287-0.3313-0.2803-0.2744-0.1921-0.0129-0.14430.1014
    t2-0.141-0.014-0.38130.16280.17830.2490.1131-0.5952-0.0532-0.18280.14960.2560.0335-0.22530.2937-0.019-0.1125-0.15760.0796-0.1416-0.0113-0.0208-0.12310.0703
    t3-0.1640.0198-0.23620.0917-0.5415-0.2208-0.07050.1144-0.34640.07810.0705-0.12190.3753-0.3927-0.04140.0642-0.1040.14620.1753-0.1653-0.0487-0.09440.0050.0094
    t4-0.1986-0.0581-0.35980.15440.009-0.0016-0.2601-0.0872-0.12410.16660.3179-0.0715-0.45380.3032-0.29610.2019-0.0230.289-0.1372-0.0607-0.1159-0.0470.10460.1406
    t5-0.2442-0.27110.15380.1082-0.08350.0299-0.1671-0.2453-0.01460.07260.0394-0.13790.0768-0.0755-0.0059-0.32640.123-0.1825-0.39110.10170.024-0.3030.4033-0.353
    t6-0.2387-0.32060.1555-0.0307-0.1049-0.03980.0611-0.19590.1133-0.1287-0.16630.1012-0.03860.013-0.13780.3329-0.05050.20170.113-0.0643-0.1920.3699-0.1338-0.5567
    t7-0.2373-0.32060.22360.0799-0.0629-0.0372-0.02440.0362-0.0785-0.1049-0.13810.04420.03750.18140.16310.1694-0.3335-0.19690.084-0.09440.12390.24180.44320.4619
    t8-0.2398-0.17410.11730.1049-0.1193-0.033-0.05330.2705-0.2415-0.08160.01650.1583-0.35620.17050.2726-0.42210.2414-0.10170.2548-0.2629-0.09-0.0526-0.2839-0.0561
    t9-0.2418-0.35510.1504-0.0210.0178-0.0634-0.0984-0.09020.0664-0.004-0.0084-0.04440.0511-0.1719-0.13580.00970.07320.1503-0.17820.24910.4132-0.0765-0.54940.3358
    t10-0.16790.33090.38120.18150.00980.16030.0235-0.0852-0.16960.0396-0.11740.02780.0052-0.1182-0.1264-0.2211-0.26680.1416-0.30790.0271-0.50.1447-0.16190.2068
    t11-0.20330.260.17410.0055-0.2049-0.12560.1961-0.25950.3987-0.0087-0.0076-0.2806-0.2303-0.18930.10140.04790.44540.13230.1209-0.1945-0.00080.04470.17570.238
    t12-0.17280.36810.13570.2789-0.01620.2802-0.19410.18960.1174-0.01020.12320.17030.10660.04410.08410.0555-0.07530.195-0.1415-0.28750.54120.12060.0225-0.2239
    t13-0.21810.2083-0.01650.3031-0.2419-0.1460.05910.05230.2704-0.02890.06760.1066-0.05620.19710.23970.1089-0.2183-0.06310.17580.6089-0.071-0.2434-0.0662-0.0875
    t14-0.15620.0460.0418-0.4323-0.32310.18590.2926-0.0479-0.02580.14410.5205-0.00210.18550.30640.0037-0.03570.0341-0.2137-0.150.0348-0.00010.2286-0.11410.0147
    t15-0.14390.0913-0.0943-0.4052-0.17340.2646-0.3018-0.16670.09980.4587-0.46580.25760.00340.09730.0469-0.0548-0.02620.07060.17150.00030.0075-0.1460.01560.0618
    t16-0.18610.0996-0.2721-0.279-0.10940.02430.35940.0708-0.0559-0.4412-0.2422-0.0228-0.22570.0022-0.1932-0.3251-0.24040.2253-0.09520.08440.2359-0.04120.147-0.0467
    t17-0.17150.17350.1697-0.41010.0499-0.0229-0.31730.1420.0025-0.28950.1770.0699-0.2722-0.3433-0.0350.3247-0.1367-0.3287-0.053-0.0664-0.0821-0.2406-0.0224-0.044
    t18-0.1920.2646-0.1115-0.1290.1902-0.1522-0.4582-0.1468-0.2189-0.2592-0.0459-0.27960.19950.16290.1009-0.12830.2035-0.01540.13640.27120.0250.38650.0042-0.0316
    t19-0.16220.10170.0317-0.20110.292-0.63460.1621-0.0403-0.12390.21690.04880.35270.06450.02910.28140.0309-0.00610.2326-0.2467-0.08210.0286-0.04630.0726-0.0414
    t20-0.222-0.1297-0.1042-0.09370.180.37830.130.2981-0.0597-0.107-0.0981-0.25480.18640.05270.42070.28640.1810.288-0.17490.0302-0.2285-0.21610.0120.0266
    t21-0.22050.1684-0.10590.140.11670.00120.29020.0432-0.31370.367-0.3004-0.2749-0.2217-0.0689-0.04060.23210.0229-0.4332-0.08050.040.20470.1073-0.1195-0.1422
    t22-0.2229-0.1-0.0753-0.09090.3305-0.0501-0.02110.13810.37210.26910.1845-0.3920.0351-0.12020.0397-0.2895-0.44120.02370.2455-0.1496-0.05630.055-0.062-0.087
    t23-0.2459-0.0663-0.11490.04950.1850.16060.07930.31160.04940.13340.13820.39240.0183-0.3761-0.228-0.08520.2993-0.00960.14430.3145-0.07340.26690.26680.0671
    t24-0.23010.11370.25430.02410.27830.03860.1896-0.1292-0.1742-0.07590.05360.02240.28040.2525-0.42240.06680.08140.01320.4174-0.10140.0323-0.42270.03870.0077

  • 主成份負荷(loadings)表:
    變數主成份1主成份2主成份3主成份4主成份5主成份6主成份7主成份8主成份9主成份10主成份11主成份12主成份13主成份14主成份15主成份16主成份17主成份18主成份19主成份20主成份21主成份22主成份23主成份24
    t1-0.6070.0496-0.42290.1479-0.0168-0.1804-0.04920.15020.3373-0.1315-0.17710.08870.20310.1409-0.1611-0.00550.0771-0.1959-0.1637-0.1584-0.1034-0.0067-0.06570.0441
    t2-0.4048-0.0199-0.49020.20160.18620.24190.1012-0.5294-0.0456-0.15290.11720.19570.0243-0.160.2026-0.0127-0.0675-0.09320.0465-0.0817-0.0061-0.0107-0.05610.0306
    t3-0.47080.0282-0.30360.1135-0.5655-0.2145-0.06310.1017-0.29680.06540.0553-0.09320.2716-0.2789-0.02850.0429-0.06240.08650.1023-0.0954-0.0262-0.04870.00230.0041
    t4-0.57-0.0828-0.46250.19120.0094-0.0016-0.2328-0.0776-0.10640.13930.2491-0.0547-0.32840.2153-0.20430.1349-0.01380.1709-0.0801-0.035-0.0624-0.02420.04770.0612
    t5-0.7009-0.38630.19770.134-0.08720.0291-0.1496-0.2182-0.01250.06070.0309-0.10540.0555-0.0536-0.004-0.21820.0738-0.1079-0.22830.05870.0129-0.15620.1838-0.1536
    t6-0.6851-0.45690.1999-0.0381-0.1096-0.03870.0547-0.17420.097-0.1076-0.13030.0774-0.02790.0093-0.09510.2225-0.03030.11930.066-0.0371-0.10340.1907-0.061-0.2422
    t7-0.681-0.45690.28740.0989-0.0657-0.0362-0.02190.0322-0.0673-0.0877-0.10820.03380.02710.12880.11250.1132-0.2-0.11640.049-0.05450.06670.12460.2020.201
    t8-0.6882-0.2480.15080.1299-0.1246-0.032-0.04770.2406-0.2069-0.06830.01290.121-0.25780.12110.1881-0.28210.1448-0.06020.1488-0.1517-0.0484-0.0271-0.1294-0.0244
    t9-0.6939-0.50610.1934-0.0260.0186-0.0616-0.0881-0.08020.0569-0.0034-0.0066-0.03390.037-0.1221-0.09370.00650.04390.0889-0.10410.14380.2225-0.0395-0.25040.1461
    t10-0.48180.47160.490.22470.01030.15570.0211-0.0758-0.14530.0331-0.0920.02120.0038-0.0839-0.0872-0.1477-0.160.0837-0.17980.0156-0.26920.0746-0.07380.09
    t11-0.58360.37050.22370.0069-0.214-0.1220.1756-0.23080.3416-0.0073-0.0059-0.2145-0.1667-0.13440.070.0320.26710.07820.0706-0.1123-0.00040.0230.08010.1036
    t12-0.49590.52460.17440.3453-0.01690.2723-0.17370.16860.1005-0.00850.09660.13020.07710.03130.0580.0371-0.04520.1153-0.0826-0.1660.29140.06220.0103-0.0974
    t13-0.62610.2968-0.02120.3752-0.2526-0.14190.05290.04660.2317-0.02420.0530.0815-0.04070.140.16540.0728-0.1309-0.03730.10270.3515-0.0382-0.1255-0.0302-0.0381
    t14-0.44840.06550.0537-0.5352-0.33740.18060.2619-0.0426-0.02210.12050.4079-0.00160.13420.21760.0026-0.02380.0204-0.1264-0.08760.0201-0.00010.1179-0.0520.0064
    t15-0.41310.1301-0.1213-0.5017-0.18110.257-0.2702-0.14830.08550.3836-0.36510.19690.00250.06910.0324-0.0366-0.01570.04170.10010.00020.004-0.07530.00710.0269
    t16-0.5340.142-0.3498-0.3454-0.11430.02360.32170.063-0.0479-0.3689-0.1898-0.0174-0.16330.0015-0.1333-0.2173-0.14420.1332-0.05560.04870.127-0.02130.067-0.0203
    t17-0.49220.24730.2181-0.50770.0522-0.0223-0.28410.12630.0021-0.24210.13870.0535-0.1969-0.2438-0.02410.217-0.082-0.1944-0.0309-0.0383-0.0442-0.124-0.0102-0.0191
    t18-0.55120.377-0.1433-0.15970.1986-0.1479-0.4102-0.1306-0.1875-0.2167-0.036-0.21380.14440.11570.0696-0.08580.122-0.00910.07970.15660.01350.19930.0019-0.0137
    t19-0.46550.1450.0407-0.2490.3049-0.61650.1451-0.0359-0.10610.18140.03820.26960.04670.02070.19420.0206-0.00360.1375-0.144-0.04740.0154-0.02390.0331-0.018
    t20-0.6373-0.1848-0.1339-0.1160.18790.36750.11630.2652-0.0511-0.0895-0.0769-0.19480.13490.03740.29030.19140.10850.1703-0.10210.0174-0.123-0.11140.00540.0116
    t21-0.63280.24-0.13620.17330.12190.00120.25980.0384-0.26880.3069-0.2355-0.2101-0.1604-0.0489-0.0280.15510.0138-0.2562-0.0470.02310.11020.0553-0.0545-0.0619
    t22-0.6399-0.1425-0.0968-0.11260.3451-0.0486-0.01890.12280.31880.22510.1446-0.29960.0254-0.08540.0274-0.1935-0.26460.0140.1434-0.0863-0.03030.0284-0.0283-0.0379
    t23-0.7058-0.0944-0.14770.06130.19320.1560.0710.27720.04230.11160.10830.30.0132-0.2671-0.1573-0.05690.1795-0.00570.08430.1816-0.03950.13760.12160.0292
    t24-0.66040.1620.32690.02990.29070.03750.1698-0.1149-0.1492-0.06350.0420.01710.20290.1793-0.29140.04460.04880.00780.2437-0.05850.0174-0.21790.01760.0033

  • 變數共通性(communality)表:
    變數取1個主成份取2個主成份取3個主成份取4個主成份取5個主成份取6個主成份取7個主成份取8個主成份取9個主成份取10個主成份取11個主成份取12個主成份取13個主成份取14個主成份取15個主成份取16個主成份取17個主成份取18個主成份取19個主成份取20個主成份取21個主成份取22個主成份取23個主成份取24個主成份
    t10.36840.37090.54970.57160.57190.60440.60690.62940.74320.76050.79180.79970.84090.86080.88680.88680.89270.93110.95790.9830.99370.99370.99811
    t20.16380.16420.40450.44510.47980.53830.54860.82880.83090.85420.8680.90630.90690.93250.97350.97370.97820.98690.98910.99580.99580.99590.99911
    t30.22170.22250.31470.32760.64740.69340.69740.70770.79580.80010.80310.81180.88550.96330.96410.9660.96990.97730.98780.99690.9976111
    t40.32490.33180.54570.58220.58230.58230.63650.64250.65390.67330.73530.73830.84620.89250.93430.95250.95270.98190.98830.98950.99340.9940.99631
    t50.49130.64050.67950.69750.70510.70590.72830.77590.77610.77980.78070.79180.79490.79780.79780.84540.85080.86250.91460.91810.91820.94260.97641
    t60.46930.6780.7180.71950.73150.7330.73590.76630.77570.78730.80430.81030.8110.81110.82020.86970.87060.88480.88920.89060.90120.93760.94131
    t70.46370.67250.75510.76490.76920.77050.7710.7720.77660.78430.7960.79710.79780.81440.82710.83990.87990.89350.89590.89880.90330.91880.95961
    t80.47360.53510.55790.57480.59030.59130.59360.65150.69430.69890.69910.71370.78020.79490.83020.90980.93080.93440.95660.97960.98190.98270.99941
    t90.48150.73760.7750.77570.7760.77980.78760.7940.79730.79730.79730.79850.79980.81480.82350.82360.82550.83340.84420.86490.91440.9160.97871
    t100.23210.45450.69460.74510.74520.76940.76990.77560.79670.79780.80630.80680.80680.81380.82140.84330.86890.87590.90820.90840.98090.98650.99191
    t110.34060.47780.52790.52790.57370.58860.61940.67270.78940.78950.78950.83550.86330.88140.88630.88730.95860.96470.96970.98230.98230.98290.98931
    t120.24590.52110.55160.67080.67110.74520.77540.80380.81390.8140.82330.84030.84620.84720.85050.85190.8540.86730.87410.90160.98650.99040.99051
    t130.3920.48010.48050.62130.68510.70520.7080.71020.76390.76450.76730.77390.77560.79520.82250.82780.8450.84630.85690.98040.98190.99760.99861
    t140.2010.20530.20820.49470.60850.64110.70970.71150.7120.72660.89290.89290.9110.95830.95830.95890.95930.97530.9830.98340.98340.997311
    t150.17070.18760.20230.4540.48680.55290.62590.64790.65520.80230.93560.97440.97440.97910.98020.98150.98180.98350.99350.99350.99360.99920.99931
    t160.28520.30540.42770.5470.56010.56060.66410.66810.67040.80650.84250.84290.86950.86950.88730.93450.95530.9730.97610.97850.99460.99510.99961
    t170.24230.30340.3510.60880.61150.6120.69270.70860.70860.76730.78650.78940.82810.88760.88820.93530.9420.97980.98070.98220.98410.99950.99961
    t180.30380.44590.46640.4920.53140.55320.72150.73850.77370.82070.8220.86770.88850.90190.90670.91410.9290.92910.93540.95990.96010.99980.99981
    t190.21670.23770.23940.30140.39430.77440.79550.79680.80810.8410.84240.91510.91730.91770.95540.95590.95590.97480.99550.99780.9980.99860.99971
    t200.40610.44020.45820.47160.50690.6420.65550.72580.72850.73650.74240.78030.79850.79990.88410.92080.93260.96160.9720.97230.98740.99980.99991
    t210.40050.45810.47660.50660.52150.52150.5890.59050.66270.75690.81230.85650.88220.88460.88540.90950.90970.97530.97750.9780.99020.99320.99621
    t220.40950.42980.43910.45180.57090.57330.57370.58870.69040.7410.76190.85170.85240.85970.86040.89780.96780.9680.98860.9960.9970.99780.99861
    t230.49810.5070.52880.53260.56990.59420.59930.67610.67790.69030.7020.7920.79220.86360.88830.89160.92380.92380.93090.96390.96540.98440.99911
    t240.43610.46230.56920.57010.65460.6560.68480.6980.72030.72430.72610.72640.76750.79970.88460.88660.8890.88910.94850.95190.95220.999711

  • 變數對主成份貢獻(contribution)表:
    變數主成份1主成份2主成份3主成份4主成份5主成份6主成份7主成份8主成份9主成份10主成份11主成份12主成份13主成份14主成份15主成份16主成份17主成份18主成份19主成份20主成份21主成份22主成份23主成份24
    t10.04470.00120.10820.01430.00030.03450.0030.02850.1550.02470.05110.01350.07880.03930.05450.00010.01660.10970.07860.07530.03690.00020.02080.0103
    t20.01990.00020.14540.02650.03180.0620.01280.35420.00280.03340.02240.06550.00110.05080.08620.00040.01270.02480.00630.020.00010.00040.01520.0049
    t30.02690.00040.05580.00840.29330.04870.0050.01310.120.00610.0050.01490.14080.15420.00170.00410.01080.02140.03070.02730.00240.008900.0001
    t40.03940.00340.12950.02380.000100.06760.00760.01540.02780.10110.00510.20590.09190.08770.04080.00050.08350.01880.00370.01340.00220.01090.0198
    t50.05960.07350.02360.01170.0070.00090.02790.06020.00020.00530.00160.0190.00590.005700.10650.01510.03330.15290.01030.00060.09180.16260.1246
    t60.0570.10280.02420.00090.0110.00160.00370.03840.01280.01660.02760.01020.00150.00020.0190.11090.00250.04070.01280.00410.03690.13680.01790.3099
    t70.05630.10280.050.00640.0040.00140.00060.00130.00620.0110.01910.0020.00140.03290.02660.02870.11120.03880.0070.00890.01540.05850.19640.2134
    t80.05750.03030.01380.0110.01420.00110.00280.07320.05830.00670.00030.02510.12690.02910.07430.17820.05830.01040.06490.06910.00810.00280.08060.0032
    t90.05840.12610.02260.00040.00030.0040.00970.00810.004400.00010.0020.00260.02960.01840.00010.00540.02260.03180.0620.17070.00590.30190.1127
    t100.02820.10950.14530.03290.00010.02570.00060.00730.02880.00160.01380.000800.0140.0160.04890.07120.020.09480.00070.250.02090.02620.0428
    t110.04130.06760.030300.0420.01580.03850.06740.1590.00010.00010.07870.0530.03580.01030.00230.19840.01750.01460.037800.0020.03090.0566
    t120.02980.13550.01840.07780.00030.07850.03770.03590.01380.00010.01520.0290.01140.00190.00710.00310.00570.0380.020.08270.29290.01450.00050.0501
    t130.04760.04340.00030.09180.05850.02130.00350.00270.07310.00080.00460.01140.00320.03890.05740.01190.04760.0040.03090.37080.0050.05920.00440.0077
    t140.02440.00210.00170.18690.10440.03460.08560.00230.00070.02080.270900.03440.093900.00130.00120.04570.02250.001200.05230.0130.0002
    t150.02070.00830.00890.16420.03010.070.09110.02780.010.21040.2170.066300.00950.00220.0030.00070.0050.029400.00010.02130.00020.0038
    t160.03460.00990.07410.07780.0120.00060.12920.0050.00310.19460.05870.00050.050900.03730.10570.05780.05080.00910.00710.05570.00170.02160.0022
    t170.02940.03010.02880.16820.00250.00050.10070.020200.08380.03130.00490.07410.11790.00120.10540.01870.1080.00280.00440.00670.05790.00050.0019
    t180.03690.070.01240.01660.03620.02320.20990.02160.04790.06720.00210.07820.03980.02650.01020.01650.04140.00020.01860.07360.00060.149400.001
    t190.02630.01040.0010.04040.08520.40270.02630.00160.01530.0470.00240.12440.00420.00080.07920.00100.05410.06090.00670.00080.00210.00530.0017
    t200.04930.01680.01090.00880.03240.14310.01690.08890.00360.01140.00960.06490.03470.00280.1770.0820.03280.08290.03060.00090.05220.04670.00010.0007
    t210.04860.02840.01120.01960.013600.08420.00190.09840.13470.09030.07560.04910.00470.00170.05390.00050.18770.00650.00160.04190.01150.01430.0202
    t220.04970.010.00570.00830.10920.00250.00040.01910.13850.07240.03410.15360.00120.01440.00160.08380.19470.00060.06030.02240.00320.0030.00380.0076
    t230.06050.00440.01320.00250.03420.02580.00630.09710.00240.01780.01910.1540.00030.14150.0520.00730.08960.00010.02080.09890.00540.07120.07120.0045
    t240.05290.01290.06470.00060.07750.00150.0360.01670.03030.00580.00290.00050.07860.06370.17840.00450.00660.00020.17430.01030.0010.17870.00150.0001

  • 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主成份6主成份7主成份8主成份9主成份10主成份11主成份12主成份13主成份14主成份15主成份16主成份17主成份18主成份19主成份20主成份21主成份22主成份23主成份24
    13.7992-1.09610.7914-0.7709-1.29220.5460.08370.14830.63750.47090.7253-0.3836-0.3551-0.84260.16720.69450.231-0.76770.39630.1533-0.4276-0.020.5722-0.4706
    20.19350.343-0.4456-0.32061.448-0.7567-0.02211.0446-0.4339-1.2818-0.63580.49460.18330.8232-0.6947-0.19781.3465-0.3956-0.66530.7542-0.2551-0.2590.9191-0.283
    30.9849-2.1542-2.03510.63740.5086-0.95180.01051.17111.45950.3516-0.3452-0.25180.05620.47250.84120.1869-0.75170.7491-0.27630.8061-0.50360.2886-0.3173-0.0645
    41.44120.8890.57341.46172.8441-0.55671.21010.374-1.0691-0.90362.7561-0.7696-0.5348-1.4394-0.70070.3807-0.1172-0.3809-0.4596-0.1949-0.41130.18830.4678-0.0809
    5-0.0658-0.5511.8953-0.95460.88751.54320.579-0.2893-0.67461.3172-0.12190.2252-0.1401-0.2810.6648-0.5739-1.1171-0.41730.22580.37530.92520.55590.18680.6551
    1412.4028-0.116-0.17412.5786-1.17640.6981-0.4216-0.1427-0.3357-0.3891-0.5812-0.92640.2036-1.35090.0088-1.339-1.531-0.0722-0.0312-0.4837-0.7030.30910.2129-0.4416
    1423.00891.14350.03271.414-0.45870.6133-0.76210.2286-0.61460.35350.70020.2616-0.5967-0.07630.79470.4291-1.33431.05430.24170.51430.1215-0.39230.1408-0.1879
    143-2.9970.90631.34080.8594-0.9475-1.45330.0406-0.69880.61340.03160.8292-1.2617-0.4639-0.01690.66490.16431.12340.2837-0.92631.18481.1582-0.35450.11110.546
    1441.06650.06431.52060.4142-0.69021.1984-0.5283-0.0975-1.412-0.51480.08891.78360.0733-0.5784-0.4325-0.4762-0.0439-1.05460.4513-0.67910.0340.1433-0.5061-0.7155
    145-4.05490.40530.7481-1.64960.27651.08651.74781.6887-0.5606-1.5122-1.5716-0.7198-1.4614-0.96050.4420.53910.40450.0796-0.5511-0.66670.0265-0.35680.39170.0975

  • 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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