奧運十項全能分析

場景：

奧運十項全能比賽，選手各項比賽部分資料如后：

Name X100m Long.jump Shot.put High.jump X400m X110m.hurdle Discus Pole.vault Javeline X1500m Rank Points Competition 1 SEBRLE 11.04 7.58 14.83 2.07 49.81 14.69 43.75 5.02 63.19 291.7 1 8217 Decastar 2 CLAY 10.76 7.40 14.26 1.86 49.37 14.05 50.72 4.92 60.15 301.5 2 8122 Decastar 3 KARPOV 11.02 7.30 14.77 2.04 48.37 14.09 48.95 4.92 50.31 300.2 3 8099 Decastar 4 BERNARD 11.02 7.23 14.25 1.92 48.93 14.99 40.87 5.32 62.77 280.1 4 8067 Decastar 5 YURKOV 11.34 7.09 15.19 2.10 50.42 15.31 46.26 4.72 63.44 276.4 5 8036 Decastar 6 WARNERS 11.11 7.60 14.31 1.98 48.68 14.23 41.10 4.92 51.77 278.1 6 8030 Decastar 7 ZSIVOCZKY 11.13 7.30 13.48 2.01 48.62 14.17 45.67 4.42 55.37 268.0 7 8004 Decastar 8 McMULLEN 10.83 7.31 13.76 2.13 49.91 14.38 44.41 4.42 56.37 285.1 8 7995 Decastar 9 MARTINEAU 11.64 6.81 14.57 1.95 50.14 14.93 47.60 4.92 52.33 262.1 9 7802 Decastar 10 HERNU 11.37 7.56 14.41 1.86 51.10 15.06 44.99 4.82 57.19 285.1 10 7733 Decastar

問題：

  • 說明選手運動強項

分析：

# 指定精準度 options(digits=4) # 清除殘餘變數 rm(list=ls()) filePath <- '/Users/RichCLee/Documents' fileName <- paste(filePath, 'PCA-2.csv', sep='/') PCA.Data <- read.table(fileName, header=T, sep=",") PCA.Data <- fix(PCA.Data) doTask <- function(f) { PCA.Analysis <- prcomp(f, data=PCA.Data, center=TRUE, scale=TRUE) # 特徵值 > 1 者即為應選擇因子 print(PCA.Analysis$sdev^2) plot(PCA.Analysis, type="line", main="陡坡圖") summary(PCA.Analysis) PCA.Analysis } # 使用所有變數分析 q <- doTask(~X100m+Long.jump+Shot.put+High.jump+ X400m+X110m.hurdle+Discus+Pole.vault+ Javeline+X1500m+Rank+Points) # 繪製因素負荷量圖 par(mfrow=c(2,2)) biplot(q, choices=c(1,2), main='因素負荷量圖') biplot(q, choices=c(2,3), main='因素負荷量圖') biplot(q, choices=c(3,4), main='因素負荷量圖') biplot(q, choices=c(4,1), main='因素負荷量圖')

Standard deviations: [1] 2.18147 1.31915 1.18950 1.06385 0.92841 0.77931 0.71446 0.64116 0.48498 0.43286 0.37545 0.00735 Rotation: PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 PC12 X100m -0.32463 0.119493 -0.12979 0.193683 -0.55373 -0.240804 0.23057 0.20959 -0.29130 0.37166 0.34559 -0.147906 Long.jump 0.34651 -0.252374 0.15321 0.006787 0.05114 0.274332 0.46820 -0.31832 -0.57710 0.15096 0.05237 0.189027 Shot.put 0.28038 0.464134 -0.01675 0.102802 0.07853 -0.182613 -0.50365 -0.20803 -0.26032 0.48849 -0.19161 0.124753 High.jump 0.26949 0.272695 -0.20103 -0.081392 -0.43408 0.651113 -0.19616 0.09813 0.09952 -0.13960 0.27728 0.198025 X400m -0.31872 0.420421 0.11055 0.083377 0.08029 0.273142 0.08639 0.27521 -0.45920 -0.32285 -0.45288 -0.134310 X110m.hurdle -0.32246 0.155406 -0.06814 0.384289 -0.12016 0.146269 0.05359 -0.78290 0.17800 -0.12784 -0.02131 -0.139415 Discus 0.24267 0.468985 0.04593 -0.256786 -0.10487 -0.501503 0.28052 -0.16158 -0.03047 -0.47136 0.17725 0.176875 Pole.vault 0.06640 -0.152842 0.59203 0.553682 -0.10959 -0.101974 -0.30693 0.12253 -0.09139 -0.28524 0.22823 0.204289 Javeline 0.14622 0.244033 -0.32827 0.562736 0.46473 0.038823 0.33706 0.24721 0.18974 0.07014 0.17210 0.178571 X1500m -0.04809 0.355629 0.65726 -0.179152 0.12352 0.208527 0.23886 0.02545 0.32736 0.35138 0.17005 -0.176447 Rank -0.35810 0.044808 -0.08343 -0.232758 0.46751 0.080954 -0.27613 -0.10069 -0.31312 -0.08500 0.62598 0.001174 Points 0.45002 0.001182 -0.05291 0.123174 0.04991 -0.003256 -0.07304 0.01241 -0.10676 -0.14576 0.15742 -0.845044