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Loading library

library(FactoMineR)
## Warning: package 'FactoMineR' was built under R version 4.2.3
library(factoextra)
## Warning: package 'factoextra' was built under R version 4.2.3
## Loading required package: ggplot2
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

View data

data(decanthlon2)
## Warning in data(decanthlon2): data set 'decanthlon2' not found
head(decathlon2)
##           X100m Long.jump Shot.put High.jump X400m X110m.hurdle Discus
## SEBRLE    11.04      7.58    14.83      2.07 49.81        14.69  43.75
## CLAY      10.76      7.40    14.26      1.86 49.37        14.05  50.72
## BERNARD   11.02      7.23    14.25      1.92 48.93        14.99  40.87
## YURKOV    11.34      7.09    15.19      2.10 50.42        15.31  46.26
## ZSIVOCZKY 11.13      7.30    13.48      2.01 48.62        14.17  45.67
## McMULLEN  10.83      7.31    13.76      2.13 49.91        14.38  44.41
##           Pole.vault Javeline X1500m Rank Points Competition
## SEBRLE          5.02    63.19  291.7    1   8217    Decastar
## CLAY            4.92    60.15  301.5    2   8122    Decastar
## BERNARD         5.32    62.77  280.1    4   8067    Decastar
## YURKOV          4.72    63.44  276.4    5   8036    Decastar
## ZSIVOCZKY       4.42    55.37  268.0    7   8004    Decastar
## McMULLEN        4.42    56.37  285.1    8   7995    Decastar
str(decathlon2)
## 'data.frame':    27 obs. of  13 variables:
##  $ X100m       : num  11 10.8 11 11.3 11.1 ...
##  $ Long.jump   : num  7.58 7.4 7.23 7.09 7.3 7.31 6.81 7.56 6.97 7.27 ...
##  $ Shot.put    : num  14.8 14.3 14.2 15.2 13.5 ...
##  $ High.jump   : num  2.07 1.86 1.92 2.1 2.01 2.13 1.95 1.86 1.95 1.98 ...
##  $ X400m       : num  49.8 49.4 48.9 50.4 48.6 ...
##  $ X110m.hurdle: num  14.7 14.1 15 15.3 14.2 ...
##  $ Discus      : num  43.8 50.7 40.9 46.3 45.7 ...
##  $ Pole.vault  : num  5.02 4.92 5.32 4.72 4.42 4.42 4.92 4.82 4.72 4.62 ...
##  $ Javeline    : num  63.2 60.1 62.8 63.4 55.4 ...
##  $ X1500m      : num  292 302 280 276 268 ...
##  $ Rank        : int  1 2 4 5 7 8 9 10 11 12 ...
##  $ Points      : int  8217 8122 8067 8036 8004 7995 7802 7733 7708 7651 ...
##  $ Competition : Factor w/ 2 levels "Decastar","OlympicG": 1 1 1 1 1 1 1 1 1 1 ...
decathlon2.active <- decathlon2[1:23, 1:10]
head(decathlon2.active[, 1:5],3) # head of 3 rows of 5 columns.
##         X100m Long.jump Shot.put High.jump X400m
## SEBRLE  11.04      7.58    14.83      2.07 49.81
## CLAY    10.76      7.40    14.26      1.86 49.37
## BERNARD 11.02      7.23    14.25      1.92 48.93
res.pca <- PCA(decathlon2.active, graph=FALSE) #Standadized data.
#View(res.pca)
print(res.pca)
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 23 individuals, described by 10 variables
## *The results are available in the following objects:
## 
##    name               description                          
## 1  "$eig"             "eigenvalues"                        
## 2  "$var"             "results for the variables"          
## 3  "$var$coord"       "coord. for the variables"           
## 4  "$var$cor"         "correlations variables - dimensions"
## 5  "$var$cos2"        "cos2 for the variables"             
## 6  "$var$contrib"     "contributions of the variables"     
## 7  "$ind"             "results for the individuals"        
## 8  "$ind$coord"       "coord. for the individuals"         
## 9  "$ind$cos2"        "cos2 for the individuals"           
## 10 "$ind$contrib"     "contributions of the individuals"   
## 11 "$call"            "summary statistics"                 
## 12 "$call$centre"     "mean of the variables"              
## 13 "$call$ecart.type" "standard error of the variables"    
## 14 "$call$row.w"      "weights for the individuals"        
## 15 "$call$col.w"      "weights for the variables"
# 4.4.1 eigenvales/variances