SOISOS

Performing a PCA after standardizing the variables and obtain estimates for the principal components for the standardized variables.

Reading in athelete’s data
ath.dat <- read.table("athelete.txt")

Standardizing the data
ath.dat.std <- scale(ath.dat)

Correlation matrix (since covariance of standardized data is correlation)
R = cov(ath.dat.std)

Eigen Values
lambda = eigen(R)$val

Eigen values are read to assess which components explain the variance the most. In this case, the first two show values above 1 therefore we will take the first two components.

[1] 1.0900625 1.0290211 0.8809163

Eigen Vector
es= eigen(R)$vec

[,1] [,2] [,3]
[1,] 0.7476122 -0.1215134 -0.6529246
[2,] -0.2827011 0.8313790 -0.4784235
[3,] 0.6009626 0.5422577 0.5871971

Three eigen vectors associated with the labmda values. The three vectors are eigen vectors of the covariance matrix and also the loadings of Principle components.

You can find the loadings (eigen vectors) by obtaining loadings of the princomp output

loadings(ath.pca)

Loadings:
Comp.1 Comp.2 Comp.3
X1 0.748 -0.122 -0.653
X2 -0.283 0.831 -0.478
X3 0.601 0.542 0.587