# How to interpret a correlation chart?

I'm learning PCA using R. I use Factorminer package.

For learning purpose I used following code

library('FactoMineR')
data(decathlon)
res.pca1 = PCA(decathlon[, 1:10], scale.unit = TRUE, ncp = 4,graph = TRUE)

It is generating a correlation chart. By looking this it is clear that first & second Principal Component are explaining 52.73% variability in the data. But I'm not sure how to interpret the variables correlation by seeing this plot.

• Your question would benefit greatly from including the actual plot... – M. Berk Feb 11 '14 at 12:15

You should look at the website of FactoMineR package: http://factominer.free.fr/classical-methods/principal-components-analysis.html

They explain the data you use. I could try an explanation by myself, but I cannot be more clear.

Here I copy/paste the fist lines of what they wrote:

The first two dimensions resume 50% of the total inertia (the inertia is the total variance of dataset i.e. the trace of the correlation matrix).

The variable "X100m" is correlated negatively to the variable "long.jump". When an ahtlete performs a short time when running 100m, he can jump a big distance. Here one has to be careful because a low value for the variables "X100m", "X400m", "X110m.hurdle" and "X1500m" means a high score: the shorter an athlete runs, the more points he scores.

The first axis opposes athletes who are "good everywhere" like Karpov during the Olympic Games between those who are "bad everywhere" like Bourguignon during the Decastar. This dimension is particularly linked to the variables of speed and long jump which constitute a homogeneous group. The second axis opposes athletes who are strong (variables "Discus" and "Shot.put") between those who are not. The variables "Discus", "Shot.put" and "High.jump" are not much correlated to the variables "X100m", "X400m", "X110m.hurdle" and "Long.jump". This means that strength is not much correlated to speed.

At the end of this first approach, we can divide the factorial plan into four parts: fast and strong athletes (like Sebrle), slow athletes (like Casarsa), fast but weak athletes (like Warners) and slow and weak (relatively speaking!) athletes (like Lorenzo).

The winners of the decathlon are those who scored the most (or those whose rank is low). The variables the most linked to the number of points are the variables which refer to the speed ("X100m", "X110m.hurdle", "X400m") and the long jump. On the contrary, "Pole-vault" and "X1500m" do not have a big influence on the number of points. Athletes who are strong for these two events are not favoured.

And so on...