I have a dataset of cave dimensions (and other variables related to their features).
The problem is that 3 of these variables are: Length, Area, and Volume. These 3 are highly correlated as they basically are: Area = Length * Length and Volume = Area * Length.
I know using PCA I can find the variables which influence the most the whole set's variation.
Is that ok to perform PCA and pick only the most 'influential' variable to my further analysis? Say, Area for example (I think Area is the best one, not sure, just a guess).
I know PCA does not choose variables. Instead, it creates new ones. However, I know the PC1 (being the major 'influencer' on the variation) is formed by loadings of the previous variables.
Does it make sense to pick then the variable which contributes with the most loadings on PC1?