# Loading Plot of a Principal Component Analysis (PCA)

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Principal component analysis (PCA) is a statistical procedure that converts data with possibly correlated variables into a set of linearly uncorrelated variables, analogous to a principal-axis transformation in mechanics.

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Contributed by: D. Meliga and S. Z. Lavagnino (May 2016)

With additional contributions by: A. Chiavassaand M. Aria

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

In the loading plot, the high correlation between two variables leads to two vectors that are very close to each other, the non-correlation leads to two vectors out of phase by , while the anti-correlation leads to two vectors that are out of phase by [2].

Snapshot 1: a strong correlation between and , non-correlation in the remaining cases . From a graphical point of view, we can see two vectors that are very close, while the others are out of phase with each other by about .

Snapshot 2: a strong correlation between and , non-correlation in the remaining cases . From a graphical point of view, we can see two opposite vectors, while the others are out of phase to each other by about .

References

[1] S. J. Press, *Applied Multivariate Analysis: Using Bayesian and Frequentist Methods of Inference*, Mineola, NY: Dover Publications, 2005.

[2] M. Aria. "L'analisi in Componenti Principali." (May 25, 2016) www.federica.unina.it/economia/analisi-statistica-sociologica/analisi-componenti-principali.

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