# Faq difference between a loading and a weighting

### Issue:

What is the difference between a loading and a weighting?

### Possible Solutions:

When performing Principal Components Analysis (PCA), you get loadings, `P`

, which are an orthonormal basis which can be used to calculate scores: `T = X*P`

or to estimate data `X = T*P'`

These operations are invertible (repeating them gives the same result) because the loadings are the eigenvectors of `X'X`

.

When using Partial Least Squares (PLS), you get loadings, `P`

, but also weights, `W`

, because the decomposition is based on `X'Y`

. The weights and loadings must be used together to calculate scores: `T = X*W*pinv(P'*W)`

From a phenomenological point of view, the weights represent features in `X`

which are related to the original `Y`

values. The loadings represent the features in `X`

which are related to the scores, `T`

, which are the given factor's estimate of `Y`

.

Note, by the way, that the weights are the ones used to calculate the regression vector (that which is used to make a prediction). Loadings are only used when calculating scores and, of course, Hotelling's T^{2}.

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