How to make prediction with PCA

I have been able to calculate the eigenvectors/values of my data sample (N samples of dimension M) and I would like to reduce the dimension to say 3. If i am correct i need to choose the first 3 eigenvectors ( with the biggest eigenvalues ).

From these 3 PCs and from an observation (in the original basis) of a new sample ( looking no开发者_如何学Cw at 3 dimensions only ).

How can i predict what will be the M-3 other values?

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Yes, by using the x most significant components in the model you are reducing the dimensionality from M to x

If you want to predict - i.e. you have a Y (or multiple Y's) you are into PLS rather than PCA

Trusty Wikipedia comes to the rescue as usual (sorry, can't seem to add a link when writing on an iPad)

http://en.wikipedia.org/wiki/Partial_least_squares_regression