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    How are the Q-residuals and Hotelling's T^2 (T2) values calculated for PLS models?

Possible Solutions:

    Q and T^2 are done in PLS exactly the as they are for PCA (see the PLS_Toolbox manual for a description) except that the basis that is being used for T^2 is the PLS loads rather than the PCA loads. For Q, we actually calculate the eigenvalues of the residual subspace and it is exactly the same as in PCA.

    For T^2, there is an approximation made of the eigenvalues. If Tcal is the column vectors of scores from your calibration model (extract from the model.loads{1,1} field) :
    f = diag(Tcal'*Tcal)/size(Tcal,1);
    f = sqrt(1./f);
    OR you can use:
    f = sum(Tcal.^2)./size(Tcal,1);
    f = sqrt(1./f);
    Either method gives you f, a normalized vector of lengths of each of your original scores. Next, you take each of those lengths and divide your new scores (Tnew) by the corresponding length: (again, here are two methods of doing it)

    Method 1:
    T2 = sum( (Tnew * diag(f)).^2 ,2);
    Method 2:
    for j=1:length(f);
     Tnew(:,j) = Tnew(:,j)*f(j);
    T2 = sum( Tnew.^2 ,2);

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