Linear Regressions to calculate the Loadings

We saw in previous post how the scores are calculated for every PLS term once we have the weights, so we start by t1 (scores on the first PLS term), and after we calculate the Loadings as regressions of X on T, so the loadings are spectra with values of "b" coefficients indeed absorbance. So they give us an idea of the importance of every wavelength in the term.

 

Every spectrum has 100 wavelength (850 to 1048 every 2 nm) so 850 is in the data point 1, 852 in the data point 2,........and 1048 in the data point 100.

 

So, we can make linear regressions on the X matrix (with its math treatment applied) on the score t1 calculated to get the value of every data point in the first loading.

 

The way to do it is:

lm(X_msc_centered[odd,10]~t1_pls)     #b=-1.247e-01
lm(X_msc_centered[odd,50]~t1_pls)     #b=-6.269e-02
lm(X_msc_centered[odd,90]~t1_pls)     #b= 1.348e-01

We can check after how this values are the same as the calculated for the PLS algorithm.