Linear combinations to improve correlation

With the data from soy meal on IFT conveyor, I select three wavelengths for this demo:
# 1022nm     datapoint 87     Protein or Oil  
#  902nm     datapoint 27     Cellulose        
#  964nm     datapoint 58     CH2 Oil          
x1<-X_msc_mc[,c(87)]
x2<-X_msc_mc[,c(27)]
x3<-X_msc_mc[,c(58)]

We have the values for Protein for these spectra.

Protein <- Prot

Let´s see the wavelengths in the mean centered MSC treated spectra

matplot(wavelengths,t(X_msc_mc),type="l",
        xlab="wavelengths",ylab="Absorbance")
abline(v=1022)
abline(v=902)
abline(v=964)

now see how the correlation becomes better in the case of the 4td plot where the X axis is a linear combination of the other 3 wavelengths

 

x1x2x3<-((139.98*x1)+(287.12*x2)+(121.02*x3))

par(mfrow=c(2,2))
plot(x1,Protein)
plot(x2,Protein)
plot(x3,Protein)
plot(x1x2x3,Protein,col="blue")

 

We have worked with this data before with PLS and PCR and what we have done here is a MLR approach. An intercept value will place the date on the same scale.