Solution 5.6 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

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  • Published: Jan 1, 2000
  • Channels: Chemometrics & Informatics

1. The graph of the scores of PC1 versus PC2 for the 25 calibration spectra is presented below.

The equivalent graph for the concentrations is given below.

2. The concentrations are given below, using a one compound model.

3. The graph of predicted against true is given below.

This graph could be interpreted in terms of the experimental design. The root mean square error (dividing by 24 which is the number of degrees of freedom) is 0.0999 mM or 35.79% (using the average). The error is very high because there are in fact 3 compounds in the mixture.

4. The concentration estimates for all three compounds are as follows.

5. The graph using MLR and all three compounds is as follows.

The errors are given below.

 

A

B

C

error (mM)

0.00726

0.00247

0.00153

error (%)

2.602

2.758

2.198

Notice that it is probably best to divide the error by 22 for the r.m.s. calculation.

6. The predictions using 3 PLS components for A are as follows.

These predictions are much better because, unlike MLR, it is not necessary to know the identity of all the components in advance, simply how many components.

The root mean square error is 0.00757 or 2.71%, almost identical to MLR.

7. A graph of predicted concentrations for all three compounds versus time, using the calibration set as a training set is as follows.

 

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