Solution 5.7 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

1. The calculations are presented, in full, below.
First PLS component (note X and c are mean centred first).

Second PLS component, starting with residuals from first component

Third PLS component, starting with residuals from second component

2. The residual sum of squares is given as follows (using centred data).

3. Three components describe the data exactly. However there are only 3 degrees of freedom in the centred dataset, because there are only four samples and the data are centred. This is an artificially small dataset, and in reality one would take many more samples.

4. The following table should be obtained, remember to add on the mean concentration.

5. The RMS error after 2 PLS components is 0.0265. Only one degree of freedom is left because there are 4 samples, 2 PLS components and the data are centred, so 4 - 2 - 1 = 1.