Solution 4.10 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

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

1. The scores plot is provided below.

The outliers are naphthalene and benzene, this is not unexpected from chemical structures.

2. The scores minus the outliers are presented below.

Notice there is some separation in the PC plot with the outliers removed, but at least one active compound would be misclassified. However only 2 PCs are used in the graphs.

3. The variance covariance matrices are given below.

4. The centroids are as follows.

Class A






Class B






The discriminant function is given below.

The information can be presented graphically.

There are a variety of answers to a cut-off value. The best values correctly classify 28 out of 30 (=93%) of the compounds. A good value depends on whether one wishes to have equal chances of misclassification in each class, or whether one wishes to reduce the change of errors in the "Active" class. A cut-off value of –0.5 would maximise the percentage correctly classified. However it might be more important to spot potential carcinogens, in which case maximising the classification of the Active class is more important than maximising the overall percentage.

5. Compound 10 is poorly discriminated with a discriminant value of
–3.390. This could have been spotted from the PCplot.

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