Design matrices and modelling

The design matrix is a key concept. A design may consist of a series of experiments performed under different conditions, e.g. a reaction at differing pHs, temperatures, and concentrations. Table 2.6 illustrates a typical experimental set-up, together with an experimental response, e.g. the rate constant of a reaction. Note the replicates in the final five experiments in Section 2.4 we will discuss such an experimental design commonly called a central composite design. 

It is normal to describe experimental data by forming a mathematical relationship between the factors or independent variables such as temperature and a response or dependent variable such as a syndietic yield, a reaction time or a percentage impurity. A typical equation for three factors might be of the form 

Notice the hat on top of die y this is because the equation estimates its value, and is unlikely to give an exact value that agrees experimentally because of error. 

Some of these terms may not be very significant or relevant, but it is up to the experimenter to check this using approaches such as ANOVA (Section 2.2.2) and significance tests (Section 2.2.4). In advance of experimentation it is often hard to predict which factors are important. 

There are 10 terms or parameters in the equation above. Many chemometricians find it convenient to work using matrices. Although a significant proportion of traditional 

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