Evaluation of Multiresponse Screening Experiments

It is a common experience that an attempted synthetic transformation does not proceed cleanly, and that, in addition to the desired product, by-products and unreacted starting material are present in the final reaction mixture. 

An early and important step will therefore be to identify which experimental factors are responsible for the gross and systematic variation of the distribution 

When there are only a few responses to consider, it is manageable to analyze each response variable separately, and then take all the results thus obtained together and make a joint evaluation. However, with more than a handful of responses such an approach will be quite difficult. 

In an experimental design, the settings of the variables are given by the row vector x = [x1. .. xk] in the design matrix. When there are several responses, the result will define a response vector, y = [yt. .. ym]. For the whole set of experiments these vectors define a response matrix, Y. 

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