The analysis of response surface data
The fitting of quadratic response surfaces involves an important and rather special application of multiple regression in which a second degree polynomial in the original independent variables is fitted to the response under analysis. This can be called multiple quadratic regression. For a very simple example refer back to Data Set 1.1 in Chapter 4. Much of the research on response surface analysis has concentrated on the design of suitable experiments and good discussions of this and of general methodology can be found in Box and Wilson (1951), Box (1954), Myers (1971), Box et al. (1978) and Davies (1978, Chapter 11). We shall concentrate here on the fitting of the polynomial and subsequent interpretation assuming that the data have already been collected. Obviously consideration of the design will enter at certain points in the discussion but the present chapter is not intended as an exposition of this aspect of the subject.
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