Regression estimation response surface designs, model

The response surface designs require at least three levels for each variable, in order to be able to detect and model curvature in the response. The model is very often an empirical second-order or quadratic one (see Eq. (6.2)). The coefficients in the second-order model are estimated using multiple regression and they allow to predict... 

Values for all variation levels are shown in Table 2.154. Select FUFE 23 as a basic design of experiment. Determine the linear regression model from experimental outcomes, Table 2.155. Assume that the obtained linear model is inadequate and that there is curvature of the response surface. To check these assumptions, additional design points were done in the experimental center so that their average is y0=0.1097 (y0—estimate of free member in linear regression, i.e. y0 — 30). Since h0 — y0 = 3 is the measure... 

It should be said that q-responses of pure components makes determination of regression coefficients of linear model possible, while q-internal and central points serve to estimate the nonlinearity of the response surface. It is useful to include in the mentioned designs of experiments q-points of "null effects" in this form ... 

From this conclusion follows, that a factorial design can be used to fit a response surface model to account for main effects and interaction effects. In the concluding section of this chapter is discussed how the properties of the model matrix X influence the quality of the estimated parameters in multiple regression. It is shown that factorial design have optimum qualities. 

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