A response curve is a mathematical function representing the relationship between the mean of a response variable and the level of an explanatory variable. The curve might be linear, a higher degree polynomial, or some nonlinear function. A response surface is a mathematical function representing the relationship between the mean of a response variable and the levels of several explanatory variables. The surface might be linear, a higher order polynomial, or a nonlinear function. In an experiment, the explanatory variables, or treatment factors, are under the control of the experimenter, and the level of each must be chosen for each experimental run. A response surface design is the set of combinations of the levels of the explanatory variables used in a particular experiment.
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