GLM Introductory Overview - Response Surface Regression
Quadratic response surface regression designs are a hybrid type of design with characteristics of both polynomial regression designs and fractional factorial regression designs. Quadratic response surface regression designs contain all the same effects of polynomial regression designs to degree 2 and additionally the 2-way interaction effects of the predictor variables. The regression equation for a quadratic response surface regression design for 3 continuous predictor variables P, Q, and R would be
Y = b0 + b1P + b2P2 + b3Q + b4Q2 + b5R + b6R2 + b7P*Q + b8P*R + b9Q*R
These types of designs are commonly employed in applied research (e.g., in industrial experimentation), and a detailed discussion of these types of designs is also presented in the Introductory Overview section of the Experimental Design module (see Central composite designs).
Between-subject designs
Within-subject (repeated measures) designs
Multivariate designs