Abstract: Methods for high dimensional regression are often discussed in studies where regressors follow continuous distributions. How well do they perform when applied to data collected by designed experiments where design points are rather isolated from each other? We initiate such a study by focusing on the method of principal Hessian direction (pHd) (Li (1992)). Quadratic regression surfaces are considered first and then extended to general nonlinear surfaces. Special attention is given to factorial designs and rotatable response surface designs. Both theoretic and empirical results are presented.
Key words and phrases: ANOVA, dimension reduction, graphics, factorial designs, principal Hessian directions, residual plots, rotatable designs, sliced inverse regression, visualization.