Consider a situation in which one is interested in two quantitative design variables (say Temperature and Pressure). In addition, there are three levels of a single qualitative factor (say Factory A, B, or C). It is felt that the design should accommodate a second-order model in the quantitative variables and interaction between the linear (quantitative) terms and the qualitative variable. (Note: No interaction between the 2 quantitative variables.)
(a) Write out the model to be fitted. (Use X’s to denote the quantitative variables and Z’s for the qualitative variable. Define all variables.)
(b) Using 15 experimental runs, construct a possible design. Give the design matrix.
(c) Show me how you know what terms you can estimate using your design.
(d) Give the allocation of the df for your 15 point design.