Dealing with the least squares regression assumptions in simulation metamodeling

The aim of this study is twofold. The first is to estimate a metamodel for a time-shared computer system using a sequential design procedure. The second is to deal extensively with the least squares regression assumptions during the metamodel development. In the first stage of the experimentation, a first-order metamodel is estimated using the two-level factorial design. Later, the design is augmented with replicated center points for curvature check. Upon the detection of the significance of the curvature, a central composite design is used for fitting a second-order metamodel, which explains the relation between the levels of the input factors, and the response of interest. In both stages, various diagnostic statistical tests such as normality test, variance homogeneity test, lack-of-fit test, etc. are carried out to make sure that the method of least squares is properly and efficiently applied.