3. Classic Assumptions Versus Simulation Practice

This chapter is organized as follows. Section 3.1 summarizes the classic assumptions of regression analysis, which were given in the preceding chapter. Section 3.2 discusses multiple simulation outputs (responses, performance measures), which are usual in simulation practice. Section 3.3 addresses possible nonnormality of either the simulation output itself or the regression residuals (fitting errors), including tests of normality, normalizing transformations of the simulation output, and jackknifing and bootstrapping of nonnormal output. Section 3.4 covers variance heterogeneity of the simulation output, which is usual in random simulation. Section 3.5 discusses cross-correlated simulation outputs created through common random numbers (CRN); the use of CRN is popular in random simulation. Section 3.6 discusses the validation of estimated regression models, including the coefficient of determination R ² and the adjusted coefficient \(R_{\mbox{ adj}}^{2}\), and cross-validation; this section also discusses how classic low-order polynomial metamodels (detailed in the preceding chapter) may be improved in practice. Section 3.7 summarizes the major conclusions of this chapter. The chapter ends with solutions for the exercises, and a long list with references for further study.