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This tutorial explains the basics of linear regression metamodels-especially low-order polynomials-and the corresponding statistical designs-namely, fractional factorial designs of resolution III (Plackett-Burman designs), IV (accounting for interactions), V (estimating individual interactions), and central composite designs (CCDs, for second-order polynomial metamodels). This tutorial assumes 'white noise', which means that the residuals of the fitted linear regression metamodel are normally, independently, and identically distributed with zero mean. This metamodel requires validation. The tutorial gathers statistical results that are scattered throughout the literature on mathematical statistics, and presents these results in a form that is understandable to simulation analysts.