The study of response surface methodology (RSM) involves both experimental planning and data modeling and analysis. Once a design is selected, and data obtained from it, models for representing the data need to be considered and fitted. During the fitting process, observations that are suspicious (e.g. outliers and/or influential points) may cause problems. Such observations need to be detected so that appropriate adjustments can be made to analysis. Thus far, the work on influence analysis of RSM is unexplored in statistical research. This will be the focus of this paper. We not only generalize the single perturbation scheme in Hampel's (1974) method, but also implement the pair-perturbation scheme in Huang et al. (2007a-c) to develop influence functions for sensitivity analysis in RSM. A simulation study and two real data examples for illustrating the effectiveness of the proposed method are provided.
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