ABSTRACT
Response Surface Methodology (RSM) comes handy when a researcher wants to
determine the value of each of the explanatory variables that simultaneously optimize the
response variables. In the modelling phase of RSM, a suitable regression model is fitted
using the data generated from the experimental design phase. The fitted model is
subsequently subjected to an appropriate optimization routine in order to obtain the
optimal solution of the study. Currently, the semiparametric model robust regression 2
(MRR2) model is considered the best regression model for handling data emanating from
response surface studies. MRR2 is a hybrid model, combining estimates of the response
(output) from both the local linear regression (LLR) and the ordinary least squares (OLS)
via mixing parameters. When MRR2 is applied in response surface studies, the current
philosophy entails the exclusion of interaction terms in the model matrix of LLR
component of MRR2 irrespective of the statistical significance of the interaction terms in
the OLS model matrix. In this paper, we present results for a problem from the literature
in which the significant interaction terms in the OLS model matrix were duly included in
LLR model matrix. A multiple response problem from the literature was used to justify
the inclusion of the interaction terms in the LLR model matrix. It is found that the MRR2
applied with the interaction terms included outperforms its counterpart both in terms of
the goodness-of-fit statistics and the desirability-based optimal solutions. Specifically,
the MRR2 with the proposed model matrix gives better prediction errors in the three
responses as well as a desirability value of approximately 77.3% as against the 47.4%
for the MRR2 which disregards the significant interaction terms in its model matrix.
KEYWORDS:Local bandwidths, Local linear regression, Model matrix, Model robust regression 2, Response surface methodology, Semi-parametric regression
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