Polynomial Regression and Response Surface Methodology: Theoretical Non-Linearity, Tutorial and Applications for Information Systems Research

Abstract

Information systems (IS) studies regularly assume linearity of the variables and often disregard the potential non-linear theoretical interrelationships among the variables. The application of polynomial regression and response surface methodology can observe such non-linear theoretical assumptions among variables. This methodology enables to examine the extent to which two predictor variables relate to an outcome variable simultaneously. This paper utilizes the expectation confirmation theory as an example and provides a methodological commentary that illustrates a step-wise process for conducting a polynomial regression and response surface methodology.

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“…Polynomial regression was added because, compared to traditional regression, it may show greater explanatory as it provides nuanced views on the relationships between different combinations of independent variables and a dependent variable in three-dimensional space [31]. This non-linear analysis is used to investigate beyond simple relationships between two or more variables and further explain the variables' interaction influence [54].…”

“…A model that does not fit can be indicated that there is no significant influence between the dependent variable and the independent variable, so there is a possibility that the model is a polynomial function [55]. The polynomial model involves a hierarchical analysis of polynomial equations, which continues until higher order and is statistically significant [54]. The higher the order used to determine the model, the more fit the model with the original data.…”

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“…The key coefficients examined in standard and MLRSA are referred to as response surface parameters (Nestler et al, 2019;Sedera & Atapattu, 2019), where the response surface is a 3-dimensional plane of predicted values on two predictors, X and Y, and an outcome, Z. Figure 2 will be used to illustrate the response surface parameters.…”