A Simple Approach for Lack-of-fit Test in Regression without Replicates

Regression is a useful tool for data analysis in business research. To check if the regression model is appropriate, we need to perform a lack-of-fit test. However, when replicates are unavailable, the existing methods for the lack-of-fit test are somewhat complicated, and therefore the test is often neglected by many research workers. The purpose of this article is to propose a simple approach to test for lack of fit in regression without replicates to facilitate the application. Testing for coincidence of regression equations for separate groups, formed by examining the residual plot, is used to evaluate lack of fit. Examples of the use of the approach are given. The effectiveness of the proposed approach is evaluated in terms of power by simulation. Sensitivity analysis is carried out to examine stability of the test. The results indicate that the proposed simple approach performs well.