Encouraging Students to Think Critically: Regression Modelling and Goodness-of-Fit

This note underscores important considerations that should be taken into account when teaching students to check for inadequacies of a given linear, nonlinear or logistic regression models. Key illustrations are provided which underscore the shortcomings of currently used procedures. A brief overview of nonlinear regression models is given in order to lay the foundation for testing for lack of fit in nonlinear models. This paper also introduces a new 'scaled' binary logistic regression model to highlight po- tential problems with the usual logistic model, and implications for choosing a robust optimal experimental design are also underscored and discussed.