Linear Models and the Meaning of “Linear”: Ebbinghaus’ Forgetting Curve as a Nonlinear Example

Students in psychology and the social sciences often equate “linear regression” with straight lines and are puzzled when models that clearly describe curves are still called linear. In this paper, I clarify the distinction between linear functions and linear models in the parameters. Using Ebbinghaus’ (1885) classic forgetting curve as a case study, I show that his model is genuinely nonlinear in its parameters, even though it can be transformed into a linear regression model by suitable transformations of the variables. I provide a simple reanalysis of his data and R code that can be used directly in methods teaching.