Fitting Models to Data as an Application of Optimization in Calculus

The teaching and learning of calculus is enhanced by applications to real-world problems. The topic of optimization (finding the maximum or minimum of a function) is a place where many calculus instructors emphasize applications. However, the breadth of applications explored in optimization is usually quite limited. In this paper, we show how the classic statistics problem of fitting a model to data can be incorporated as an application of optimization techniques in single and multivariable calculus classes. In particular, we introduce the reader to the method of maximum likelihood estimation, illustrate its use via a number of examples, and provide a link to a larger collection of worked examples online. We also describe the positive impact that including this material had on student attitudes in a calculus class.