Statisticians have long employed linear regression models in a variety of circumstances, including the analysis of sports data, because of their flexibility, ease of interpretation, and computational tractability. However, advances in computing technology have made it possible to develop and employ more complicated, nonlinear, and nonparametric procedures. We propose a fully nonparametric nonlinear regression model that is associated to a local correlation function instead of the usual Pearson correlation coefficient. The proposed nonlinear regression model serves the same role as a traditional linear model, but generates deeper and more detailed information about the relationships between the variables being analyzed. We show how nonlinear regression and the local correlation function can be used to analyze sports data by presenting three examples from the game of baseball. In the first and second examples, we demonstrate use of nonlinear regression and the local correlation function as descriptive and inferential tools, respectively. In the third example, we show that nonlinear regression modeling can reveal that traditional linear models are, in fact, quite adequate. Finally, we provide a guide to software for implementing nonlinear regression. The purpose of this paper is to make nonlinear regression and local correlation analysis available as investigative tools for sports data enthusiasts.
JQAS, an official journal of the American Statistical Association, publishes research on the quantitative aspects of professional and collegiate sports. Articles deal with subjects as measurements of player performance, tournament structure, and the frequency and occurrence of records. Additionally, the journal serves as an outlet for professionals in the sports world to raise issues and ask questions that relate to quantitative sports analysis.