Regression and Residual Analysis in the Spectroscopic Study of Conjugated Dyes

The study of conjugated dyes within the framework of the one-dimensional particle-in-a-box (1D PIB) model is a fundamental experiment in undergraduate physical chemistry curricula. This work extends the analysis of this commonplace experiment with the inclusion of regression and residual analysis, which allows students to explore data fitting, parameterization, and model testing in a controlled fashion. The work herein describes an instructor-led activity to optimize an empirical factor used in a 1D PIB model for a series of cyanine dyes and their respective visible absorption spectra. Students gain experiential use of regression and residual analysis within a process that facilitates a consistent experience for all, independent of the quality of data collected. This makes for an effective educational tool for teaching regression and residual analysis and model parameterization.