The benefits of teaching inverse regression alongside Least Squares Regression: Deeper comparisons for undergraduate research

This article is a continuation of the authors’ previously published article, later referred as “Part I”, and entitled, “The benefits of teaching inverse regression alongside Least Squares Regression: Graphical and numerical comparisons”. In Part I of this companion series, a foundational exposition comparing Inverse Regression and Least Squares Regression was undertaken using temperature data for thirty-two American cities. Deeper relationships are explored in this article (Part II of this series). The goal is to contrast the estimates provided by both regression methods using a collection of corollaries that are accessible to undergraduate mathematics and science students who have studied Least Squares Regression. Collectively, these two articles demonstrate how to purposely enhance a general discussion of Least Squares Regression.