The benefits of teaching inverse regression alongside Least Squares Regression: Deeper comparisons for undergraduate research
Keywords:
Regression, Inverse Regression, Least Squares, Temperature Data, UndergraduatesAbstract
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.
References
Gao, D. and Scariano, S. M. (2021). “The Benefits of Teaching Inverse Regression Alongside Least Squares Regression: Graphical and Numerical Comparisons”, Research Journal in Advanced Sciences, https://royalliteglobal.com/rjas/article/view/457.
Harter, W. L. (1974). “The Method of Least Squares and Some Alternatives: Part I, Vol. 42, No. 2, (Aug., 1974), pp. 147-174.
Peck, R. (2015). Statistics: Learning from Data, Cengage Learning, Stamford, CT.
Peck, R., Olsen, C, and Devore, J. (2015). Statistics and Data Analysis, 5th ed. Cengage Learning, Boston, MA.
Weiss, N. (2012). Elementary Statistics, 8th ed. Addison-Wesley, Boston, MA
Stigler, S. M. (1981). “Gauss and the Invention of Least Squares,” Annals of Statistics, Vol. 9, No. 2, 465-474. https://projecteuclid.org/download/pdf_1/euclid.aos/1176345451
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