The benefits of teaching Inverse Regression alongside Least Squares Regression: Graphical and numerical comparisons
Keywords:
Regression, Inverse Regression, Least Squares, Temperature Data, UndergraduatesAbstract
A good, college-level first course in descriptive and inferential statistics must include the topic of Least Squares Regression. Indeed, most modern statistics textbooks discuss linear regression as soon as the concept of statistical correlation is understood. This article demonstrates how to enhance a general discussion of Least Squares Regression with the concept of Inverse Regression. In Part I of this bipartite exposition, foundations are laid, and graphical and numerical comparisons are developed. Deeper relationships are then explored in Part II of this series.
References
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.
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
Weiss, N. (2012). Elementary Statistics, 8th ed. Addison-Wesley, Boston, MA.
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