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Abstract
Within the undergraduate mathematics curriculum, the topic of simple least-squares linear regression is often first encountered in multi-variable calculus where the line of best fit is obtained by using partial derivatives to find the slope and y-intercept of the line that minimizes the residual sum of squares. A markedly different approach from linear algebra, which could also be introduced in multi-variable calculus, obtains the regression line by vector projection. The latter viewpoint offers elegant proof of the equation relating the total, explained and unexplained variations. Consideration of data with the same regression line and correlation opens the door for a “mini-research experience” (MRE). A sequel MRE gives rise to an open Research Experience for Undergraduates topic to analyze reflection sequences and a fundamental connection between complex analysis and regression analysis. A few general guidelines and basic goals for MREs are included for those whose main interest is in undergraduate research.
Additional information
Notes on contributors
Paul Isihara
Paul Isihara, a math professor at Wheaton College (IL), has taught calculus every year for over three decades and supervised many MREs/REUs over the past 15 years.
Elisabeth Congdon
Elisabeth Congdon, after completing a Master’s degree in pure mathematics a year ago, served one year as an adjunct calculus professor at Wheaton College (IL), before entering a Ph.D. in mathematics at North Carolina State University.
Terry Perciante
Terry Perciante, an emeritus math professor at Wheaton College (IL), is a leader in fractal geometry and chaos theory pedagogy having worked in conjunction with an international research team at the University of Bremen in northern Germany.