Mini-research Experience in Simple Linear Regression. Issue 7 (9th August 2018)

• Record Type: Journal Article
• Authors: Isihara, Paul; Congdon, Elisabeth; Perciante, Terry
• Is Part Of: PRIMUS. Volume 28:Issue 7(2018)
• Page Start: 699
• Page End: 716
• Publication Date: 2018-08-09
• Subjects: Mini-research experience (MRE) -- simple least-squares linear regression -- 0-mean data -- calculus optimization -- vector projection -- data reflection -- reflection sequences -- complex analysis -- Fibonnaci sequence; Mathematics -- Study and teaching (Higher) -- Periodicals; 510.711
• DOI: 10.1080/10511970.2017.1405855
• Languages: English
• ISSNs: 1051-1970

Abstract

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.