Visualization of Lines of Best Fit

Authors

  • Michael J. Bosse Appalachian State University
  • Michael Rudziewicz US Army
  • Gregory S. Rhoads Appalachian State University
  • Eric S. Marland Appalachian State University

DOI:

https://doi.org/10.4256/ijmtl.v18i3.38

Abstract

Humans possess a remarkable ability to recognize both simple patterns such as shapes and handwriting and very complex patterns such as faces and landscapes. To investigate one small aspect of human pattern recognition, in this study participants position lines of "best fit" to two-dimensional scatter plots of data. The study investigates the variation in participants' fits and whether there is some consistent metric being used in fitting the lines. For example, is there a natural tendency toward fitting lines similarly to one of the standard regression lines: vertical, horizontal, or orthogonal. This study also investigates the effect of outliers on the line a participant fits to a scatter plot with a strong linear trend and provides guidance for future inquiries.

Author Biographies

Michael J. Bosse, Appalachian State University

Michael. J. Bossé is the Distinguished Professor of Mathematics Education and MELT Program Director at Appalachian State University, Boone, NC. He teaches undergraduate and graduate courses and is active in providing professional development to teachers in North Carolina and around the nation. His research focuses on learning, cognition, and curriculum in K-16 mathematics.

Michael Rudziewicz, US Army

Michael Rudziewicz is an Intelligence Analyst for the U.S. Army. He has taught precalculus and college algebra while earning a Graduate Degree in Mathematics from Appalachian State University, Boone, NC. He has researched topics involving researching patterning recognition and linear regression.

Gregory S. Rhoads, Appalachian State University

Gregory S. Rhoads is an associate professor in the Department of Mathematical Sciences at Appalachian State University, Boone, NC. He teaches a wide range of courses in mathematics at the undergraduate and graduate level. His research interests include complex analysis, history of mathematics, and innovative curriculum.

Eric S. Marland, Appalachian State University

Eric S. Marland is Professor and Chair of the Department of Mathematical Sciences at Appalachian State University, Boone, NC. His primary research focuses on mathematical analyses of environmental systems, sustainable practices, and climate change policies. He is also heavily involved in outreach activities for k12 students, teachers, and mentors.

References

Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics 52(3), 215-241.

Embse, C. V. (1997). Visualizing least-square lines of best fit. The Mathematics Teacher 90(5), 404-408.

Leng, L., Zhang, T., Kleinman, L., & Zhu, W. (2007). Ordinary least square regression, orthogonal regression, geometric mean regression and their applications in aerosol science. Journal of Physics: Conference Series 78 012084, doi:10.1088/1742-6596/78/1/012084. Retrieved from http://iopscience.iop.org/article/10.1088/1742-6596/78/1/012084/pdf.

Mosteller, F., Siegel, A. F., Trapido, E., & Youtz, C. (1981). Eye fitting straight lines. The American Statistician 35, 150-152.

Moore, D. S., Notz, W. I., & Fligner, M. A. (2015). The basic practice of statistics, Instructor's edition (7th ed.). New York: W. H. Freeman.

Motulsky, H. J., & Ransnas, L. A. (1987). Fitting curves to data using nonlinear regression: A practical and nonmathematical review. The FASEB Journal 1(5), 365-374.

Rousseeuw, P. J., & Leroy, A. M. (1987). Robust regression and outlier detection. New York: Wiley.

Downloads

Published

2017-12-06

Issue

Vol. 18 No. 3 (2017): International Journal for Mathematics Teaching and Learning

Section

Articles