Work in Progress - The Rod-Spring Approximation: An Intuitive Approach to the Best-Fit Least-Squares Linear Approximation

Best Fit Least-Squares (BFLS) is a required technique for many STEM subjects. It is a method to compute a linear model for a set of data points. Due to its utility, BFSL is frequently taught to STEM students before they have sufficient mathematical experience to follow the mechanics of a derivation. Not only does this fail to produce procedural and conceptual understandings, but also it encourages students to view formulae and algorithms as things to be looked up, rather than derived. This is discourages students from developing productive dispositions. In this paper, we describe the "Close Fit Rod-Spring" (CFRS) approach to the problem. This approach computes the resting position of a rigid rod, which is connected by vertically oriented springs to a set of data points. This method of derivation results in two linear equations that may be solved for the slope and intercept of the best fit line. The result is equivalent to BFSL. However, it is achieved in an intuitively understandable and mathematically accessible way for high school students.