The application of linear regression to data analysis is traditionally a tedious calculation delegated to a computer. This article presents a physical model to facilitate an intuitive way of thinking about the slope of a fit. In this simple model, data points are envisioned as beads applying torques on a massless, rigid, horizontal rod. To illustrate how this model can help colleagues directly address special questions about fits, the model is applied to two situations in which there are repeated measurements of data. This rod-and-bead model also arrives at the coefficient of determination formula in a very straightforward way and makes the recollection of the least-squared slope formula and coefficient of determination much easier.
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PAPERS| October 01 2020
A physical model for intuiting linear regression
Phillip Cervantes, Patricia Purdue, Jeffrey Steele; A physical model for intuiting linear regression. Am. J. Phys. 1 October 2020; 88 (10): 795–800. https://doi.org/10.1119/10.0001509
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