A simple algebraic derivation of the equation for a line of best fit

Abstract We present a simple algebraic derivation of the equation for a line of best fit. Unlike conventional derivations, which require multi-variable calculus, our argument relies on elementary algebra alone, and avoids more advanced notation (such as the sigma summation symbol) by exploiting routine data averages. In this way, our approach demystifies the process of computing a linear regression, and is likely to be of interest to students and instructors alike. We illustrate the main results with a worked example taken from an introductory physics context.