Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data in the sense of a least squares fit. Whether it be simple linear regression or nonlinear regression, this topic opens the door to applying the mathematical ideas about lines, as well as curves (from families of exponential, power, logarithmic, polynomial, sinusoidal, and logistic functions) to situations from all walks of life. From an instructor's perspective, these applications provide additional ways to reinforce the key properties of each family of functions. From the students' point of view, they see how the mathematics being learned has direct application in modeling a very wide variety of situations. Moreover, these methods are precisely the same mathematical ideas that the students encounter in all of their quantitative courses, so the mathematics becomes much better linked to the other disciplines. Fortunately, these capabilities are generally built into graphing calculators and spreadsheets such as Excel, so it becomes very simple to incorporate the methods into courses at this level. In this article, the authors develop an algebra-based derivation of the regression equations that simultaneously reinforces other concepts that one would treat in college algebra and precalculus.