Derivation of the least squares line for a set of bivariate data entails minimizing a function of two variables, say the line's slope and intercept. Imposing the requirement that the line pass through the mean point for the data reduces this problem to a 1-variable problem easily solved as a single-variable Calculus exercise. The solution to this problem is, in fact, the solution to the more general problem. We illustrate with a dataset involving charitable donations.
Constantine, Ken, "Linear Regression as a 1-Variable Optimization Exercise" (2003). ACMS Conference Proceedings 2003. 5.
Applied Mathematics Commons, Computer Sciences Commons, Higher Education Commons, History of Science, Technology, and Medicine Commons, Mathematics Commons, Science and Mathematics Education Commons, Teacher Education and Professional Development Commons