The Y's and why not's of line of best fit

This article presents a sequence of explorations and responses to student questions ( Why not use perpendicular deviations? Why not minimize the sum of the vertical deviations? Why not minimize the sum of the absolute deviations? Why minimize the sum of the squared deviations?) about the rationale for the commonly used tool of line of best fit. A noncalculus-based motivation is more feasible than is often assumed for each aspect of the least-squares criterion "minimize the sum of the squares of the vertical deviations between the fitted line and the observed data points."