Centroids, Vectors, and Least Squares

A mechanical model is presented which corresponds to the mathematical problem of determining the straight line best fitting a series of points according to the least squares criterion. The model consists essentially of a bar in equilibrium under the action of suitably arranged springs. By applying certain relationships between centroids of points and vectors in equilibrium, two points can be located which determine the correct line. A graphic method can thereby be developed for drawing the line without any calculations. The technique is illustrated for the case of three points.