 Each experimental observation will contain some error, formula_48, and so we may specify an empirical model for our observations,

There are many methods we might use to estimate the unknown parameter "k".Since the "n" equations in the "m" variables in our data comprise an overdetermined system with one unknown and "n" equations, we estimate "k" using least squares.The sum of squares to be minimized is

The least squares estimate of the force constant, "k", is given by

We assume that applying force causes the spring to expand.