Suppose we which to determine the extension of a spring, y, as a function of the force F applied to it. We know that the extension of the spring is proportional to the force applied to it (this is Hooke's law), so we know that y = kF , where k is some constant. To estimate k we take a series of n measurements with different amounts of force, creating a dataset (Fi,yi), where i = 1, ..., n. Each observation contains some measurement error, ui, giving us the following empirical model