2. In physics, Hooke's law states that the force F that is applied to an ideal spring is proportional to the displacement y (i.e., F = Icy for some constant k). Consider a spring in which I: is unknown. Various masses are attached, and the resulting displacements are observed. Using these observations, determine the least squares estimate for k. y(inch) 11.1 15.4 17.5 22 26.3 F(lb) 5 7 8 10 12 Substituting the given values, we get: k = (11.15 + 15.47 + 17.58 + 2210 + 26.3*12) / (11.1^2 + 15.4^2 + 17.5^2 + 2242 + 26.3^2) = 0.424 Therefore, the least squares estimate for k is approximately 0.424