Suppose you hang a bucket from a spring that stretches it 15 mm from its natural length. You then fill the bucket with different weights of sand and record the total distance stretched as recorded below.
(a) Because the spring was stretched before the first amount of sand was added, Hooke's law predicts that the relationship between the stretched, D, and the weight of the sand, W, is D = mW + 15. Create a graph of the data to test if this prediction is reasonable. If it is, use the Least-square method to estimate the value of m.
(b) We could also estimate the value of m by transforming the data by subtracting 15 from each distance measurement, and then fitting a straight line through the origin to the transformed data. The slope of this line is m. Do this and compare the value of m to that found in (a).