1. Imagine you have collected a set of data {i } that you think should obey a linear rela- tionship y(x) = ax + b. The following is a procedure for determining the optimal choice of a and b. This is example of data fitting. (a) Let Y; = y(i). Define J = ||Y, - :||2. What kind of objects are Y and J? (b) Note that J vanishes if Y; = yi, but that if Yi + yJ > 0. For this reason, J provides a measure of how well the relation y(x) represents the data. Least-squares fitting means to find a and b such that J is minimized J. Write down the necessary conditions to minimize J. (e) Solve the problem in (b) by recasting the conditions in matrix form. (d) In the assignment file you will find a comma separated filed data.csv with 3; in column one and wi in column two. Find a and b for the data therein. Plot the data and superimpose y(x). You can complete this in excel but python or matlab would be easier