1. The problem statement, all variables and given/known data Suppose that you are given a set of observations (tk,yk), k = 1,...,M. You plot these points on a sheet & it seems that the relationship between (t,y) could be approximated with a second order polynomial. a) Write down the model in the form y = Ax + c. Specify the vectors & matrices & give interpretation to all terms. b) Write down the least squares estimate x(hat) for x. c) Let the elements of x bear a physical interest. How could you assess the accuracy of the estimate x(hat)? d) How would you assess the stability of the problem if max(k,j) |tk-tj| is very small? It may help if you draw a picture. Or better still, study the structure of the matrix A. 2. Relevant equations 3. The attempt at a solution a) Not sure on this one. b) Isn't that just using the definition of least squares. c) Not sure on this one. d) Not sure on this one.