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.
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.