(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that you are given a set of observations (t_{k},y_{k}), 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) |t_{k}-t_{j}| 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.

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# Least squares

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