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Homework Help: What I want is the uncertainty in the coefficients

  1. Jul 23, 2009 #1
    1. The problem statement, all variables and given/known data
    I was given a set of data from a Ion engine experiment. I fitted the data with an 8th order polynomial that seems pretty reasonable. What I want is the uncertainty in the coefficients.
    One way I read was through the design matrix.

    2. Relevant equations
    [tex] C_{ij}=(A^T A)^{-1} [/tex]

    3. The attempt at a solution
    The square root of the diagonals give the uncertainties. But my matrix in not invertible since its not square.
    What am I missing?
  2. jcsd
  3. Jul 23, 2009 #2

    The Electrician

    User Avatar
    Gold Member

    The matrix A may not be square, but

    [tex] (A^T A) [/tex]

    is square, so it's invertible.
  4. Jul 23, 2009 #3
    Thank you. Yes it turns out square but the inverse gives me problems.
    Maybe I am using the command wrong.
    Here are the results of a test.

    I threw in .1 just for error sake. My model is a+bx+cx^2. The uncertainties are suppose to be given by the square root of the diagonals of
    [tex](A^T A)^{-1} [/tex] A being the design matrix.

    Attached Files:

  5. Jul 24, 2009 #4
    Never mind I got it.
    I was able to find the covariance matrix and the associated uncertainties. I feel stupid.
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