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Errors in fitting to data, relationship to residue

  1. Feb 6, 2012 #1
    Hi,

    I'd like to fit a straight line to some data which is noisey with gaussian noise with some st dev.

    Using least squares, I can estimate the slope and intercept. I'd like to know the uncertainty in these numbers. I can find the residue, I believe this is a measure of the variance of the noise.

    Using a simulation with N points, each with noise st dev. σ, I find the variation in estimated slope is proportional to σ/(√N^3), which I can't explain, I'd have expected sigma over root N, as for the standard error.

    Any help would be fantastic. I just want to know what error to quote with my fitted gradient.

    Mike
     
  2. jcsd
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