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Help me to make best fit with error

  1. Mar 12, 2008 #1

    I have a set of datapoints (x_i,y_i) and I am gonna make a best fit to y = c*Exp(a/x)

    Making the fit isn't the problem (Mathematica, etc. can handle this), but what I need is the error on a.

    What I have done so far is something like this:

    P(c,a | {x_i,y_i} ) = k * P( {x_i,y_i} | c,a ) using Bayes.

    And then

    P({(x_1,y_1),(x_2,y_2),...}|c,a) = product of ( P(x_i,y_i | c,a) ) for all i's.

    which is proportional with

    product of ( P(y_i | x_i, c,a) )

    But I can't get any further than this :)

    Can any one help me with this ?

    Thanks in advance
  2. jcsd
  3. Mar 13, 2008 #2


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    How are you defining the error on 'a'? Totally missing what you mean!
  4. Mar 14, 2008 #3


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    Homework Helper

    y = c*Exp(a/x)
    Log y = Log c + a (1/x)
    v = d + a z where v = Log y, d = Log c and z = 1/x.

    Now you have a linear regression that you can compute with any type of software that will print out the standard errors for the regression parameters d and a. For example, Excel. Or use the Regress function in Math'ca (after you enter Needs["LinearRegression`"]).
    Last edited: Mar 14, 2008
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