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Homework Help: Least Squares Fit

  1. Dec 3, 2009 #1
    1. The problem statement, all variables and given/known data
    For the following data, find the least squares fit of the given form

    2. Relevant equations

    3. The attempt at a solution
    So I tried to linearize the equation by taking the natural log of everything

    that when I run into a problem, I eliminate the x's.
    My question is, is there another way to linearize the equation or should I continue though?
  2. jcsd
  3. Dec 4, 2009 #2
    That's not right. In particular,
    [tex] \ln (ae^{-x} + be^x) \neq \ln (ae^{-x}) + \ln (be^x) [/tex]
  4. Dec 4, 2009 #3


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    Science Advisor

    There is no reason to linearize anything. Nor are you trying to fit the curve to those points- just the "least squares" fit.

    If [itex]h(x)= ae^{x}+ be^{-x}[/itex] then [itex]h(1)= ae+ be^{-1}[/itex]. Since you are told that y= 14 when x= 1, the "error" is [itex]ae+ be^{-1}- 14[/itex] and the "error squared" is [itex](ae+ be^{-1})^2[/itex]. Similarly, for x= 2, y= 10, the "error squared" is [itex](ae^2+ be^{-2}- 10)^2[/itex].

    For all 5 x,y pairs, the sum of errors squared is [itex](ae+ be^{-1}- 14)^2[/itex][itex]+ (ae^2+ be^{-2}- 10)^2[/itex][itex]+ (ae^3+ be^{-3}- 8)^2[/itex][itex]+ (ae^4+ be^{-4}- 6)^2+ (ae^6+ be^{-6}-5)^2[/itex]. Find a and b to minimize that.
  5. Dec 4, 2009 #4
    What procedure would I use to find a and b? I know about the error...would I convert the sum of the errors squared into normal equations?
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