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Math Help - least square fit method

  1. #1
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    least square fit method

    i have to least square fit function l=C/(1+e^(at))

    here i have e^(at) in denominator how to bring it in terms of
    Y=AX+B

    PLEASE HELP.
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  2. #2
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    Re: least square fit method

    are you saying you have a data set that you expect can be modeled by $\dfrac C {1+e^{a t}}$ and you want to estimate $a$ and $C$ from a least squares fit to your data?
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  3. #3
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    Re: least square fit method

    YES I KNOW FOR y=e^(at) we take log on both sides and compare with linear function y=ax+b
    but here e^(at) is in denominator
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  4. #4
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    Re: least square fit method

    Quote Originally Posted by prasum View Post
    i have to least square fit function l=C/(1+e^(at))
    here i have e^(at) in denominator how to bring it in terms of Y=AX+B
    You cannot on a direct way. Use a non-linear method of regression : Nonlinear regression - Wikipedia, the free encyclopedia
    Nevertheless, it can be transformed to a linear regression thanks to a method using an integral equation, paper published on Scribd : Régressions et équations intégrales
    page 17 : see the computation in the case y=a+b*exp(c*x)
    To apply in your case : l=C/(1+e^(A*t)) , let y=1/l ; a=b=1/C ; c=A
    The publisched method requires to be slightly adaped in the particular case a=b. Contact me if you intend to try this method.
    Last edited by JJacquelin; April 25th 2014 at 11:11 PM.
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