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Linerization of non-linear models

  1. Mar 6, 2009 #1
    Hello,
    I'm a student from Lithuania. I have found in one forum topic your discussion about non-linear equation convertion into a linear form.. I have some problem with that...Could you help me, please? :)
    For, example, I have two non-linear models:
    1. y = a [1/(1+b/(c+x))]*exp(-d*x)
    2. y = a*exp[b*(1-exp(-c*x))/c - d*x]
    And I want to convert it into linear equation, for fitting linear regression theory, of course, I could fit a newton or other method, but there are some problems with initial values. So, I would like to see the results of fitting to these models a linear regression and compare with iterative methods.

    So, could you help me?

    I think, that these two models linear form will be:
    1. ln(y) = ln(a) - ln(1+b/(c+x)) - d*x + err
    2. ln(y) = ln(a) + b(1-exp(-c*x))/c - d*x
    lnln(y) = lnln(a) + ln(b/c)-ln(b/c)-c*x -ln(d) + ln(x)

    the main problem is, how to estimate unknow a,b,c,d parameters...using for example, SAS programe package.

    I would waiting from you any help.

    With best regards, Ms. Dovile.
     
  2. jcsd
  3. Mar 6, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    ?? None of your suggested "two models linear form" are linear.
     
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