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I am stuck in trying to solve the following:

Given two points $(x_{1}; y_{1})$ and $(x_{2}; y_{2})$, to determine the parameters $a$ and $b$ in the equation:
$$y=\frac{e^{a+bx} - e^{a}}{1+e^{a+bx}}.$$
In other words, I have two unknowns and two set of points, so there's for sure a solution, but how can the following system of equation be rewritten explicitly on $a$ and $b$?

$$\left\{\begin{matrix} y_{1}&=\frac{e^{a+bx_{1}} - e^{a}}{1+e^{a+bx_{1}}}\\ y_{2}&=\frac{e^{a+bx_{2}} - e^{a}}{1+e^{a+bx_{2}}} \end{matrix}\right.$$

Should I implement an equation solver instead? In which case, do you have any suggestion on the method?

Thanks very much, I hope it's not a too stupid question :)

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    oops misread your question, never mind2010-12-06
  • 0
    can you figure out good initial estimates for $a$ and $b$, should you choose the iterative route? Then Newton-Raphson should do the job.2010-12-07

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