How to Make Initial Guesses for Parameters in a Nonlinear Model?

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The discussion focuses on making initial parameter guesses for the nonlinear model defined by the equation y = a + b*Ln(x) + c*x. Participants confirm that the model is linear in terms of the parameters a, b, and c, allowing for the application of least squares analysis. By substituting data pairs (x_i, y_i) into the equation, users can create a linear system to solve for the parameters effectively. This approach simplifies the calibration process using existing data.

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I have calibration data and I'm want to use the following model:

y = a + b*Ln(x)+ c*x

I'm looking for a way to make initial guesses for the three paramaters a, b and c.

Is there any way to linearize this expression so that I can use least squares analysis to determine values for a, b and c.
 
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Your problem is already linear in a, b and c (which are the variables you're trying to fit).

edit: to be a bit more explicit, given a pair of data values (x_i, y_i) you get a the following equation

a*1 + b*Ln(x_i) + c*x_i = y_i

which is a linear combination of the unknowns (a, b, c).
 
Last edited:

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