Aproximate data with this equation (or linearize the equation)

Question

I have found an equation that describes the behaviour of a phisical system:

$$ y=a_1e^{-a_2x} + a_3 + a_4x + a_5e^{{-a_6} / {(1-x)}}$$

Now I have data of that physical system and I want to aproximate the data with this equation because polinomials do not apromiate well enough untill 15th degree.

From the university courses I remember to aproximate data by exponential equations like $y = ae^{-bx}$ by aplying logarithms and making it linear, then we did least squares aproximation and undo the variable change.

I do not see how to make such a change for my main equation. is it even possible?

Basically I want to get the $a_n$ coefficients from data. What do you suggest?

Thanks in advance.

Answer 1

Let me suggest that you use some software for performing nonlinear regression such as nls in the R (or S) library. You will need to provide initial estimates of the parameters.