multivariable regression, known structure, calculate coefficients

Hi, I have the equations for calculating the corrosion rate (r_corr) of different materials (e(1) steel, e(2) zinc, e(3) copper, e(4) aluminium, see below). (According to ISO 9223).

My goal is now to create a fifth equation for another type of material. I have generated data where r_corr was measured along P_d, RH (relative humidity), T and S_d.

How can you calculate the coefficients (marked below in yellow) for the new material? I want to use the structure of the equations below. So to speak:

r_corr = a * P_d^b * exp(c * RH + f_St) + d * S_d^e*exp(f * RH + g * T)

Thank you very much!

Answer 1

[the cyclist]

If you have the Statistics and Machine Learning Toolbox, you should be able to use the fitnlm function.

[Ansgar Elles]

Thanks, i've tried it out, but so far I cant get convergence.

[the cyclist]

I'm not too surprised. With 7 free parameters, you'll like need a lot of data to fit a stable statistical model.

If you can post your data, it might help people have some more specific ideas.