How to extract linear fits from a semilog plot?

I have a semilog plot of current vs Voltage through a device. I want to extract multiple linear fits in different regions as shown in the black dashed lines on the plot below.

I have the x and y data and have tried the curve fitting app but have trouble fitting multiple lines in these specific regions. Is there somewhere I should be looking for guidance on this or is anyone aware of how to do this? I plan to do this quite often and would like to establish a good system of fitting.

[Suvansh Arora]

In order to better assist you, please attach the dataset you are using.

[Mathieu NOE]

helo

yu may have to do a specific function for your job

see for example :

Bode plot with asymptotes - File Exchange - MATLAB Central (mathworks.com)