How to minimize the relative approximation error?

Question

Algorithms

There is a set of measurements and reference values ​​for them. With the help of LSM I approximate a straight line and after applying the coefficients I get more accurate measurement values. The essence of LSM is to minimize the squares of the absolute deviation, so often the relative errors increase in this case (for small measurement values). Tell me how to make it so that when approximating, the relative error is minimized, and not the absolute one? Thanks in advance.

Answer 1

Well, just minimize the sum of squares of the relative error. Yes, the task becomes non-linear, but now this is not a problem, especially if there are few parameters. Take, for example, Python, choose an algorithm from scipy.optimize and go...