Non-linear least squares

Non-linear least squares is like trying to fit puzzle pieces together. Say you have a big puzzle with lots and lots of little shapes. You know what the picture is supposed to look like when it's finished, but some of the puzzle pieces don't fit exactly right.

So, you have to move the pieces around and try different things until everything fits together as closely as possible.

In math, we call this "minimizing the distance between the puzzle pieces and the final picture." This is what non-linear least squares does.

It helps you figure out the best way to fit a curve or a surface to a bunch of data points, even if the curve or surface isn't a simple, straight line. It's like finding the best puzzle piece to fit with another one, but with a lot more math involved.

Non-linear least squares can be used in all kinds of fields, from physics and engineering to economics and biology. It's a powerful tool for making sense of complicated data sets and finding patterns that might not be obvious at first glance.