>>14266651You're right, but the fact that it has an exact analytical solution (a.k.a. it is invertible) means there are a LOT of computational cheats you can use.
The problem has one unique solution, and has NO other minima. You can use fixed point algorithms and quickly get to your solution set.
Linear regression is a well-posed problem and this makes it superior to many many other techniques because many nonlinear problems are not well posed (there are often multiple solutions not to mention multiple local minima). It's why linear regression and all the different methods for linearizing a problem are the first things anyone is taught (or should be taught at least)