I'm analyzing the Least Squares Fitting algorithm on this site.
You can read there:
The condition for $R^2$ to be a minimum is that $ \frac{\partial (R^2)}{ \partial a_i} = 0$
But I learned that this condition stands for extremum. Minimum or maximum!
How to proof that $R^2$ (the sum of squares) achieves there it's minimum?
I'm interested in a simple two dimensional proof.