Regression error function minimization problem

Question

Could somebody please help with this problem. There is a little explanation in this link: meaning of some lines in a book

But it is still a bit ambiguous to me.

Answer 1

HINT

For easier notation, let $J(u,v) = \frac1n \sum_{i=1}^n (y_i-u-vx_i)^2$ and let $(u^*,v^*)$ denote the values at which $J$ achieves its minimum. Then, since $J$ is smooth, from calculus we know that $$ \left. \frac{\partial J}{\partial u} \right|_{u = u^*,v = v^*} = 0 = \left. \frac{\partial J}{\partial v} \right|_{u = u^*,v = v^*} $$ Can you find both partial derivatives?