Question

Hi can anyone show how to use second derivative test to prove that the deviation of linear regression has a local minimum but not a maximum? thanks

Answer 1

The second derivative test \[f_{aa} f_{bb} - f_{ab}^2\]reduces to 4n^2( VAR(X)) where VAR(x) = \[1/n \sum_{i=1}^{n} (x_i - \mu)^2\] and \[\mu = 1/n \sum_{i=1}^n x_i\]. This is always positive, hence not a saddle point. \[f_{aa} = 2 \sum_{i=1}^n x_i^2\] which is always positive, hence a local minimum.

Answer 2

Thank you so much