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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
 one year ago
 one year ago
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
 one year ago
 one year ago

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pgerritsonBest ResponseYou've already chosen the best response.0
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.
 one year ago

sunsunsun1225Best ResponseYou've already chosen the best response.0
Thank you so much
 one year ago
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