Why Is the First Derivative Zero in Least Squares Optimization?

[Amany Gouda]

Hello Sir,

I would studying the theory of least square and I find that the derivative of the error summation between the predicated line points and the true data is equal zero. Why the first derivative is equal zero?

 

[haruspex]

Hello Sir,

I would studying the theory of least square and I find that the derivative of the error summation between the predicated line points and the true data is equal zero. Why the first derivative is equal zero?

I'm partly guessing exactly what you did, but I suggest it is because the method finds the line that minimises the sum square of errors, and when a smooth function is at a maximum or minimum the slope (derivative) of the function is zero.

 

[Amany Gouda]

You are right, I have the same opinion regarding the answer. But is there a prove to this fact?

 

[haruspex]

You are right, I have the same opinion regarding the answer. But is there a prove to this fact?

A proof of which fact? That at an extremum the derivative is zero?

 

[Amany Gouda]

Unfortunately, there is a prove but I didn't reach to it.

 

[Mark44]

Unfortunately, there is a prove but I didn't reach to it.

What does this mean? Did you find a proof but were unable to follow the logic of it?