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In a neural network class I'm taking the error measure is defined as:

enter image description here

If the purpose of squaring the difference of the predicted and target values is to always have a positive value, then why not just use the absolute value of the difference instead?

Secondly, why is the summation halved?

Many thanks for the help!

In a neural network class I'm taking the error measure is defined as:

enter image description here

If the purpose of squaring the difference of the predicted and target values is to always have a positive value, then why not just use the absolute value of the difference instead?

Secondly, why is the summation halved?

Many thanks for the help!

In a neural network class I'm taking the error measure is defined as:

enter image description here

If the purpose of squaring the difference of the predicted and target values is to always have a positive value, then why not just use the absolute value of the difference instead?

Secondly, why is the summation halved?

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Error Measures, why is the sum halved? why not use the absolute value?

In a neural network class I'm taking the error measure is defined as:

enter image description here

If the purpose of squaring the difference of the predicted and target values is to always have a positive value, then why not just use the absolute value of the difference instead?

Secondly, why is the summation halved?

Many thanks for the help!