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A comment on Simple example of machine learning in TensorFlow. Parent comment
The following answer is about standard deviation but the desired properties from squaring is also relevant to your question:
http://stats.stackexchange.com/questions/118/why-square-the-...
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The following answer is about standard deviation but the desired properties from squaring is also relevant to your question:
http://stats.stackexchange.com/questions/118/why-square-the-...