I know the reason for using squared values is so the values don’t get cancelled out. Why not absolute values? I get it when calculating error metrics that squaring can punish the model more for bigger errors, but I don’t get the reason here.
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My stats professor told us absolute values can be used but the math is harder. I see that’s elaborated on already.
Where absolute is used is in electrical engineering to make digital filters. The standard method uses Chebyshev approximation of the second kind followed by the Remez exchange algorithm. This finds the best fitting polynomial with absolute error.
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