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Why do we use SSE (the sum of squared errors) in calculations. Why do not we use the sum of errors? Could you explain please?

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marked as duplicate by Glen_b♦, gung♦, Nick Stauner, Nick Cox, ttnphns Apr 20 '14 at 6:10

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    $\begingroup$ I presume you meant "sum of absolute errors" for sum of errors. $\endgroup$ – ttnphns Apr 19 '14 at 14:09
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    $\begingroup$ The main reasons are two: 1) SSE is related to the estimating of the mean (See closely related question); 2) SSE and the mean are naturally related to linear algebra computations (see e.g. this). Still, absolute error is used sometimes too (for example when the central tendency is median). $\endgroup$ – ttnphns Apr 19 '14 at 14:15
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    $\begingroup$ Basically a duplicate of this, where in turn this is linked as 'essentially a duplicate'. Another near duplicate is this. There are others as well. $\endgroup$ – Glen_b♦ Apr 19 '14 at 17:14
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Errors can be both positive or negative. So if you just add them up (without squaring them), then the positive terms will cancel out the negative terms. This means that you are actually ignoring the errors that you have in your fitted model which is not good. But if you square them and find sum of squared errors, all the errors (i.e. both negative and positive) are taken into account since squaring makes all of them positive.

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