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$\Sigma(X-\bar{X})$

Could someone please clarify: does the sum of deviations (not squared) of a variable from its mean have to equal anything special, like 0, or is it just any number?

Also, do I understand correctly that in a regression, the sum of squared deviations of y from the mean is minimized, but not equal to 0?

COOLSerdash
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1 Answers1

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The sum of the deviations from the mean of a measurement is always equal to 0. The proof is as follows:

$$\Sigma(x_i-\bar x)= \Sigma x_i-\Sigma\bar x= \Sigma x_i-\bar x\Sigma1 = \Sigma x_i-\bar x.n = \Sigma x_i-\Sigma x_i = 0$$

In a regression however it s the sum of the Squared Deviations of the Errors that is minimized (i.e. the sum of the of squares of actual y value minus predicted y value) which does not neccesarily have to be 0.

Nuzhi
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