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Aug 27, 2019 at 4:56 comment added mkt @DilipSarwate All excellent points, thanks again.
Aug 26, 2019 at 22:04 comment added Dilip Sarwate A couple of additional embellishments to your answer: (i) $n$ must be even (say $n=2k$) and (ii) exactly $k$ residuals must have value $+\sigma$ and exactly $k$ residuals must have value $-\sigma$, which of course means that all residuals have absolute value $\sigma$ as you state, but (ii) ensures that the residuals sum to $0$ as they must. The residuals are the deviations from the mean and so must sum to zero.
Aug 26, 2019 at 8:57 history edited mkt CC BY-SA 4.0
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Aug 25, 2019 at 14:35 vote accept Perl Del Rey
Aug 25, 2019 at 9:41 history edited mkt CC BY-SA 4.0
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Aug 25, 2019 at 9:26 vote accept Perl Del Rey
Aug 25, 2019 at 14:35
Aug 25, 2019 at 9:14 history edited mkt CC BY-SA 4.0
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Aug 25, 2019 at 8:56 vote accept Perl Del Rey
Aug 25, 2019 at 9:26
Aug 25, 2019 at 4:49 comment added mkt @DilipSarwate Thanks for the input
Aug 25, 2019 at 4:48 history edited mkt CC BY-SA 4.0
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Aug 25, 2019 at 0:41 comment added user20160 @mkt Thanks for the kind words. Your answer is correct and concise (+1)
Aug 24, 2019 at 18:42 comment added mkt @DilipSarwate I was pondering this when user20160 added a much better answer that covers it in more detail than I could.
Aug 24, 2019 at 17:56 comment added Dilip Sarwate Could you give an example of the other scenarios that you envision? I mean an example other than a scalar multiple (when all the residuals are $\pm \sigma$ instead of $\pm 1$) of the example above.
Aug 24, 2019 at 14:07 history edited mkt CC BY-SA 4.0
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Aug 24, 2019 at 13:09 history answered mkt CC BY-SA 4.0