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Interpretation of the variance of a slope is unclear because the OP seems to be confused by notation, and therefore the notation in the question is confusing. StatStudent pointed this out in the comments, and suggested (correctly in my opinion) that the question could be answered by resolving this confusion.

I went ahead and edited the notation to better reflect what StatStudent (and I) thought the OP meant, but then had second thoughts.

What's the right thing to do here? I'm torn between making the question clear to future readers, but potentially making the answers and comments confusing, or leaving the question confusing (and maybe harder to find by searching) but then having the answers correspond better to the question as it was asked.

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    $\begingroup$ See e.g. meta.stats.stackexchange.com/questions/2810/… The suggestion there was that you don't correct conceptual errors. Trivial notation slips could be fine, but confused notation that suggests confusion of ideas remains part of the problem. Suggesting a better notation is then part of a good answer. At most, add a separate EDIT to the question with different notation, but my preference remains putting that in an answer and explaining why. $\endgroup$
    – Nick Cox
    Jan 27, 2016 at 21:10
  • $\begingroup$ @NickCox thanks for the pointer. $\endgroup$
    – shadowtalker
    Jan 27, 2016 at 21:18
  • $\begingroup$ @NickCox, it could make sense to turn you comment into an answer. $\endgroup$
    – Richard Hardy
    Jan 29, 2016 at 9:22
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    $\begingroup$ @RichardHardy Thanks, but I think this looks more like a duplicate. $\endgroup$
    – Nick Cox
    Jan 29, 2016 at 9:29

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