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I have a question about my Cross Validated post: The formula of a coefficient from a regression with 3 independent variables (not in matrix form)

I posted the original question today and immediatelly it got marked as duplicate. The warning about it being a duplicate states: "This question was marked as an exact duplicate of an existing question. If this question is different, please edit it to explain how it is different".

As anyone can clearly see, the question is not a duplicate. To the point that the moderator who marked it as duplicate, justified in the comments why he did so despite of the fact that he/she knows it is not an exact duplicate - on the contrary to what the warning of "marked as duplicate" says.

I would go even as far as saying that the question is not only not a duplicate, but it is exactly building on the one that it was accused as being a duplicate from. The whole point in my question was exactly to understand how to generalize the problem to more than 2 variables because I got confused with the generalization.

If needed, I could easily ask the question in terms of "how to generalize it to the case of n variables". So, my first question here in the meta:

1) would that make it an acceptable question if re-ask it terms of generalizing to X_n?

2) or, what if I re-ask and show what I got for the 3-variable case and ask what is wrong?

Note that I am interested in the generalization case up to $X_n$ and only asked a question about 3 variables to simplify. Also note that I am specifically interested in not using the matrix form, for learning purposes.

Finally, because I think that in this case the moderator abused the meaning of "duplicate" just to block a question he/she thought didn't need an answer, the last bit to ask here is:

3) aren't there any limits for the extent to which the rules can be strecthed? If one finds answering a question to be non-sensical, that's fine. Don't answer. But this alone does not qualify a question as duplicate according to the very rules of this site.

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    $\begingroup$ Hi @blipblop and welcome to CrossValidated! I can see why whuber closed your question as a duplicate, but I also agree with you that it's not really a duplicate. I guess we tend to take a bit of a liberal view on duplicates here and sometimes questions get closed even though the OPs would prefer to keep them open. This can happen & is fine. You can edit your question to clarify why it is not a duplicate. In particular, you can specify that you went through the linked thread already. Any edit will put your question into a reopen review queue and if 5 people vote to reopen it will get reopened. $\endgroup$ – amoeba Feb 12 '17 at 22:27
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    $\begingroup$ Re (2): please do not re-ask! Instead, you can edit your question to show what you got. This might be a good idea. Re (1): the general form is probably not answerable at all. $\endgroup$ – amoeba Feb 12 '17 at 22:29
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    $\begingroup$ I agree with @whuber that a line has to be drawn somewhere; & that the result you're asking for is neither use nor ornament - if it's for learning purposes you'd be better off working it out yourself (though with two & three predictors ought to be enough to understand what's going on). By the way, see Overzealous marking as duplicate: the question which yours was closed as a duplicate of was itself once closed as a duplicate. whuber's concern that we might "accumulate a growing list of versions of this question" seems to be well founded :) $\endgroup$ – Scortchi Feb 13 '17 at 10:51
  • $\begingroup$ @Scortchi "though with two & three predictors ought to be enough to understand what's going on". Precisely. Having an answer about two predictors does not exhausts what is needed to help people struggling with this. The three-cases would precisely show how to extend it properly to the generic case - e.g. not accounting for the relationship between $X_2$ and $X_3$. But, as I suspected, there is no point in discussing all this - the fact that a moderator finds a question to be "neither use nor ornament" will always be enough to close down a question. No matter whether it fits the rules. $\endgroup$ – blipblop Feb 13 '17 at 19:59
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    $\begingroup$ Oops! Sorry - I was including the intercept / thinking of the no. simultaneous equations to be solved. Regarding what constitutes a duplicate in general, we're not obliged to spell it out with legalistic precision, & have never tried to do so; @whuber's explained his reasoning in this case. And note that other users can & do reverse moderators' decisions to close: so far one's voted to re-open your question, & three to leave it closed. $\endgroup$ – Scortchi Feb 13 '17 at 21:28
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    $\begingroup$ @Scortchi I voted to reopen because I find OP's case quite convincing. I can see why the Q could have been initially closed as a duplicate, but after OP's repeated & well-explained protests, I, frankly, find it puzzling that people do not vote to reopen. Closing duplicates should, among other things, help OPs quickly find good answers. If OP read the duplicate link, gave it some thought, and still does not consider their question answered (and can explain why), then I feel we basically have to reopen it. Otherwise we fail to help and, worse, make a pose out of it. $\endgroup$ – amoeba Feb 13 '17 at 23:02
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    $\begingroup$ @amoeba: I don't agree that we have to - the CV community surely have a right to decide for ourselves what kind of questions we want here - , but given that the question's not wildly off-topic, the OP's not convinced by the arguments that answering it would be rather pointless, & I can't see any positive harm in it; I'd be inclined to re-open it just to show goodwill. If there are a few more votes to re-open, I'll add mine. But I still say the OP would be helped a great deal more by careful study of the comments & the three linked posts - they're certainly not getting short shrift here. $\endgroup$ – Scortchi Feb 14 '17 at 16:58
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I am happy to debate this, and would not be offended to be found on the wrong side of the debate. But let's get the facts into the open. For the record, here are the explanations I provided for why the question was closed.

I realize the duplicate is only for three predictors. [I meant to write "two", btw.] However, there has to be an end somewhere, lest we accumulate a growing list of versions of this question where "two" becomes "three" becomes "four" ad infinitum and ad nauseam. At some point--and I sincerely think it has occurred by the time there are two independent variables (which, with a constant, actually make three)--it becomes clear that these questions are asking for painful elaboration of the complicated formulas lurking behind the matrix equations, and as such they have no interest for statistics or computation.

Generalization is incredibly obvious: use matrices. If you really want to unfold the formulas for matrix inversion into sums and products, then go ahead. But I stand by my opinion that this is of no interest or use in statistics or machine learning.

You might find it informative, as well as useful, to know that as soon as you have a formula for even one independent variable, you can leverage it into an algorithm for any number of independent variables. I have explained this in answers at stats.stackexchange.com/questions/46185 and stats.stackexchange.com/questions/17336, inter alia. I'm not saying there's anything the matter with your question or that it's somehow stupid--it's not. It's just that it makes no sense--and would even be counterproductive--to attempt an answer in light of the facts I have brought forward.

My concern is a simple one: if we do not allow trivial duplications of this sort to count as duplicates, then we risk encumbering the site with redundant answers. How should we respond to the hypothetical person who says their question about how to apply a t-test differs from one exactly like it (involving a sample size of $98$) because they have a dataset of size $99$ instead of $98$? I appeal to your reason and common sense: if anyone capable of understanding the question as asked could reasonably be expected to recognize that a purported duplicate is purely and obviously a mathematical variation of the same question, then the purported duplicate counts as an "exact" duplicate.

(The present case goes beyond this fundamental concern insofar as I see no interest for statistics or machine learning in writing out the formulas separately for matrix products and inverses for two, three, four, ... dimensions. Anyone can look those up and apply them as they see fit. But that's not the basic, original reason for voting to close this question.)

Another twist in this case is the artificiality of demanding that answers not use matrix notation. I view such questions as being similar to others that ask for some algorithm or procedure that has already been given elsewhere on the site, but the OP demands an answer in some other language. We close those questions, too.

Please note that I am not trying to preclude related questions. This one could be made on topic in numerous ways, such as by asking what are efficient methods to compute OLS estimates; why do people not use formulas like Cramer's Rule to compute those estimates; or even why do all explicit formulas use matrix notation?

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