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The post, General expression for $\hat \beta_1$ in multiple linear expression is asking for a closed form expression of part of the coefficient vector in a linear regression model. Nevertheless it has been closed as a duplicate of a question asking for a closed form solution form the entire coefficient vector.

To me it is not really clear that these two questions are the same. Actually to me it is pretty clear that they are not the same under one interpretation.

Overall the question is a little unclear, but the present closure of the question makes it more difficult to clarify what the OP was really interested in.

What I do not understand is how this comes to be a duplicate of the cited question.

(I am partly asking with the following discussion in mind Are we closing questions too fast?)

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    $\begingroup$ I agree that the duplicate I selected for closure was not a duplicate, but was based on a misreading. However, I had no qualms about closing it because this issue (of computing partial regression coefficients) has occurred so frequently that anyone familiar with the site should have no problems finding excellent duplicates. The problem with not closing questions fast enough is that later on we have to merge the answer threads, which is a pain and can leave some puzzling dangling references for future readers. $\endgroup$ – whuber Dec 10 '19 at 14:57
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    $\begingroup$ @whuber "has occurred so frequently that anyone familiar with the site should have no problems finding excellent duplicates" The problem is that not everybody is familiar with the site, and those is who the site should serve. So now we see five questions linked as duplicate. But, they all see different to me, which one is the real duplicate? Maybe it doesn't seem so excellent after all? (or do we from now on divert to vague links or indirect hints to answers instead of clear full answers?) $\endgroup$ – Sextus Empiricus Dec 10 '19 at 21:01
  • $\begingroup$ Right--not everyone is that familiar with the site. Only a few thousand people at most can do a good job of identifying duplicates in most instances. That's why we can be helpful to everyone else. $\endgroup$ – whuber Dec 10 '19 at 21:10
  • $\begingroup$ Fair enough anyone can make a mistake misreading a question, but making the mistake worse by linking to questions that simply do not provide what the OP is asking for is not in my opinion being »helpful«. $\endgroup$ – Stop Closing Questions Fast Dec 10 '19 at 21:35
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I agree that the question is different.

The best thing to do is, I guess, improve the question in order to make it more clear.

This is stated in the help information

If you see a question and do not agree that it truly is a duplicate, edit it to highlight the differences, then try to get it reopened by casting a reopen vote.

That is what I tried. I have changed some format and text of the question in order to make the question more clear, and especially/hopefully make more clear the difference with the questions that is linked as duplicate.


What I do not understand is how this comes to be a duplicate of the cited question?

I can imagine that this may stem from the fact that the expression $Y = \beta_1X_2 + \beta_2 \cdot X_2$ looks very much like $Y = \beta_1X_2 + \beta_2 X_2$. Also, the original question was not very correct in expressing the meaning of $X_2$, a matrix instead of a vector, by stating $\beta_2,X_2 \in \mathbb{R}^k$

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    $\begingroup$ On the contrary, the best thing to do is to find the duplicates. After ten years and over 100K answered questions we can be confident that any basic question about a fundamental statistical tool will have good answers somewhere on the site. Searching the site is not easy: it requires understanding the question and experience and creativity in guessing how else the question might have been phrased before. One of the greatest services our regular readers can provide is to suggest suitable duplicates. $\endgroup$ – whuber Dec 10 '19 at 15:08
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    $\begingroup$ @whuber Indeed, I've memorized somewhat arcane sets of words which are unique to specific, high-quality duplicates so that I can search them more easily... $\endgroup$ – Sycorax says Reinstate Monica Dec 10 '19 at 15:51
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    $\begingroup$ @whuber, my answer was specific for the case when somebody feels that the close reason is not entirely correct (because the duplicate is not a close enough duplicate). Sure, if there are even more potential duplicate questions then it could help to look them up and link them (this is not so trivial for people <100k rep who do not know all questions by heart). Even then, I am personally feeling helped by the fact that this question has received an answer instead of being immediately closed. Due to the new answer by the OP, I have learned something which I had not learned otherwise. $\endgroup$ – Sextus Empiricus Dec 10 '19 at 16:43
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    $\begingroup$ @whuber Closing a question because it is duplicate, but none of the linked questions being duplicates of each other.... I find that something like a double standard. Neither do I see any of those duplicate questions where the answer by Jesper would be a good fit. The specific question might be very close to the others, but I believe that the real issue should be whether the specific question is the same. Each of the new duplicate links that you have added is still different. $\endgroup$ – Sextus Empiricus Dec 10 '19 at 16:47
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    $\begingroup$ @whuber a closing with a big list of alternative questions (I count five, but somehow none of them are duplicates of each other)... does that really help the OP? I guess that any person that has this same question about an expression for a coefficient $\beta_i$ instead of the vector $\beta$ will only be more confused after being directed to that big list of "duplicate" questions. $\endgroup$ – Sextus Empiricus Dec 10 '19 at 16:52
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    $\begingroup$ I figure that pointing to five different ways of answering the question has a better chance of communicating a solution to the OP than pointing to just one way. Your implicit assumption that "duplicates" is a transitive relation is incorrect: a thread can be considered a duplicate when it concerns a different question but nevertheless happens to answer the current one. The answer received by this thread is so close to several existing answers that I'm pretty sure we'll need to merge it with one of the dups. $\endgroup$ – whuber Dec 10 '19 at 18:51
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    $\begingroup$ @whuber you were pointing to five different ways to ask the question, but zero of them provide a good way to answer the question. I get that "duplicates" do not need to be transitive, but at the same time we should not believe that there is one (or five) questions that can ask any other variation.. $\endgroup$ – Sextus Empiricus Dec 10 '19 at 20:34
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    $\begingroup$ It is a grey/nuanced area. My answer here is just based on the colored viewpoint from somebody that was helped by the particular question and answer (and not by any of the suggested duplicates). Therefore, I strongly disagree with the suggestion that it would have been better to close the question (since for me, personally, it was not better). $\endgroup$ – Sextus Empiricus Dec 10 '19 at 20:38
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    $\begingroup$ I can not find the link (help documentation is difficult to find back on SE) but I remember the 'rule' that the idea of duplicate questions is not whether or not an answer to another question is also answering the question but about whether the question is the same as the other question. $\endgroup$ – Sextus Empiricus Dec 10 '19 at 20:43
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    $\begingroup$ "I figure that pointing to five different ways of answering the question has a better chance of communicating a solution to the OP than pointing to just one way." This might also be considered as: 'we do not like to consider your question, but you might try to figure out the answer yourselve by looking in one of these five questions', while at the same time the current answer under the question is answering the question better (more specifically) than any of the answers under the alternative questions. (the vaguely pointing to five other questions makes the duplicate reason only weaker). $\endgroup$ – Sextus Empiricus Dec 10 '19 at 20:51
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    $\begingroup$ There's no vague pointing: the close reason gives explicit links. As far as I can tell, each of those links has a clear explicit answer to the question. The non-antagonistic interpretation of the state of affairs is that people here have worked hard to identify a wide array of solutions likely to appeal to just about anyone. $\endgroup$ – whuber Dec 10 '19 at 21:12
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    $\begingroup$ It is vague because you select five options and follow it with "has a better chance of communicating a solution" (that is like saying, 'here is a bunch of questions that are a bit the same maybe you are lucky to find something useful'). What I would expect from a duplicate is another single question that clearly asks the same and also has answers that directly help the OP. If you can not bring down the list to one single duplicate, then is it really a duplicate? $\endgroup$ – Sextus Empiricus Dec 10 '19 at 21:14

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