This is a series of side-notes to @Glen_b's excellent answer.
Editing is a public service. Even some small edits can just clean up a post and make it easier for everyone to read, which is a positive contribution. Often an edit can change a question that looks too messy to wade through to one that looks readable. Editing can and should help the OP, who should get more and quicker attention (and, although this is a side-effect, who should also get feedback on their presentation for future questions). It helps others too.
Editing does not impart a moral judgment. We can't confidently and consistently distinguish between over-hasty, lazy presentation and someone struggling with one, two or even all three of a second language; statistics they really don't understand; and a medium that is unfamiliar. That said, I will on occasion comment firmly that a question (or answer) is just too messy to be worth anyone's time to edit. If the OP isn't able or willing to fix the presentation, then that is the end of the story: we are all volunteers here and there is no obligation to be infinitely helpful.
Changing just one small thing requires a careful decision. It will bump the question momentarily to the top of the active list. Some people are irritated to re-open a post of interest to find one minute change. But even threads that have seen many posts can carry errors worth correcting. Nevertheless, for this and other reasons, it is good advice that if you edit, edit everything that you spot as deserving change, so as to make the edit worthwhile.
Editing just the title can be valuable too. Posters can be especially blind to typos in the title. Considering that titles are key for later searches, even trivial misspellings can be a nuisance. It's common that titles are too long and/or carry useless words (please help; question about; how to analyse my data). On the other hand, sometimes you need to flag to posters that they should think up a better title themselves. (It's a fact of life in a forum that some members use eccentric or inadequately informative titles as a criterion for what to ignore, so improving them may seem a disservice too.)
Edits can be of any aspect of presentation (text, mathematics, code or data presentation), but as far as possible should only clarify, not change, the statistical content that defines the question being asked.
So you can edit grammar, spelling, punctuation and style, but you should not change strange or even incorrect uses of statistical terms, or any other dubious statistical content, even if obvious to you. Naturally, you should only change the language if you are confident that you are right (or have better taste or style...)! (Don't worry too much about this; a mistaken edit can be reversed.)
Content that should be removed includes greetings (at the beginning of a post) or signatures (at the end) and any material that looks irrelevant to the question. That includes polite (or even not so polite) expressions of how confused the poster is, how much time they have already spent working on the problem, how grateful they will be for an answer and (especially) how urgent or important the question is. Other comments that can usually be cut include claims that the question is quick, easy or simple: sometimes such claims are just wrong, and when they are right they don't illuminate the question.
The aim is not to deny the human side underlying a question, but to focus exclusively on the technical content at its heart. In a busy world, being able to read that content quickly and easily is a bonus for all. (I leave open whether it's a benefit that editing sometimes makes it clearer that there is no underlying precise and concise question.)
There is, as often, a small tension between the immediate, short-term aim of helping the original poster and the ultimate, longer-term aim of building an archive of high quality answered questions that should be of interest or use to many readers (in many cases, long after a poster may have disappeared from the forum). But any errors, omissions, or confusion in the statistical content of a question are likely to be part of the OP's problem and should be left as posted. Someone who edits a question need have no intention of answering it, but it can be helpful to publicise difficult points through comments. For example, you say that you want to apply multivariate regression, but you only have one response variable, so I think you mean multiple regression.
Similarly, you can introduce or improve mark-up of mathematics, code and data, but should not change even poor notation choices, which could be part of the problem. I would correct trivia, as when someone has posted $\beta2$, but it's evident that they mean $\beta_2$, but if in doubt, do not edit, but rather comment. There seems to be a square missing from your variance formula.
I think that it is rare that you should replace someone's graph. But here is a further situation where that does seems right: when presented with a very crude hand-drawn graph that someone has scanned or photographed, you may without loss be able to do a much better job.
Similarly, you should be very cautious about editing any code, especially if it seems likely or certain that incorrect or inappropriate code is much or all of the real problem. In such cases it is the role of answers to explain and even to improve or correct the code. There are limited exceptions. For example, very long code lines are awkward if not annoying to read whenever they require scrolling horizontally. Editing the code to fit within the visible question window -- using whatever essentially cosmetic change ensures that -- is a small public service. Further, simple things that you can do may include inserting blank lines to divide the code into smaller coherent blocks. But you need to be sure that you are not changing the meaning of the code or affecting whether it will run as written. If in doubt, do not touch.
It is often a good idea to edit the tags supplied for a post. Posters often omit tags that are highly relevant (e.g.
data-transformation) or specify tags that are fairly useless (e.g.
mathematical-statistics for almost any post). A sensitive exception is the
self-study tag, which ideally should be added only by the original poster to show self-awareness of the condition. Otherwise, disagreement over tags is easy enough to fix, so it is fine to edit if you are confident that you can improve tags.
Appendix: Statistics typos: a miscellaneous list
This is a list of some common typos arising in statistical literature.
The following statisticians' surnames end with "s", so watch out.
Thus whatever is
attributed to them is tagged with (e.g.) Jeffreys or Jeffreys', but not
Harold Jeffreys 1891-1989
Colin L. Mallows 1930-
John P. Mills fl.1926 (Mills ratio)
Samuel Stanley Wilks 1906-1964 (but note Martin Bradbury Wilk 1922-2013)
Frank Yates 1902-1994
Here are some other surnames that are often mangled in writing.
Ole Eiler Barndorff-Nielsen 1935-
Carl Harald Cramér 1893-1985 (NB accent)
Student 1876-1937 was William Sealy Gosset (not Gossett)
Richard A. Leibler 1914-2003 (not Liebler)
George Pólya 1887-1985 (NB accent)
Alfréd Rényi 1921-1970 (NB accents)
Henry Scheffé 1907-1977 (NB accent)
Gideon Schwarz 1933-2007 (not Schwartz) (BIC)
Hermann Amandus Schwarz 1843-1921 (not Schwartz) (Cauchy-Schwarz)
Leonard Henry Caleb Tippett 1902–1985 (not Tippet)
Frank Wilcoxon 1892–1965 (not Wilcox or Wilcoxin)
Charles P. Winsor 1895-1951 (not Windsor; hence Winsorize not Windsorize)
Some people cited in statistics share surnames. Were they relatives?
Bernoulli family. There were lots of them.
Playfair family. John Playfair (1748-1819) was brother of William
Pearson family. Karl Pearson (1857-1936) was father of Egon S. Pearson
Coxes. Gertrude M. Cox (1900-1978) was unrelated to David R. Cox
Kendalls. Maurice G. Kendall (1907-1983) was unrelated to David G.
Some bad Greek and Latin is common.
"polychotomous" is bad Greek, probably arising from a misunderstanding
of "dichotomous", which is "dicho" + "tomous", not "di" + "chotomous".
"polytomous" is better.
One criterion, two or more criteria. So never "a criteria".
"data" in Latin means "given things" and is a plural. What this implies
for modern languages is discussable. See also comments below.
"strata" in Latin is another plural. "stratum" is the singular.
Some people want to insist that "heteroskedastic" and "homoskedastic"
are the correct spellings. (There was no "c" in ancient Greek.) This
argument was published in Econometrica. Oddly enough, the spellings
"heteroscedastic" and "homoscedastic" are due to Karl Pearson, who was
no enemy of "k"; he changed his own name from Carl and founded the
journal Biometrika. Fans of "k" should promise to write of
mikroekonomics and makroekonomics on the grounds that all the pertinent
roots of those words are all Greek too. See an entire dedicated thread here.
Finally, here is some not yet idiomatic English (prejudices ahead).
The expressions "a data" (to mean a dataset) and "a code" (to mean a
program) are not yet part of standard English. They are already
Using "skew" to mean "bias" is unfortunate, but general English usage has shifted strongly that way in recent years.
On the grey area between statistical terms we know (and sometimes love) and uses or abuses of the same words within and beyond statistics and science, see also the thread here.