QUESTION: Can I say “Coming!” for “I am coming!”, and why?
In some languages we can remove the subject (and sometimes a verb too) from a sentence. In Toy Story 3, the kid says "Coming!" instead of "I am coming!" to her mother.
My questions are:
1.) Can I say "Coming!" instead of "I am coming!" in English?
2.) If I can, when can I remove the subject and verb?
3.) And would this be considered standard English?
= = = ANSWER = = =
Your question is asking about "ellipsis of subject pronoun + auxiliary", which is a topic that comes up often on grammar and linguistics forums/sites. It is a good question.
So, instead of saying:
we often simply say:
What has happened is that the pronoun "I" and the auxiliary verb "am" has been ellipted out. This kind of ellipsis, where the subject pronoun and an auxiliary is omitted, is part of the bigger topic of ellipsis.
Instead of having me bumble about and perhaps mis-speak here and there, allow me to type in here some related excerpts from a reputable grammar source, such as the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL), pages 1540-1.
CGEL, section "7.8 Further cases of ellipsis", subsection "7.8.1 Ellipsis of grammaticised words at the beginning of a main clause", page 1540:
A range of grammaticised items, such as personal pronouns and auxiliaries, can be omitted from the beginning of a main clause in casual style. In general, this type of ellipsis in not dependent on the presence of an antecedent.
(a) Ellipsis of personal pronoun subject
 i. Hope you're right. Can't think what I was doing. -- [I]
. . .
This occurs mainly with 1st person I and the dummy pronouns it and there, as in these examples. . . .
That section had good info, but allow me to skip ahead to the part that is related to your specific example. On page 1541:
Ellipsis of subject pronoun + auxiliary
i. Glad you think so. Never seen anything like it! -- [I + am/have]
ii. Strange how the ants come in when it's about to rain. -- [It + is]
The omitted material is shown on the right. The most likely pronoun is 1st person I or dummy it, while the most likely auxiliary is be. Perfect have is retrievable in [i] by virtue of the past participle seen. Sorry is particularly common here: Sorry to have kept you waiting. Without a complement and used as an apology, sorry is hardly to be regarded as elliptical: its status is comparable to that of thank you.
And so, you can see that your example fits into that above category ([74.i]), where the subject pronoun and auxiliary is ellipted: "I am coming!" ==> "Coming!"