shoot up vs increase

shoot up is not a noun while increase is a noun.

Word	Noun	Adjective	Verb	Adverb
shoot up	No	No	Yes	No
increase	Yes	No	Yes	No

As verbs, increase is a hypernym of shoot up; that is, increase is a word with a broader meaning than shoot up:

shoot up (noun)	increase (noun)
	the act of increasing something
	the amount by which something increases
	a change resulting in an increase
	a process of becoming larger or longer or more numerous or more important
	a quantity that is added

shoot up (verb)	increase (verb)
rise dramatically	become bigger or greater in amount
	make bigger or more