regress vs drop off

regress is a noun but drop off is not a noun.

Word	Noun	Adjective	Verb	Adverb
regress	Yes	No	Yes	No
drop off	No	No	Yes	No

As verbs, drop off is a hyponym of regress; that is, drop off is a word with a more specific, narrower meaning than regress:

Other hyponyms of regress include fall back, fall behind, recede.

regress (noun)	drop off (noun)
returning to a former state
the reasoning involved when you assume the conclusion is true and reason backward to the evidence

regress (verb)	drop off (verb)
go back to bad behavior	change from a waking to a sleeping state
get worse or fall back to a previous condition	fall to a lower standard
go back to a previous state	fall or diminish
go back to a statistical means	retreat
	remove (cargo, people, etc.) from and leave