regrets (Noun) — A polite refusal of an invitation.
regrets (Noun) — Sadness associated with some wrong done or some disappointment. ex. "he wrote a note expressing his regret"
regrets (Verb) — Feel remorse for; feel sorry for; be contrite about.
regrets (Verb) — Feel sad about the loss or absence of.
regrets (Verb) — Decline formally or politely. ex. "I regret I can't come to the party"
regrets (Verb) — Express with regret. ex. "I regret to say that you did not gain admission to Harvard"