-(이)야 is a casual "이에요/예요" which is for nouns.
For example you would say "전 미국 사람이에요" in 존댓말, but you can say "나 미국 사람이야" to your close friends.
I should point this out, 아니요 is not a polite version of 아니야.
Casual Korean : 아니. No.
Honorific Korean : 아니요.
Casual Korean : 아니야. It's not. / I'm not. / s/he's not. / They're not
Honorific Korean : 아니에요.