Because the explicit assertions in the examples are both effectively denials (expressed in negated form), standard usage would precede the assertion with No.
This principle applies even if you're actually agreeing with someone - as in, for example,...
"You're such a coward! You're not a man at all, are you?"
"You're quite right. No, I'm not a man. I'm just a mouse"
...where it would be unusual/confusing to use Yes in the highlighted position.
It's the opposite of how "question tags" work (if the assertion is positive, the tag is negative, and vice-versa). Thus I don't have a brain, do I? and I'm not a man, am I?, as opposed to I have a brain, don't I? and I'm a man, aren't I?