Do you need a parents signature to fly at 14 or 15?

Yes. For any party not yet attaining their majority, a letter signed by a parent (and also often needing a notary) is absolutely necessary. Airline tickets are a "contract" between the purchaser and the airline, and a minor may not conclude any contract unless they have a legal guardian or parent do it for them, or they are emancipated and have the proof. In any case, it also comes down to the cost of liability. The insurance companies won't allow any minor child (usually under 18) to fly alone due to the nature of the risks of flying, unless a "release" from a parent or legal guardian is first obtained.