what factors including "doubt" would result regret?
Are you asking which factors, beside doubt, would result in feelings of regret?
Feelings of guilt or shame could result in regrets.
Negative consequences, such as loss of a relationship, or a job, or the loss of anything that was valued, could cause regrets.
Unanticipated or unintended consequences could cause regrets.
Failing to act could cause regrets.
is doubt equivalent of regret?
Doubt is a state of uncertainty, while regret is a state of remorse or sadness, often about some action or decision which was done wrong or turned out badly, or which resulted in disappointment. I don't see them as being at all equivalent.