suppose you are caught out in the rain and get drenched and cold. Which type of feedback loop would cause your body to start shivering to keep warm?

When the core body temperature drops, the shivering reflex is triggered to maintain homeostasis.

Negative feedback.

Explanation:

The negative feedback system is the one that most occurs in the body, being considered by many authors as the primary mechanism for maintaining homeostasis. It causes a negative change in relation to the initial change, that is, a stimulus contrary to the one that led to the imbalance.

An example of this can be seen in the question above. As has been said, negative feedback causes a reaction contrary to what is causing an imbalance in the body. In that case, when you get cold your body is cooling, then the body starts to shake to generate heat in the body and warm it up.