An idea/belief is to a as a research prediction is to a

 an idea/belief is to a theory as a research prediction is to a hypothesis.  OR an idea/belief is to a study as a research prediction is to a hypothesis

Explanation:  Analogies are often a mystery. You have to get into the mind of the person who created it, and you guess what that person was thinking.

If you have a word bank, it may help to narrow down the choices if there is a right answer to be scored. If it is completely open-ended, make your own choice of some words that have a similar relationship to the given terms and be prepared to explain your reasoning.

To me, a scientist or researcher might do a study to see if others have similar or differing ideas and beliefs about some observed phenomena and then develop a theory. The researcher might want to predict the outcome of an experiment to prove a theory. That would be stated as a testable hypothesis.

The word theory might be a better choice for the first blank, now that I'm thinking about it

I saw that the question has been up for over an hour with no other takers, so I'm just hoping this helps you. Maybe it will generate some discussion if others think there is a better answer.