Predict is, literally, pre – decir — to say beforehand. Pre means “before” and the dict- maps almost exactly to the Spanish decir.
How come the decir has an extra -t in it to be predict? Because the Latin predecire took the grammatical form of predicatus and this form grew into English (via the French influence). A prediction in Spanish, after all, is predicho!
Thus, it is a cousin of many English words such as diction and dictionary.