It's rather formal. More natural would be "Do not say what you lack adequate evidence for", or "Do not say that which you lack adequate evidence for".

It's also a way of obeying the obsolete / dubious / mistaken rule "Never end a sentence with a preposition". You will note that both of Bill's alternatives end in "for". But as he also says it's perfectly good, grammatical English.

@PeterJennings That's literally only a followed rule of English in Jamaica. Funny story. If you want to hear it, reply and I'll move this to chat.

@gotube I looked up that "rule" here on ELL and over on EL&U and the answers all came down to "It's a made up rule that has no basis in standard English grammar". Apparently it's a hangover from Latin grammar (where it really is a rule) adopted by some 18th century grammar books but having no validity in English. Google it and read the first hit you get. By all means move this to a chat, I'd like to hear any funny stories.

@PeterJennings All that's basically true, but the details are hilarious. The story, as I understand it, is that there was a grammar (I believe called "The English Accidence" by Joshua Poole, but I can't find verification on that point) that was briefly popular in the mid 1600s. It included a rule about keeping prepositions in front of their objects, though without specifically mentioning not ending a sentence with one.

The book was considered an (otherwise) excellent book, so people assumed that this rule about prepositions was also correct and everyone else was wrong. The rule was never followed anywhere on Earth until British colonizers, starting in 1655, used the book to introduce English to the then Spanish-speaking population of Jamaica.

Having no previous concept of English, Jamaican learners absorbed the rule completely, and still today, speakers of Jamaican Standard English will twist sentences into a knot (from our perspective) to keep all prepositions in front of their objects. Poole (or whomever)'s utter grammatical fantasy became an ironic reality.