How can I update and then restore? I've just been sent a replacement iPhone. I don't have a computer at the moment so I've gone to restore it during the set up. It shows the latest iPhone backup as 08:42 which is the one that I want to restore to but it won't allow me to restore to it as it says iOS 8.3 Required.

How can I update it so that I can restore it? I could set it up as a new iPhone and then update it, but when I wipe it to get back to the restore screen I'll be in the same situation surely.
I have realised that wiping the iPhone does not downgrade it, so it was as simple as setting it up as a new iPhone, updating it, wiping it, and then restoring.

This can all be done without a computer (as per my question), unlike the other answers.