Restore an iPhone from iCloud backup of newer iOS version
You cannot downgrade unless one of the following is true:


Apple is still signing installations of the previous version of the OS to which you wish to downgrade, or
Your phone is jailbroken, you have saved your SHSH blob from the prior version, and you have a way to run a replay attack with that SHSH blob to trick the device into believing Apple is still signing that version.


You can determine whether a particular version of iOS is currently being signed for a given device on ipsw.me. Simply change 8.2 in the URL to the version you want to check, such as 8.0 or 8.3.

This list of updates, from the same website, shows when Apple starts and stops signing a given version.

In your case, 8.2 stopped being signed on 5/4/15. Therefore it is no longer possible to downgrade. Generally the window is about a month or so after a new version is released.