LinkedList Implementation in Java
The name LinkedListImplementation seems a little awkward, especially if someone else may try to use it.  It's understandable that you want to avoid using the same name as the official class, in which case you can consider MyLinkedList as the class name.
There's no need for that stray return at the end of clear() since it's a void function.
I'm not sure why those statements in main() are commented out.  Testing for exceptions is okay.  But, perhaps this indicates that you should have actual unit testing using JUnit.  main() would then initiate these tests without the need to comment out any of them.