I did posted this video years ago together with another that was removed due to copyright reason. In that It was explained that this composition was made by Carmen believing that music was public domain, but in fact that music was of Sergei Rachmaninov's Piano Concerto No. 2 in C minor. Later Carmen agreed with Rachmaninov state to add his name in authors, as it should be from the beginning.
Another video of Eric Carmen singing his song "All by Myself"... aired for tv show "UK Gold" during 1976 in UK... by that time the song was #26 in British charts reaching later #12. In this version Carmen sing and play without playback... together with group (which is noticed by the sign he made to the group in minute 3:43 to enter in the closing part).