Farewell Nobita
Feeling jealous of Shizuka showing feelings for a friend transferring, Nobita uses the What-If Phone Booth to make it such that his family are transferring to America. But when his friends - especially Shizuka- express their grief for him leaving, Nobita realizes his mistake and tries to use the Booth to undo the incident. However, the machine breaks leaving Doraemon to find a way to fix it before he and Nobita's family move to America for good. This episode would be remade as "Goodbye to You" in 2004, and both would be remade as Goodbye to You in the 2005 series.
Aired 12/08/1983EP 724 - Farewell Nobita

Doraemon
Nobi Nobita is a 4th-grade boy in Tokyo. One day, a round, blue cat-style robot (minus ears) pops up in his desk drawer. Nobita's great-great-grandson (or something) lives in the 22nd Century, but thanks to Nobita's mistakes, the entire family is living in poverty. To rectify this, Nobita's descendent is sent Doraemon back to the past, to help prevent Nobita from making mistakes. Of course this is a difficult task since Nobita is the weakest and least intelligent child in his class. Doraemon does, however, have a 4-dimensional pocket on his front, which contains cool gadgets from the future. With these toys, Doraemon will try to help Nobita. Unfortunately, Nobita also has the bad habit of misusing Doraemon's gadgets and landing himself in yet more trouble?
(Source: AnimeNfo)