If I didn’t know any better, I would say that Back to the Future was influenced by The Karate Kid and maybe vice-versa since Columbia produced the latter after losing interest in producing the former. The fact that Ralph Macchio was on the shortlist for the role of Marty McFly says it all really. In 1984, Daniel LaRusso was a more iconic character than Alex Keaton in Family Ties despite the latter being a popular sitcom. As for the aforementioned movies, I have noticed a dozen similarities…
1) The teenaged protagonist’s only male friend is an old guy who is an eccentric loner.
2) The main theme of the story is bullying.
3) The old guy is a technician who teaches the teenager his specialty.
4) There is a shot where two people are in a dining establishment and the space that exists between them allows us to see the group of bullies outside.
5) The teenager drives the old man’s main vehicle in the first act.
6) The old man sees a photo of the young boy’s girlfriend.
7) The boy attends a school dance.
8) The bully tries to win over the main girl.
9) The bully bullies in the cafeteria (albeit this was a deleted scene in The Karate Kid).
10) A bald school staff member prevents further confrontation between the protagonist and the main bully.
11) A bullied boy learns to fight after doing a domestic chore (i.e. half of this became a deleted scene in Back to the Future).
12) The old man gives the young man a vintage car for his date.