By the way, por la manera By the way, a proposito. para introducir idea o phrase For the way, causa. A proposito, voy a la playa, ¿ me gustaria acompñar? By the way, I'm going to the beach, want to go with me?. Sé que me quieres por como me mires. I know you like/love me by the way you look at me. Lo admiro por como le cuidas a tu abuela. I admire you for the way that you care for your grandmother. By es una palabra muy importante y funciona mucho como por y para en el español. Pasamos por tí. We'll come by for you. Viajamos por avion. We travel by plane.

I believe the correct one is "by the way". It is used when adding on to an idea, before or after the idea is mentioned: "By the way, I like your shirt." "I also like they way you did your hair, by the way." Hope this helps!