Micha is right, "residencia" can be the place where students live, but "residencia" actually means "the place where someone lives" (not only students) Some examples: Residencia de ancianos = asylum. Residencia habitual = where someone normally lives. Residencia de verano = where someone lives in the summer. (recidencia doesn't exist in spanish but "residencia" is misspronounced that way in spoken Spanish in some places in the south of spain)

Me parece recidencia es una lugar donde quedar los estudiantes. "de" es una preposición y "la" es para identificar recidencia (feminina en este caso)