Simple answer: Yes. But, it depends on more details. There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related).
The residence test only applies to QCs.
Next it matters what " renting my own apartment" really means. If you are only away at school and living off campus, you are still considered as living with your parents, for tax purposes.