No, that alone does not answer the support question. Being away at school means you are still considered to live your parents. There home is considered part of your support.
There are two separate support issues for students. Whether you provide more than half your support determines whether your parents can claim you as a dependent. But, if they don't; you may still not be able to claim the refundable tuition credit. The 2nd issue is do you support yourself with earned income.
There's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. A full time unmarried student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. You must have actually paid tuition, not had it paid by scholarships & grants. It is usually best if the parent claims that credit. You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.
With the tax law change, effective 2018, most students will get the same refund whether they claim themselves or not. The personal exemption has been eliminated and the standard deduction increased.
The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf The support value of a home is the fair market rental value, divided by the number of occupants.
