"letting a parent claim you" is not the question. Your parent has the absolute right to claim you (if it meets the IRS rules to claim you). You have no influence or decision in the process The decision to claim you rests with them, not you. And you can not refuse to let them claim you. it doesn't work like that.
As far as the amount of a tax refund you will be eligible to receive? No.
"letting a parent claim you" is not the question. Your parent has the absolute right to claim you (if it meets the IRS rules to claim you). You have no influence or decision in the process The decision to claim you rests with them, not you. And you can not refuse to let them claim you. it doesn't work like that.
And even if they don't claim you, if you qualify as their dependent you have to say yes you can be claimed.
When you have to answer you are a dependent
Here are the rules for claiming a dependent. Do you qualify as a dependent?
With the tax law change, effective 2018, most dependents will get the same refund whether they claim themselves or not. The personal exemption has been eliminated and the standard deduction increased.
However, you only qualify for an education credit, if you are not claimed as a dependent.
While technically there is a provision that allows your student-dependent to claim a federal tuition credit, from a practical matter it seldom works out. A student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he/she supports himself by working. She cannot be supporting herself on student loans & grants and 529 plans and parental support. It is usually best if the parent claims that credit.
If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable)