Technically, you must check the box that says "I can be claimed as a dependent" if you can be claimed, even if the other person chooses not to claim you.
You can be claimed as a dependent under either of two sets of rules.
A. You can be claimed as a "qualifying child" dependent if you are under 19, or under 24 while a full time student or disabled, and you live with your parent, and you do not earn more than half your own support. For being a dependent, you are deemed to "live with" your parent even when you are temporarily absent, and college is considered a temporary absence, assuming you return to your parents home for summers, etc. There is no black letter rule on when you can say you no longer live with your parent, it depends on the facts of each case. If you have permanently moved out and set up an independent home, you might be able to say that you no longer live with your parent and can't be a dependent.
B. You can be claimed as a "qualifying relative" dependent if you are any age and live anywhere, but you earn less than $4050 of taxable income and your parent provides more than half your support.
If you are a full time student, then you may be a dependent of the relatives you live with. You can be a dependent of another relative besides a parent -- the types of relatives who could claim you as a dependent are an older sibling, a grandparent, or an aunt or uncle. If you are living with one of these types of relatives while being a full time student, they can claim you unless you provide more than half your own support.
Support you pay for yourself includes tuition you pay (whether from earnings or from loans in your name), travel, entertainment, clothes, and so on. Support that your relatives provide you includes a share of the home's rental value, utilities, and food, among other things. (In other words, if the home would rent for $2000 per month, and there are 5 people living there, your relatives get credit for providing you with $400 per month of rent.) There is a worksheet for the support test here <a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p501.pdf">https://www.irs.gov/pub/irs-pdf/p501.pdf</a>
If your relatives provide more of your support than you do, and if you are a full time student, and they are the right kind of relative, then they can claim you instead of your parents.
If none of those things are true then no one can claim you and you can amend.
Here are the amending instructions. You need a separate amended return for each year, and mail them in separate envelopes.
Amend <a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/replies/3288565">https://ttlc.intuit.com/replies/3288565</a>