The decision to not live at home anymore is a big one. And living with a group of people can present it's own set of stresses, different to living with your parents.
This may well be the right decision for you, but the outcome is going to be best if you plan carefully. Your parents may also be more respectful of your choice if you can demonstrate it is one you have made responsibly.
Parents being parents, one of the best ways to do this is through budgeting, and it's also one of the best things you can do for yourself. It will help you decide if you really can manage living on your own, of if you're not quite ready.
Things to look at include your average monthly income vs. your average monthly outgoings: rent, heat, electricity, water, food.
Do you know how to plan a balanced, healthy weekly shopping trip on a budget? Do you know what your average bills on top of rent are likely to be?
What will you do if you or one of your friends becomes ill in the flat? Do you have access to affordable healthcare?
If you are living independantly of your parents, are you prepared to learn about and face filing taxes each year?
Do you and your flatmates have agreements about noise, overnight guests, music, food, and all the things that drive people CRAZY when they live together?
Do you know what your legal position is? Will you still need them to sign school forms or other forms for you even after you're 16?
If you can sort through all this and write it all down in an organised way, you'll be in a better position to show yourself and your parents you are ready. Hopefully, this will help them respect you and your choice, but if not, you will be better prepared to go it alone.
Give them time, and be the adult if you have to. Call weekly to let them know you are fine, cheerfully, even if they hang up on you, and keep the communication lines open. Eventually, they may relent. They certainly won't stop caring.
Think carefully, and good luck.
Hope this helps,