You don't say how old you are, but I can assure you that most jobs that pay a living wage require at least a high school diploma and many require you to be 18 years of age. No job that a typical high school kid will be employed in (fast food, retail) will pay a wage that will allow you to easily live independently and pay for/go to school. It just won't work. No judge is going to just cut you loose to try it, either.
Stick it out at home and when you're 18, execute your plan then.
Meanwhile, if you work a part time job, save your money. When you do move out, you'll need a lot of start-up money for deposits and rent.
And it's more than you think!

