If you have a desire to start your own business, and this is combined with a desire for it to be a web design entity, then you are going to need a certain amount of education to be able to combine them both. It is possible to be self-taught in both of the responsibilities that come with this type of endeavor.
If your business is going to be based on design, then you are going to have to know the principles behind this. You are going to have to develop the skills. You can do this through a combination of education and experience.
Being a Business Owner
You may have all the skills and expertise that you need to be a designer. However, if you are going to operate your own business, then you need the education and skills to be a business operator. What this comes down to, is that you want to focus your education on one sector for your design, and the other sectors for being able to run your business. Aside from the task, you have to do as a designer, you also have the administrative and operational skills that are going to be required for the business segment.