Yes, you need to file.

How many days were spent in CA (a) on business and (b) shopping, skiing, takin' in the sun...., i.e. total days in CA and how many business days in CA. My guess is that the W-2 is answering that 47% of the income was derived in CA. 

Start to clarify your vagueness with FTB pub 1031 You can get your own copy by starting here https://www.ftb.ca.gov/forms/Search/Home/Index