Can/Should I change my legal residency to New York from New Jersey?

So basically, after I filed my state taxes, I found out I owed the state of NJ extra money from the money I made in New York that was not withheld for NJ. Essentially, NJ gets a share of the money I make out of state since Im still, technically, a permanent resident of NJ. I probably will never work in NJ for the... show more So basically, after I filed my state taxes, I found out I owed the state of NJ extra money from the money I made in New York that was not withheld for NJ. Essentially, NJ gets a share of the money I make out of state since Im still, technically, a permanent resident of NJ. I probably will never work in NJ for the foreseeable future, so I was wondering if it would make sense to change my residency to New York to avoid giving NJ money that I should not have to give to NJ. My family does have a house in NJ where we spend all summer and most holidays, and I am a full time student at New York University, so I spend way more time in New York than I do in New Jersey. Can I change my residency to New York, and should I?
Update: SUMMER/VACATION HOUSE IS IN NEW YORK, NOT NEW JERSEY...
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