I'm trying to restore from backup from my mac-book to my iphone?

Whenever i try this it comes up saying that my phone does not have enough memory but its a brand new phone with nothing on it how can i fix this?!

Not sure what difference it being brand new would make, If It has 16gb and this is used, for example, this will apply to any phone irrespective of It's age. How much memory does it come with and how much of this is used - that is what we need to know. With this information we should be able to help a bit more.