"New Year" or "New Year's" resolution
This site uses "New Year" as in "Yoga as a new year resolution".
While this site chooses "New Year's" as in " Making a New Year's Resolution".
Who is right ?
It's usually "new year's resolution", and it's usually plural.
In British English you hear both. I'd use the second, but the first works, though purists might want to put a hyphen: new-year resolution. I'm not sure I like the hyphen and, anyway, prefer to use the possessive as the resolution does belong to the new year. In fact, given that most don't last beyond the first couple of days of the year, there is a very strong case for the possessive here.
- Optimistically, I've recently made some new year's resolutions,
Hoping to bring to some old problems some brand new solutions.
(Naturally, after saying it is usually plural I heard someone speak of a new year's resolution. Nevertheless, they usually come in bunches.)