Did the laws against smoking in public places work? We need to know because sooner or later (maybe right now, infact) someone will try to get them repealed.
So here is an analysis. You can't do a randomised trial with laws, so the analysis is before-and-after. Sometmes it's easy to see an abrupt change as a law is introduced, but not here. The graph is seesawing all over the place with random variation but to my eye there is a general downward drift from about 2003 onwards. Trouble is, it isn't an abrupt change on the day the law came in on 2 July 2007.
Thinking about it, you wouldn't really expect that. Laws of this type (unlike tax changes...) take time to become introduced and embedded; in general social laws lag, not lead, public opinion. You can't pass a law like this unless most people already agree with it. The same was true of seat belt laws.
The statisticians have used Poisson regression because the data are counts (whole numbers).
We should also congratulate the authors for presenting the raw data as a graph. If all they had given us was the statistics, we might have fored a very different opinion. Always look for some unmodified data in a paper! - it's suprising how often all you get is odds ratios / adjusted rates etc etc/