Alaska and Nevada have some of the highest rates of suicide, but those areas are not suitable for farming. Another article posted earlier in this thread indicates population density isn't a factor, and the map seems to show that as well (Nebraska and Minnesota have low suicide rates and low density). Date of statehood is nothing more than a coincidence.
This suggests that farmers are concentrated in a central strip: http://www.slate.com/articles/technology/future_tense/2012/0...
The map top right here indicates correlation with population density, as you suggested: http://en.wikipedia.org/wiki/List_of_U.S._states_by_populati...
And the first map on this US history page suggests those areas were late to the state party. Would that have had a strong impact? http://en.wikipedia.org/wiki/History_of_the_United_States_(1...