Looking at the state ranks made me think of population density, since it appears to be correlated.
1. Alaska: Population density=1.2 people per square mile, Suicide Rank=1
2. Wyoming: Population density=5.8 people per square mile, Suicide Rank=3
3. Montana: Population density=6.8 people per square mile, Suicide Rank=4
4. North Dakota: Population density=9.7 people per square mile, Suicide Rank=14
5. South Dakota: Population density=10.7 people per square mile, Suicide Rank=25
6. New Mexico: Population density=17 people per square mile, Suicide Rank=2
7. Idaho: Population density=19 people per square mile, Suicide Rank=11
8. Nebraska: Population density=23.8 people per square mile, Suicide Rank=41
9. Nevada: Population density=24.6 people per square mile, Suicide Rank=5
10. Utah: Population density=33.6 people per square mile, Suicide Rank=9
http://www.insidermonkey.com/blog/population-density-by-state-and-suicide-rates-1580/
"...There’s no correlation—zero—between a states’ suicide rate and religion, marriage rates, or single occupancy homes. State economic growth or unemployment don’t line up, either. Economically struggling states like Michigan and Indiana, for instance, had suicide rates near the national average, while booming North Dakota was well above. Depression would seem to be a precursor to suicide, but depression, which is highest in the Deep South and Appalachia and low in the inland West, doesn’t correlate with suicide, either. Is it possible that there’s something about the inland West that makes depressed people more likely to commit suicide? That’s what the data suggests.
"If anything correlates with suicide rates, it’s a states’ population density: In populous areas, suicide rates are low; in the sparsely populated hinterlands, suicide rates are high. Perhaps depression and loneliness is particularly harsh in desolate areas, and maybe it’s easier to cope in a major city like D.C. or New York. A more intriguing possibility is gun ownership, which, like suicide rates, is highest in the West and lowest in the Northeast. The relationship between gun ownership and suicide isn’t hard to envision, since more than half of suicides are by firearm. Therefore, accessible firearms could plausibly increase suicide rates. Then again, the South has high levels of gun ownership and higher levels of depression than the inland West, but suicide is rarer in Alabama than Montana."
https://newrepublic.com/article/113253/increase-suicide-us-not-due-marriage-or-religion-decline