An Interesting Academic Study on the Correlation between Firearms in Homes, and Suicides Using Firearms

Switzerland is dissimilar in size and any number of other criteria; however it IS similar to the U.S. in having a high number of homes with firearms in them.  I offer a few choice excerpts from the 3 page scientific article.

Firearm suicides and availability of firearms: The Swiss experience

Abstract
This study aimed to examine the association between the availability of firearms at home and the proportion of firearm suicides in Switzerland in an ecological analysis.  The data series were analyzed by canton and yielded a fairly high correlation (Spearman's rho= 0.60).  Thus, the correlation holds also at a sub-national level.

Introduction
The link between the availability of firearms at home and firearm suicide has been unequivocally demonstrated since the 1990s using international data.[5,9,10,12,15]

and

The association was checked with a regression analysis by adjusting for further variables of interest which represented the urbanicity-rurality and religious affiliation dimensions.  The initial Spearman correlation between the proportion of the service industry work force and the proportion of the service industry work force and the proportion of firearm suicides was moderate...and the correlation between the proportion of Catholics and the proportion of firearm suicides was low.  In the ordinal regression analysis the proportion of households owning firearms remained the only relevant predictor of the proportion of firearm suicides.

Conclusion
To sum up, this study provides further evidence suggesting an association between the availability of firearms and the proportion of suicides committed with a firearm. In Switzerland as in other developed countries with a high risk of firearm suicides (USA, Nordic countries, France, Austria, Croatia, Serbia) [2] enhancing preventive efforts is an urgent issue for public health and health policy. Although the issue of method substitution remains unresolved, means restrictions for firearm suicides may present a lesser policy challenge than other strategies for suicide prevention.[14]

So, the upshot is, there is a correlation internationally which holds true for countries between one type of gun violence - suicides - and the prevalence of guns.  The recommended solution to reduce firearm suicides was to reduce the prevalence of firearms.