One state (DC) had an extremely low rate of gun ownership but it also had the highest rate of gun murders among all states. DC was excluded from the plot above, but if DC is added, the negative relationship becomes a bit stronger. In the plot below DC is the dot that shows over 16 murders per 100,000 people.
So, we are getting either a weakly negative correlation or no correlation at all between gun ownership and gun murder rates. We know that the existence of correlation between two variables does not imply causation. But, if there is an absence of correlation, this signals either no relationship between the two variables or a really weak relationship masked by other, more powerful factors.
Thus, our rudimentary statistical analysis suggests that more guns does not mean more gun violence in the US.
Then again, some people argue that the US is in some ways different from the rest of the world. Let's check if this is true for the correlation between gun ownership and gun violence. The diagram below shows gun ownership rates and gun murder rates for different countries.