On a smaller scale, such as in certain cities, I think you could easily correlate a relationship between affluence and crime. Generally speaking crime of all kinds is lower among affluent communities. The graph represents nationwide statistics; might a case be made for a correlation to increasing housing prices? It's generally accepted among economists that increasing real estate prices made homeowners feel wealthier. Steadily increasing real estate prices encouraged "creative" mortgage products, permitting the less affluent to become homeowners, all of which arguably contributed to a virtuous cycle of increased spending, consumption, and economic growth.
It's now evident that cycle's momentum has slowed. I hope it doesn't happen, but if there is an economic recession hastened by mortgage defaults and/or declines in real property values in the near future, there might be a reversal of the declining crime rates we've seen for the past 10-15 years.
When I lived in NJ a state trooper gave a presentation to our community group in which he pointed out that crime in our neighborhood was almost unheard of since it was generally known (to criminals seeking easy prey) that most homeowners there kept guns in their homes. However, I should also point out our neighborhood was a relatively affluent one.
I believe the prevalence of CCW is a contributing factor to lower crime rates, but at best it's only one factor. You can't, for instance, correlate radically lower crime rates in New York City over the past 20 years with CCW since that right is effectively denied. Newark, NJ, Washington DC and Chicago are supposedly gun-free zones but violent crime in those cities is rampant. I don't think anyone would consider those cities nearly as affluent as NYC though.
There's almost certainly a relationship between affluence and gun ownership also. It could be argued that guns are purchased with discretionary income. No discretionary income, no guns. Therefore affluence, lawful gun ownership, and crime are probably all related.
As always correlation is not equal to causation.