  We report on a quantitative analysis of relationships between the number of
homicides, population size and other ten urban metrics. By using data from
Brazilian cities, we show that well defined average scaling laws with the
population size emerge when investigating the relations between population and
number of homicides as well as population and urban metrics. We also show that
the fluctuations around the scaling laws are log-normally distributed, which
enabled us to model these scaling laws by a stochastic-like equation driven by
a multiplicative and log-normally distributed noise. Because of the scaling
laws, we argue that it is better to employ logarithms in order to describe the
number of homicides in function of the urban metrics via regression analysis.
In addition to the regression analysis, we propose an approach to correlate
crime and urban metrics via the evaluation of the distance between the actual
value of the number of homicides (as well as the value of the urban metrics)
and the value that is expected by the scaling law with the population size.
This approach have proved to be robust and useful for unveiling
relationships/behaviors that were not properly carried out by the regression
analysis, such as i) the non-explanatory potential of the elderly population
when the number of homicides is much above or much below the scaling law, ii)
the fact that unemployment has explanatory potential only when the number of
homicides is considerably larger than the expected by the power law, and iii) a
gender difference in number of homicides, where cities with female population
below the scaling law are characterized by a number of homicides above the
power law.
