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We report on a quantitative analysis of relationships between the number ofhomicides, population size and other ten urban metrics. By using data fromBrazilian cities, we show that well defined average scaling laws with thepopulation size emerge when investigating the relations between population andnumber of homicides as well as population and urban metrics. We also show thatthe fluctuations around the scaling laws are log-normally distributed, whichenabled us to model these scaling laws by a stochastic-like equation driven bya multiplicative and log-normally distributed noise. Because of the scalinglaws, we argue that it is better to employ logarithms in order to describe thenumber of homicides in function of the urban metrics via regression analysis.In addition to the regression analysis, we propose an approach to correlatecrime and urban metrics via the evaluation of the distance between the actualvalue 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 unveilingrelationships/behaviors that were not properly carried out by the regressionanalysis, such as i) the non-explanatory potential of the elderly populationwhen 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 ofhomicides is considerably larger than the expected by the power law, and iii) agender difference in number of homicides, where cities with female populationbelow the scaling law are characterized by a number of homicides above thepower law.

Distance to the scaling law: a useful approach for unveiling relationships between crime and urban metrics