Linear and Nonlinear Relationships Between

Linear and Nonlinear Relationships Between Variables

Post a description of two variables that have a positive linear relationship and two variables that have a negative linear relationship in the research articles you reviewed. Then, explain the implications on the studies if each of those variables had a curvilinear relationship instead.

According to the article "Assessing the relationship between alcohol outlets and domestic violence: Routine activities and the neighborhood environment," there has long been a known positive linear relationship between "alcohol outlet density" (i.e., liquor stores, bars, and other sources of alcohol) and the crime of assault (Roman & Reid 2012). The relationship is a positive, linear one in the sense that the greater the number of sources of alcohol, the greater the chances someone will engage in violent crime. The implied causal relationship is between the temptation to abuse alcohol (a drug which lower inhibitions) and the drug's encouragement for persons who are predisposed to do so to engage in violent activities, although only a correlation is established in the article. If a curvilinear relationship existed, this would call into question the direct association between alcohol and violent behavior (for example, if the assaults only increased near bars but not near liquor stores).

The article hypothesized that a similar positive linear relationship would exist between outlets for alcohol and domestic violence complaint calls to police. However, the findings were somewhat more complex: there was a positive relationship between domestic violence calls to police and the presence of off-premise outlets like liquor stores, but "on-premise outlets (specifically restaurants and nightclubs) were associated with a decrease in domestic violence" (Roman & Reid 2012). The causal relationship for this negative linear relationship is unclear. Furthermore, "the association of domestic violence in areas of high densities of off-premise outlets was found to be high during the weekend but not during the weeknight" suggesting a potentially curvilinear association due to "different routine activities for domestic violence offenders during the week" (Roman & Reid 2012). The negative linear relationship between on-premise alcohol outlets and decreased domestic violence calls suggest a potentially mitigating effect of being in a 'social' area, while a curvilinear relationship would similarly complicate matters regarding routine behaviors and how they disrupt or support domestic violence activities.