## A Simple Regression Analysis of Crime Rates and Gun Policy in Australia

Gun control advocates often to point to Australia’s 1996 gun ban success as rationale for restricting firearms in the United States. They’ll often tout Australia’s reduced homicide rate to justify the claims of success. A simple regression analysis tells a much different story.

A quick look at a time series plot of Australia’s homicide rate leads one to believe that the 1996 gun ban has been effective at reducing crime. The 1993 rate is 1.88 homicides per 100,000 while the 2011 rate is 1.21 homicides per 100,000. The 2011 rate is nearly 38% less than the pre-ban high of 1.95 per 100,000 in 1995.

figure 1 – Homicide Rate Over Time

However, a simple first order regression analysis of homicide rate over time as the dependent variable considering the gun ban as the predictor variable suggests no relationship exists.

In order to consider the gun ban as a predictor, the variable was assigned values corresponding to the status of the gun ban. For years where no ban was in place, the variable was set equal to 0. For years where the ban was in place the variable was set equal to 1. Since the ban took effect in May of 1996 making it in place effectively half the year, that year was assigned a variable value of ½.

**For a regression model to be a good predictor of the dependent variable**, four conditions must be met:

- The probability plot of residuals, measures of the dependent variable variability, suggests that they are normally distributed.
- The variance inflation factors, measures of multicollinearity, the statistical phenomenon in which predictor variables are correlated, are less than 3.
- The R
^{2}adjusted value, the percentage of the response variable variation is explained by a linear regression model, is greater than 30%. - It must also be reasonable and pass a common sense test.

The probability plot of residuals for homicide rate vs gun ban suggests that they are normally distributed

figure 2 – Probability Plot of Residuals (Homicide Rate vs Gun Ban)

Variance inflation factors are not relevant measures as there is only one predictor variable. The regression equation is reasonable. However, the R^{2} adjusted value is less than 30% at 20.8%.

figure 3 – Regression Analysis of Homicide Rate vs Gun Ban

The model is not a good predictor. Australia’s gun ban has had no statistically significant effect on homicide rate. In fact, during the same time period homicide in the US trended down by nearly 47% while gun ownership increased to pre-1993 levels.

A regression analysis was also applied to total violent crime data in the same manner as was done for homicide data. The R^{2} adjusted value is greater than 30%. This suggests a correlation.

figure 4 – Regression Analysis of Total Violent Crime Rate vs Gun Ban

However the probability plot of residuals suggests they are not normally distributed. The significant outlier at the 4% level is of concern. This suggests that no relationship between total violent crime rate and the gun ban exists.

figure 5 – Probability Plot of Residuals (Total Violent Crime Rate vs Gun Ban)

The model is not a good predictor.

However, when we consider assault and sexual assault, we do see a correlation and can derive defensible models.

**The regression analysis for Sexual Assault Rate vs Gun Ban** yields an R^{2} adjusted value of 47%.

figure 6 – Regression Analysis of Sexual Assault Rate vs Gun Ban

The probability plot of residuals suggests the residuals are normally distributed.

Figure 7 – Probability Plot of Residuals (Sexual Assault Rate vs Gun Ban)

The model is a defensibly a good predictor.

**The regression analysis for Sexual Assault Rate vs Gun Ban** yields an R^{2} value of 56%.

figure 8 – Regression Analysis of Assault Rate vs Gun Ban

The probability plot of residuals suggests the residuals are normally distributed.

Figure 9 – Probability Plot of Residuals (Assault Rate vs Gun Ban)

The model is a defensibly a good predictor.

**Conclusion**

Australia’s gun ban had no statistically significant impact on homicide or overall violent crime. The ban was also accompanied by a nationwide “gun buy back” at great expense. At this point, there is no attributable value realized for those efforts and expense.

In fact, assault and sexual assault rates increased as a result of the gun ban indicating a negative realized value.

At the same time, all segments of crime in America trended down despite a rise in gun ownership.

This simple regression analysis study suggests that relaxed gun control reduces crime more effectively than strict gun control.

**Resources:**

http://www.abs.gov.au/ausstats/abs@.nsf/mf/3105.0.65.001

http://www.aic.gov.au/publications/current%20series/facts/1-20/2012/1_recorded.html

http://www.abs.gov.au/websitedbs/d3310114.nsf/Home/Animated+Historical+Population+Chart

http://www.aic.gov.au/publications/current%20series/facts/1-20/2012/1_recorded.html

http://www.aic.gov.au/dataTools/facts/vicViolentCol.html

http://www.aic.gov.au/statistics/violent%20crime/sexual%20assault.html

http://www.aic.gov.au/statistics/violent%20crime/assault.html

http://www.aic.gov.au/statistics/violent%20crime.html

http://www.ncpa.org/sub/dpd/?Article_ID=17847

http://www.abs.gov.au/ausstats/abs@.nsf/Lookup/4524A092E30E4486CA2569DE00256331

http://www.aic.gov.au/publications/current%20series/tandi/341-360/tandi359/view%20paper.html

http://www.gunpolicy.org/firearms/region/australia

http://www.aic.gov.au/statistics/homicide.html

http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2010/crime-in-the-u.s.-2010/tables/10tbl01.xls

http://www.gallup.com/poll/150353/self-reported-gun-ownership-highest-1993.aspx

**Other links of interest:**

http://www.factcheck.org/2009/05/gun-control-in-australia/

http://freerepublic.com/focus/f-news/2225517/posts

http://www.washingtonpost.com/blogs/wonkblog/wp/2012/08/02/did-gun-control-work-in-australia/

http://www.ballinaadvocate.com.au/news/new-plan-unveil-tackle-out-of-control-gun-violence/1992835/