Firearms vs. Intentional Homicide
The data clearly supports your opinion
Argument 1
Fit linear regression weighted by population.
Call:
lm(formula = d$homicides_per_100000 ~ d$firearms_per_100, weights = d$population)
Weighted Residuals:
Min 1Q Median 3Q Max
-176815 -11915 -1625 10797 296963
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.586611 0.777875 7.182 3.63e-11 ***
d$firearms_per_100 0.004989 0.035629 0.140 0.889
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 54680 on 141 degrees of freedom
Multiple R-squared: 0.000139, Adjusted R-squared: -0.006952
F-statistic: 0.01961 on 1 and 141 DF, p-value: 0.8888Firearms are not statistically significant.
Gross domestic product (at purchasing power parity) per capita can be a strong confounding variable, so fit another regression.
Call:
lm(formula = d$homicides_per_100000 ~ d$firearms_per_100 + d$gdp_ppp_per_capita,
weights = d$population)
Weighted Residuals:
Min 1Q Median 3Q Max
-176118 -8873 -1370 10367 301062
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.548e+00 9.632e-01 6.798 2.82e-10 ***
d$firearms_per_100 6.500e-02 5.040e-02 1.290 0.1993
d$gdp_ppp_per_capita -1.136e-04 6.794e-05 -1.673 0.0966 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 54330 on 140 degrees of freedom
Multiple R-squared: 0.01973, Adjusted R-squared: 0.005731
F-statistic: 1.409 on 2 and 140 DF, p-value: 0.2478Even after controlling for GDP (PPP) per capita, firearms are still not statistically significant.
Conclusion: the effect of firearms on homicide, if it exists, must be small.
Argument 2
Number of firearms and homicide rate are not normally distributed, as evidenced by the following Q-Q plots:
Transform both variables by taking the log. After that, Q-Q plots look better:
Fit linear regression weighted by population to the transformed variables:
Call:
lm(formula = log(d$homicides_per_100000) ~ log(d$firearms_per_100),
weights = d$population)
Weighted Residuals:
Min 1Q Median 3Q Max
-46680 -1515 1040 3956 30481
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7630 0.1577 4.838 3.4e-06 ***
log(d$firearms_per_100) 0.1787 0.0795 2.248 0.0261 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 7805 on 141 degrees of freedom
Multiple R-squared: 0.0346, Adjusted R-squared: 0.02775
F-statistic: 5.053 on 1 and 141 DF, p-value: 0.02614Firearms are statistically significant and have positive coefficient in the regression.
Conclusion: more firearms means more homicide.
Argument 3
Fit linear regression weighted by number of homicides. Homicides are rare, therefore variance of homicide rate estimates is primarily driven by number of homicides rather than by population. There is no cirular reasoning here - we’re predicting homicide rate rather than absolute number of homicides.
Exclude countries with gross domestic product (at purchasing power parity) per capita lower than the median because we are primarily interested in developed countries.
Call:
lm(formula = s$homicides_per_100000 ~ s$firearms_per_100, weights = s$population *
s$homicides_per_100000)
Weighted Residuals:
Min 1Q Median 3Q Max
-580852 -120505 -62910 -33140 1155015
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 27.55908 1.85457 14.860 < 2e-16 ***
s$firearms_per_100 -0.26474 0.06658 -3.976 0.00017 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 196800 on 69 degrees of freedom
Multiple R-squared: 0.1864, Adjusted R-squared: 0.1746
F-statistic: 15.81 on 1 and 69 DF, p-value: 0.0001701Firearms are statistically significant and have negative coefficient in the regression.
Conclusion: in developed countries, more firearms means less homicide.
Data Sources
Intentional homicide rates per 100,000 population as of 2012, Global Study on Homicide 2013 https://www.unodc.org/gsh/
Total population as of 2012, The World Bank http://data.worldbank.org/indicator/SP.POP.TOTL
GDP, PPP as of 2012, The World Bank http://data.worldbank.org/indicator/NY.GDP.MKTP.PP.CD
Firarms per 100 population, 2007 Small Arms Survey http://www.smallarmssurvey.org
Data
country homicides_per_100000 population gdp_ppp firearms_per_100
1 Afghanistan 6.5 29726803 57473689811 4.4
2 Albania 5.1 2900489 27981946252 8.6
3 Algeria 1.4 37439427 502937371131 7.6
4 Angola 10.8 22685632 0 17.3
5 Argentina 7.0 42095224 0 10.2
6 Armenia 2.2 2978339 22035101326 12.5
7 Australia 1.1 22728254 979558023390 15.0
8 Austria 1.0 8429991 378088354544 30.4
9 Azerbaijan 2.2 9295784 150344872492 3.5
10 Bahamas 29.7 372388 8648379510 5.3
11 Bangladesh 2.6 155257387 429055450182 0.5
12 Barbados 7.8 281580 4411222957 7.8
13 Belarus 3.6 9464000 162879596713 7.3
14 Belgium 1.7 11128246 459785570514 17.2
15 Belize 45.1 336707 2733682254 10.0
16 Benin 6.3 10049792 18350608451 1.4
17 Bhutan 3.8 743711 5390490978 3.5
18 Bolivia 12.1 10238762 60378682117 2.8
19 Bosnia and Herzegovina 1.6 3828419 35871851726 17.3
20 Brazil 26.5 202401584 3080598391714 8.0
21 Bulgaria 1.9 7305888 116641261815 6.2
22 Burkina Faso 0.7 16590813 25664955309 1.1
23 Burundi 4.7 10124572 7387878936 1.2
24 Cabo Verde 11.1 500870 3132402917 5.4
25 Cameroon 2.8 21659488 58786137853 2.8
26 Canada 1.6 34754312 1469441272598 30.8
27 Central African Republic 13.6 4619500 4291389079 1.0
28 Chad 9.4 12715465 25386331049 1.1
29 Chile 3.1 17388437 368340067789 10.7
30 China 0.8 1350695000 15147732172364 4.9
31 Colombia 30.7 46881018 565053014246 5.9
32 Comoros 8.0 733661 1011778388 1.8
33 Congo 10.5 4286188 24861693076 2.7
34 Costa Rica 8.4 4654148 64381320881 9.9
35 Côte d'Ivoire 12.4 21102641 59138290441 2.4
36 Croatia 1.2 4267558 90103577142 21.7
37 Cyprus 2.0 1129303 28124471336 36.4
38 Czech Republic 1.0 10510785 300939794171 16.3
39 DPRK 4.7 24763353 0 0.6
40 Congo 13.5 70291160 45836065765 1.4
41 Denmark 0.7 5591572 243569213747 12.0
42 Djibouti 7.0 853069 2500247239 2.8
43 Dominican Republic 22.0 10155036 119165850359 5.1
44 Ecuador 12.4 15419493 162021913158 1.3
45 El Salvador 41.5 6072233 47704961183 5.8
46 Equatorial Guinea 3.6 773729 29713759224 19.9
47 Eritrea 7.8 4892233 0 0.5
48 Estonia 4.9 1322696 33402707310 9.2
49 Ethiopia 8.1 92191211 115801785214 0.4
50 Fiji 3.0 874158 6718116315 0.5
51 Finland 1.6 5413971 217692078041 45.3
52 France 1.2 65639975 2445463259385 31.2
53 Gabon 9.4 1613489 28898919790 14.0
54 Gambia 9.6 1807108 2888561526 0.8
55 Germany 0.7 80425823 3506641955571 30.3
56 Greece 1.5 11092771 278085247530 22.5
57 Guatemala 34.6 15368759 107247768582 13.1
58 Guinea 9.0 11628767 14175308962 1.2
59 Guinea-Bissau 10.3 1714620 2354937861 1.6
60 Guyana 17.5 758410 4901321313 14.6
61 Haiti 10.2 10288828 16599415572 0.6
62 Honduras 91.0 7736131 35818018094 6.2
63 Hungary 1.4 9920362 223766790703 5.5
64 Iceland 0.3 320716 12988375547 30.3
65 India 3.5 1263589639 6252659013279 4.2
66 Indonesia 0.6 248037853 2343796853305 0.5
67 Iran 4.8 76156975 1282942956414 7.3
68 Ireland 1.2 4586897 210031721225 8.6
69 Israel 1.7 7910500 252538837177 7.3
70 Italy 0.9 59539717 2114541653658 11.9
71 Jamaica 39.1 2707805 23168389163 8.1
72 Japan 0.3 127561489 4540944805895 0.6
73 Jordan 2.4 6318000 72933787659 11.5
74 Kazakhstan 9.0 16791425 367593276627 1.3
75 Kenya 6.5 42542978 115620561511 6.4
76 Kosovo 4.9 1805200 15411689979 19.5
77 Kuwait 1.9 3419581 268287695231 24.8
78 Lao 7.2 6473050 29639067434 1.2
79 Latvia 4.8 2034319 42291242695 19.0
80 Lebanon 4.2 4440728 74919852759 21.0
81 Liberia 3.3 4190155 3285716931 1.6
82 Libya 2.5 6283403 144300306966 15.5
83 Lithuania 6.8 2987773 72001647509 0.7
84 Malawi 1.8 15700436 11979877674 0.7
85 Maldives 3.0 385000 4376769905 6.5
86 Mali 11.2 16112333 24339267752 1.1
87 Malta 2.8 419455 11860592735 11.9
88 Mauritania 11.4 3777067 13409540152 1.6
89 Mexico 21.5 122070963 1967366758397 15.0
90 Mongolia 7.2 2808339 28042513769 1.9
91 Montenegro 2.7 620601 8520641718 23.1
92 Morocco 1.2 32984190 233872326203 5.0
93 Myanmar 2.5 52543841 0 4.0
94 Namibia 17.5 2291645 20665956414 12.6
95 Netherlands 0.9 16754962 777074774133 3.9
96 New Zealand 0.9 4408100 145168597607 22.6
97 Nicaragua 11.3 5877034 26250476362 7.7
98 Niger 4.7 17635782 15569666617 0.7
99 Nigeria 10.3 168240403 909312073482 1.5
100 Norway 0.5 5018573 333049428144 31.3
101 Pakistan 7.8 177392252 790969340036 11.6
102 Panama 17.2 3743761 68226128114 21.7
103 Paraguay 9.7 6379162 47484890737 17.0
104 Peru 9.6 30158768 333118476305 18.8
105 Philippines 8.8 96017322 590529699970 4.7
106 Poland 1.0 38063164 888379405857 1.3
107 Portugal 1.1 10514844 283905003633 8.5
108 Qatar 8.1 2015624 272833772102 19.2
109 Republic of Korea 0.8 50004441 1601229237842 1.1
110 Moldova 6.7 3559519 15039023521 7.1
111 Romania 1.7 20058035 369472222527 0.7
112 Russian Federation 9.2 143201676 3445923030943 8.9
113 Saudi Arabia 6.2 29496047 1466149749002 35.0
114 Senegal 8.1 13780108 30636635377 2.0
115 Serbia 1.2 7199077 92189416159 37.8
116 Sierra Leone 1.8 6043157 9533885456 0.6
117 Singapore 0.2 5312400 408991572889 0.5
118 Slovenia 0.7 2057159 58497379765 13.5
119 Somalia 5.6 10033630 0 9.1
120 South Africa 30.7 52341695 659331766441 12.7
121 Spain 0.8 46773055 1514892949436 10.4
122 Sri Lanka 3.2 20328000 207501328659 1.5
123 Sudan 6.5 37712420 146015564110 5.5
124 Suriname 9.3 528535 8303763649 13.4
125 Sweden 0.7 9519374 417609076968 31.6
126 Switzerland 0.6 7996861 446683740874 45.7
127 Tajikistan 1.3 7930929 18917091955 1.0
128 Macedonia 1.4 2069270 24570713132 24.1
129 Togo 9.4 6745581 8885081687 1.0
130 Trinidad and Tobago 28.3 1341579 40995979617 1.6
131 Tunisia 3.1 10777500 115574478893 0.1
132 Turkey 4.3 74099255 1348311030981 12.5
133 Turkmenistan 4.3 5172941 65612131535 3.8
134 Uganda 11.7 35400620 60029340654 1.4
135 United Arab Emirates 0.8 8952542 547401997472 22.1
136 United Kingdom 1.0 63700300 2395634891520 6.2
137 Tanzania 8.2 48645709 108081966288 1.4
138 United States 4.7 314112078 16163158000000 88.8
139 Uruguay 7.9 3396753 63757573886 31.8
140 Uzbekistan 3.3 29774500 142589673528 1.5
141 Venezuela 53.6 29854238 537961457365 10.7
142 Yemen 6.8 24882792 91416226977 54.8
143 Zimbabwe 7.5 14565482 24446028322 4.4