The data are on the homicide rate in Detroit for the years 1961-1973. The codes for the data are in the appendix (see below).

Crime trends and violence have been the subject of debate for years as citizens, policy makers, and law enforcement seek ways to effectively mitigate its impact on communities. A typical response to an increase in crime has been to increase police presence. But what other factors affect the homicide rate? In a city like Detroit, notorious for its crumbling industries and infrastructure, I chose to look at:

  1. The number of police officers (per 100,000) - The police are an important part of maintining the rule of law.
  2. Unemployment rate - There is a strong link between crime and poverty, and the unemployment rate serves as a proxy for measuring poverty.
  3. Number of gun licenses - This is a proxy for gun prevalance.
  4. Weekly Earnings - Whilst unemployment may be low, people may be in poorly paying jobs. This is another way to account for poverty.
  5. The assault rate (per 100,000) - there may be a link between the general level of violence, and homicide.

To begin:

hom = read.csv("C:/Users/Idontcare/Desktop/Homicides.csv")
attach(hom)

Contd:

head(hom)
##      FTP UEMP   MAN    LIC     GR CLEAR     WM  NMAN   GOV   HE     WE
## 1 260.35 11.0 455.5 178.15 215.98  93.4 558724 538.1 133.9 2.98 117.18
## 2 269.80  7.0 480.2 156.41 180.48  88.5 538584 547.6 137.6 3.09 134.02
## 3 272.04  5.2 506.1 198.02 209.57  94.4 519171 562.8 143.6 3.23 141.68
## 4 272.96  4.3 535.8 222.10 231.67  92.0 500457 591.0 150.3 3.33 147.98
## 5 272.51  3.5 576.0 301.92 297.65  91.0 482418 626.1 164.3 3.46 159.85
## 6 261.34  3.2 601.7 391.22 367.62  87.4 465029 659.8 179.5 3.60 157.19
##     HOM   ACC    ASR
## 1  8.60 39.17 306.18
## 2  8.90 40.27 315.16
## 3  8.52 45.31 277.53
## 4  8.89 49.51 234.07
## 5 13.07 55.05 230.84
## 6 14.57 53.90 217.99
summary(hom)
##       FTP             UEMP             MAN             LIC        
##  Min.   :260.4   Min.   : 3.200   Min.   :455.5   Min.   : 156.4  
##  1st Qu.:269.6   1st Qu.: 3.825   1st Qu.:528.4   1st Qu.: 216.1  
##  Median :272.7   Median : 4.750   Median :572.6   Median : 528.4  
##  Mean   :298.5   Mean   : 5.633   Mean   :555.9   Mean   : 533.7  
##  3rd Qu.:325.3   3rd Qu.: 7.025   3rd Qu.:598.1   3rd Qu.: 800.6  
##  Max.   :390.2   Max.   :11.000   Max.   :613.5   Max.   :1131.2  
##        GR             CLEAR             WM              NMAN      
##  Min.   : 180.5   Min.   :58.90   Min.   :359647   Min.   :538.1  
##  1st Qu.: 227.7   1st Qu.:77.72   1st Qu.:412779   1st Qu.:584.0  
##  Median : 492.1   Median :87.85   Median :456648   Median :673.0  
##  Mean   : 505.5   Mean   :83.03   Mean   :459125   Mean   :664.5  
##  3rd Qu.: 722.9   3rd Qu.:91.25   3rd Qu.:505136   3rd Qu.:736.2  
##  Max.   :1029.8   Max.   :94.40   Max.   :558724   Max.   :819.8  
##       GOV              HE              WE             HOM        
##  Min.   :133.9   Min.   :2.910   Min.   :117.2   Min.   : 8.520  
##  1st Qu.:148.6   1st Qu.:3.195   1st Qu.:139.8   1st Qu.: 8.898  
##  Median :183.5   Median :3.530   Median :156.2   Median :17.965  
##  Mean   :182.0   Mean   :3.821   Mean   :164.1   Mean   :23.284  
##  3rd Qu.:213.7   3rd Qu.:4.305   3rd Qu.:178.4   3rd Qu.:32.965  
##  Max.   :230.2   Max.   :5.760   Max.   :258.1   Max.   :52.330  
##       ACC             ASR       
##  Min.   :39.17   Min.   :218.0  
##  1st Qu.:44.45   1st Qu.:266.7  
##  Median :47.48   Median :298.9  
##  Mean   :47.41   Mean   :302.8  
##  3rd Qu.:50.83   3rd Qu.:321.1  
##  Max.   :55.05   Max.   :473.0

I have assumed that my distribution is normal because I am dealing with rates and populations. As a result, an ordinary least squares model will suffice. Note that a GLS model will output the same estimates.

mod = lm(HOM ~ FTP + UEMP + LIC + WE + ASR, data = hom)

summary(mod)
## 
## Call:
## lm(formula = HOM ~ FTP + UEMP + LIC + WE + ASR, data = hom)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.83117 -0.31438 -0.09139  0.29605  1.09775 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -45.800445   2.991492 -15.310 4.90e-06 ***
## FTP           0.049329   0.025266   1.952 0.098735 .  
## UEMP          1.286998   0.175461   7.335 0.000328 ***
## LIC           0.024017   0.001400  17.155 2.51e-06 ***
## WE            0.221771   0.021875  10.138 5.36e-05 ***
## ASR          -0.006960   0.008183  -0.850 0.427695    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8219 on 6 degrees of freedom
## Multiple R-squared:  0.9985, Adjusted R-squared:  0.9972 
## F-statistic: 795.9 on 5 and 6 DF,  p-value: 2.235e-08

Given that we only have 11 data points, we have to be wary about the conclusions we can draw. With a small number of observations, outliers can heavily influence that data. With this in mind, we can be confident that a relationship exists, with the independent variables explaining over 99% of the variance in homicides in Detroit. The small F-stat shows that the R-squared value is significantly different from zero.

Looking at the indpendepent variables, it is interesting to note that the number of police officers and the assault rate does not have a significant effect on homicides, based on the model. In relation to the assault rate, this may be the result of ‘escalation’, i.e. in the presence of guns, an assault can escalate into a homicide. The seeming ineffectual police presence could point to deeper social problems - like poverty - which is the driver of crime.

In our model, an increase in the unemployment rate causes the homicide rate to rise be 1.2. In essence, Detroit with a population on approximately 1.5 million people, 18 people will be killed if the unemployment rises by 1%.

APPENDIX: The data are on the homicide rate in Detroit for the years 1961-1973. FTP - Full-time police per 100,000 population UEMP - % unemployed in the population MAN - number of manufacturing workers in thousands LIC - Number of handgun licences per 100,000 population GR - Number of handgun registrations per 100,000 population CLEAR - % homicides cleared by arrests WM - Number of white males in the population NMAN - Number of non-manufacturing workers in thousands GOV - Number of government workers in thousands HE - Average hourly earnings WE - Average weekly earnings HOM - Number of homicides per 100,000 of population ACC - Death rate in accidents per 100,000 population ASR - Number of assaults per 100,000 population

The assumption of normality seems reasonable as the error terms roughly follow a normal distribution. However, without more data points, it is difficult to guage how reasonable this assumption is.

res = resid(mod)
qqnorm(res)
qqline(res)

library(MASS)
rstud = studres(mod)
hist(rstud)