Crime Statistics Analysis

Determinants of Crime in North Carolina Counties (1987)

Team: Cristopher Benge | Joy First | Kevin Kory

UC Berkeley, Master of Information and Data Science | Fall 2019 W203: Statistics for Data Science | G. Kleeman, PhD

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Overview

This study applies OLS regression to investigate the determinants of crime across 90 North Carolina counties using 1987 data. We develop three nested model specifications to evaluate the effects of deterrence (arrest and conviction rates), economic conditions (wages, tax revenue), and demographics on county-level crime rates. Our analysis yields actionable policy recommendations while carefully addressing model assumptions and limitations.

Read the Full Report (PDF)

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Key Findings

Finding	Effect	Policy Implication
Arrest probability	1% increase → 0.04% decrease in crime rate	Invest in investigation and clearance rates
Conviction probability	1% increase → 0.04% decrease in crime rate	Support prosecutorial capacity
Police per capita	Positive correlation (endogeneity concern)	More police deployed where crime already high
Construction wages	Higher wages → lower crime	Economic opportunity reduces crime
Young male population	Higher % → higher crime	Target prevention programs to at-risk demographics

Recommended Model

Model 2 balances explanatory power with parsimony:

crmrte ~ prbarr + prbconv + log(polpc) + taxpc + wcon + pctymle + log(pctmin80)

• Adjusted R²: ~0.44
• F-statistic: Significant (p < 0.001)
• Passes heteroscedasticity tests
• Residuals approximately normal

Model 1 omits important demographic controls; Model 3 risks overfitting with limited observations.

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Data

Source & Context

County-level crime statistics from 90 North Carolina counties (1987), sourced from Cornwell and Trumbull (1994). The dataset captures law enforcement, economic, and demographic characteristics used to study crime determinants.

Key Variables

Variable	Description	Notes
crmrte	Crimes committed per person	Dependent variable
prbarr	Probability of arrest	Ratio: arrests/offenses
prbconv	Probability of conviction	Ratio: convictions/arrests
polpc	Police per capita	Log-transformed in models
taxpc	Tax revenue per capita	Proxy for county resources
wcon	Weekly wage, construction	Economic opportunity measure
pctymle	% young males (15-24)	Demographic risk factor
pctmin80	% minority (1980 census)	Log-transformed in models

Data Cleaning

Step	Action	Result
Missing values	Removed 6 rows with NA in prbarr or prbconv	97 → 91 rows
Duplicates	Removed duplicate entry for county 193	91 → 90 rows
Type conversion	Converted prbconv from factor to numeric	—

Limitations

IID Assumption Violation: The 10 missing counties are the lowest-populated counties in North Carolina. This is not random missingness—the sample systematically excludes rural counties, potentially biasing estimates for policies targeting less populated areas.

Counties in the dataset (shaded) vs. missing counties

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Methodology

Approach

We employ Ordinary Least Squares (OLS) regression with a nested model strategy: starting with core deterrence variables, then adding controls to test robustness and reduce omitted variable bias.

Feature selection used two complementary methods:

• Exhaustive subset selection via leaps::regsubsets()
• Stepwise regression using AIC criterion

Model Specifications

Model	Variables	Purpose
Model 1	prbarr, prbconv, log(polpc), taxpc, wcon	Core deterrence + economic factors
Model 2	Model 1 + pctymle, log(pctmin80)	Adds demographic controls
Model 3	Model 2 + wser, wfed, additional controls	Full specification (robustness check)

Diagnostics Summary

Assumption	Test	Model 2 Result
Linearity	Residuals vs. Fitted	No systematic pattern
Normality	Q-Q Plot, Shapiro-Wilk	Approximately normal
Homoscedasticity	Breusch-Pagan	No significant heteroscedasticity
Multicollinearity	VIF	All VIF < 5

Diagnostic plots for recommended Model 2

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Repository Structure

File	Description
Crime Analysis & Policy Recommendations.pdf	Final report
first_kory_benge-lab_3.Rmd	R Markdown analysis source
first_kory_benge-lab_3.tex	LaTeX report root file
EDA.ipynb	Exploratory data analysis notebook
crime_v2.csv	Source dataset
chapters/	LaTeX chapter files (introduction.tex, eda.tex, analysis.tex)
images/	Generated visualizations and plots

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Reproduce the Analysis

# Install dependencies
install.packages(c("tidyverse", "car", "lmtest", "leaps",
                   "stargazer", "corrplot", "gridExtra"))

# Render the analysis
rmarkdown::render("first_kory_benge-lab_3.Rmd")

To compile the LaTeX report:

pdflatex first_kory_benge-lab_3.tex

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Team

	Name	Contact
	Cristopher Benge	Website
	Joy First	Email
	Kevin Kory	Email

License

This project is licensed under the MIT License - see LICENSE.txt for details.

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Distribution of crime rates across North Carolina counties