Descriptive Statistics Table
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variable Mean Median Variance SD
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Property crime rate 2,999.220 2,993.600 258,517.000 508.446
Violent crime rate 427.315 418.200 2,764.814 52.581
-----------------------------------------------------------Investigating Property Crime and Violent Crime
FBI’S UCR crime report 2000-2019
Introduction
The FBI’s Uniform Crime Reporting (UCR)¹ program, a cooperative statistical effort, is utilized nationwide in collecting, analyzing, and publishing uniform crime data. Established in 1930, the program serves as the nation’s primary source for crime statistics, incorporating data provided voluntarily by “over 19,000 city, university, college, state, tribal, and federal law enforcement agencies” under the National Incident-Based Reporting System (NIBRS). Crime in the United States², reported by the FBI under the UCR, establishes categories of offenses from 2000-2019. From this data, it can be hypothesized that some of the reported crimes under the given time range reveal a relationship when analyzed collectively. If my model is correct, then there will be a positive linear relationship between property crime rate [X] and violent crime rate [Y]. Furthermore, a control for year might demonstrate a necessary avoidance in shared time trends that would otherwise tie a direct relationship between violent and property crime.
Descriptive Statistics
Histogram 1
Histogram 2
Scatterplot
Code
library(ggplot2)
ggplot(crime_in_the_U.S., aes(x = `Property crime rate`, y = `Violent crime rate`)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE) +
labs(title = "Violent Crime Rate vs Property Crime Rate",
x = "Property Crime Rate (per 100,000)", y = "Violent Crime Rate (per 100,000)") +
theme(legend.position = "none")`geom_smooth()` using formula = 'y ~ x'
Indicates a clear positive relationship between property crime rates and violent crime rates from 2000-2019. A linear upward trend suggested a strong linear association between the two variables.
Correlation and Covariance
The correlation (r = 0.933) between Violent crime rate and Property crime rate was very strong and positive. This indicates that the two variables closely moved together between 2000 and 2019, and years that contained higher property crime rates tended to have higher violent crime rates. The covariance (24,941.42) between the two variables, also positive demonstrated a similar movement in general increase and decrease over time.
OLS Regression of Violent and Property Crime Rates
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Dependent variable:
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`Violent crime rate`
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`Property crime rate` -0.008
(0.065)
Year -9.095
(5.545)
Constant 18,729.490
(11,334.830)
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Observations 20
R2 0.888
Adjusted R2 0.875
Residual Std. Error 18.599 (df = 17)
F Statistic 67.429*** (df = 2; 17)
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Note: *p<0.1; **p<0.05; ***p<0.01
Call:
lm(formula = `Violent crime rate` ~ `Property crime rate` + Year,
data = crime_in_the_U.S.)
Residuals:
Min 1Q Median 3Q Max
-28.63 -11.81 2.30 14.90 24.09
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.873e+04 1.133e+04 1.652 0.117
`Property crime rate` -8.451e-03 6.452e-02 -0.131 0.897
Year -9.095e+00 5.545e+00 -1.640 0.119
Residual standard error: 18.6 on 17 degrees of freedom
Multiple R-squared: 0.8881, Adjusted R-squared: 0.8749
F-statistic: 67.43 on 2 and 17 DF, p-value: 8.253e-09The OLS regression model was statistically significant overall (F = 67.43, p < .001) and explained (R² = 0.888) 88.8% of the variation in violent crime rates from 2000-2019. After controlling for year, property crime was not a statistically significant predictor of violent crime (p = .897).
Conclusion
The positive relationship initially observed between the two variables in the scatterplot may have been attributed by broader long-term trends rather than a direct relationship. Year, a control variable used in the OLS regression model, accounted for longer trends in national crime and distinguished broader time-related declines within overall crime in the given time period. Upon the findings of the regression analysis, the property crime rate after controlling for year was not a statistically significant predictor of violent crime rate and the original strong relationship weakened, implying that other national-crime trends might have driven the two variables . Furthermore, the negative coefficient under year reflected a general decline in crime rates across the 2000-2019 time period, implying that the correlation might have been more of a decreasing trend over time both variables moved similarly in. While the results initially supported the hypothesis in property crime rates and violent crime rates sharing a positive relationship, a weakened relationship revealed by the regression model demonstrated the hypothesis was only partially supported by the results. In a weaker resulting relationship, concerns in the scope of the content of the origins of these national-trends arise. Whether regional (state), economic, or demographic changes were factors in the variation of this decline are additional questions raised that, through research, might otherwise reveal relationship differences across cities and states.
Notes
This analysis is observational and time-series based. The findings within the analysis of this demonstration should be interpreted cautiously. More advanced approaches and larger datasets could provide additional insight into the relationship between violent and property crime trends. This investigation and its results rely on a national time-series data set (Table 1) provided by the FBI’s Uniform Crime Reporting program. The provided crimes are reported by volume and rate per 100,000 inhabitants, and (within violent crime) include offenses of murder, rape, robbery, and aggravated assault.
Works Cited
¹Crime/Law Enforcement Stats (UCR program) | Federal Bureau of Investigation. Accessed May 8, 2026. https://www.fbi.gov/how-we-can-help-you/more-fbi-services-and-information/u.
²“2019 Crime in the United States - Table 1.” ucr.fbi.gov. Accessed May 8, 2026. https://ucr.fbi.gov/crime-in-the-u.s/2019/crime-in-the-u.s.-2019/tables/table-1.