Loading and Preparing the Data

knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
library(tidyverse)
library(readxl)
library(janitor)
library(ggplot2)
library(maps)
library(ggcorrplot)
Florida <- read_xlsx("Florida County Crime Rates.xlsx")
FloridaRenamed <- Florida %>%
  rename(
Crime        = C,
Income         = I,
HighSchoolGrad = HS,
UrbanPop       = U
) %>%
  mutate(
    County = str_to_title(str_trim(County))
  )

glimpse(FloridaRenamed)
## Rows: 67
## Columns: 5
## $ County         <chr> "Alachua", "Baker", "Bay", "Bradford", "Brevard", "Brow…
## $ Crime          <dbl> 104, 20, 64, 50, 64, 94, 8, 35, 27, 41, 55, 69, 128, 69…
## $ Income         <dbl> 22.1, 25.8, 24.7, 24.6, 30.5, 30.6, 18.6, 25.7, 21.3, 3…
## $ HighSchoolGrad <dbl> 82.7, 64.1, 74.7, 65.0, 82.3, 76.8, 55.9, 75.7, 68.6, 8…
## $ UrbanPop       <dbl> 73.2, 21.5, 85.0, 23.2, 91.9, 98.9, 0.0, 80.2, 31.0, 65…
summary(FloridaRenamed)
##     County              Crime           Income      HighSchoolGrad 
##  Length:67          Min.   :  0.0   Min.   :15.40   Min.   :54.50  
##  Class :character   1st Qu.: 35.5   1st Qu.:21.05   1st Qu.:62.45  
##  Mode  :character   Median : 52.0   Median :24.60   Median :69.00  
##                     Mean   : 52.4   Mean   :24.51   Mean   :69.49  
##                     3rd Qu.: 69.0   3rd Qu.:28.15   3rd Qu.:76.90  
##                     Max.   :128.0   Max.   :35.60   Max.   :84.90  
##     UrbanPop    
##  Min.   : 0.00  
##  1st Qu.:21.60  
##  Median :44.60  
##  Mean   :49.56  
##  3rd Qu.:83.55  
##  Max.   :99.60

Exploratory Data Analysis

summary_stats <- FloridaRenamed %>%
  summarise(
    mean_crime = mean(Crime),
    median_crime = median(Crime),
    min_crime = min(Crime),
    max_crime = max(Crime),
    range_crime = max(Crime) - min(Crime),

    mean_income = mean(Income),
    median_income = median(Income),
    min_income = min(Income),
    max_income = max(Income),
    range_income = max(Income) - min(Income),

    mean_HS = mean(HighSchoolGrad),
    median_HS = median(HighSchoolGrad),
    min_HS = min(HighSchoolGrad),
    max_HS = max(HighSchoolGrad),
    range_HS = max(HighSchoolGrad) - min(HighSchoolGrad),

    mean_urban = mean(UrbanPop),
    median_urban = median(UrbanPop),
    min_urban = min(UrbanPop),
    max_urban = max(UrbanPop),
    range_urban = max(UrbanPop) - min(UrbanPop)
  )

knitr::kable(as.data.frame(t(summary_stats)))
V1
mean_crime 52.40299
median_crime 52.00000
min_crime 0.00000
max_crime 128.00000
range_crime 128.00000
mean_income 24.51045
median_income 24.60000
min_income 15.40000
max_income 35.60000
range_income 20.20000
mean_HS 69.48955
median_HS 69.00000
min_HS 54.50000
max_HS 84.90000
range_HS 30.40000
mean_urban 49.55821
median_urban 44.60000
min_urban 0.00000
max_urban 99.60000
range_urban 99.60000 
Grad_Income_Graph <- ggplot(FloridaRenamed, aes(x = HighSchoolGrad, y = Income)) +
  geom_point(color = "green") +
  geom_hline(yintercept = 0, linetype = "dashed") +
  geom_smooth(se = FALSE, color = "black", linetype = "solid")+
  labs(
    title = "How Graduation Rate Impacts Income",
    x = "High School Graduation Rate",
    y = "Income"
  )

print(Grad_Income_Graph)

Income appears to rise with high school graduation rates (though it appears relatively stable past 75%).

UrbanPop_Crime_graph <- ggplot(FloridaRenamed, aes(x = UrbanPop, y = Crime)) +
  geom_point() +
  geom_smooth(method = "lm", se=TRUE) +
  labs(
    title = "Crime vs Urban Population",
    x = "Urban Population",
    y = "Crime"
  ) +
  theme_minimal()

print(UrbanPop_Crime_graph)

Crime appears to rise with urban population.

fl_map <- map_data("county") %>%
  filter(region == "florida") %>%
  mutate(subregion = str_to_title(subregion))  


fl_map_data <- fl_map %>%
  left_join(FloridaRenamed %>% rename(subregion = County),
            by = "subregion")


ggplot(fl_map_data, aes(long, lat, group = group, fill = Crime)) +
  geom_polygon(color = "white", linewidth = 0.2) +
  coord_quickmap() +
  scale_fill_gradient(low = "lemonchiffon", high = "red", na.value = "grey90") +
  labs(
    title = "Florida Counties: Crime Rate",
    fill  = "Crime Rate"
  ) +
  theme_void()

Correlation Analysis

cor_data <- FloridaRenamed %>%
  select(Crime, Income, HighSchoolGrad, UrbanPop)

cor_matrix <- cor(cor_data, use = "complete.obs")

cor_matrix
##                    Crime    Income HighSchoolGrad  UrbanPop
## Crime          1.0000000 0.4337503      0.4669119 0.6773678
## Income         0.4337503 1.0000000      0.7926215 0.7306983
## HighSchoolGrad 0.4669119 0.7926215      1.0000000 0.7907190
## UrbanPop       0.6773678 0.7306983      0.7907190 1.0000000

Urban population shows the highest correlation with crime. This is a strong correlation. All the correlations are positive. Some, such as “Crime/UrbanPop”,“Income/HighSchoolGrad”, “Income/UrbanPop”, “HighSchoolGrad/UrbanPop”, are strong. The others are all moderate.

ggcorrplot(
  cor_matrix,
  lab = TRUE,       
  lab_size = 4,     
  method = "square",
  type = "lower",   
  outline.col = "white",
  title = "Correlation Matrix: Crime and Socioeconomic Variables"
)

Building Regression Models

simplecrimemodel <- lm(Crime ~ UrbanPop, data = FloridaRenamed)

summary(simplecrimemodel)
## 
## Call:
## lm(formula = Crime ~ UrbanPop, data = FloridaRenamed)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -34.766 -16.541  -4.741  16.521  49.632 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 24.54125    4.53930   5.406 9.85e-07 ***
## UrbanPop     0.56220    0.07573   7.424 3.08e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.9 on 65 degrees of freedom
## Multiple R-squared:  0.4588, Adjusted R-squared:  0.4505 
## F-statistic: 55.11 on 1 and 65 DF,  p-value: 3.084e-10
Twowaycrimemodel <- lm(Crime ~ UrbanPop + Income, data = FloridaRenamed)

summary(Twowaycrimemodel)
## 
## Call:
## lm(formula = Crime ~ UrbanPop + Income, data = FloridaRenamed)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -36.130 -15.590  -6.484  16.595  48.921 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  39.9723    16.3536   2.444   0.0173 *  
## UrbanPop      0.6418     0.1110   5.784 2.36e-07 ***
## Income       -0.7906     0.8049  -0.982   0.3297    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.91 on 64 degrees of freedom
## Multiple R-squared:  0.4669, Adjusted R-squared:  0.4502 
## F-statistic: 28.02 on 2 and 64 DF,  p-value: 1.815e-09
Fullcrimemodel <- lm(Crime ~ UrbanPop + Income + HighSchoolGrad, data=FloridaRenamed)

summary(Fullcrimemodel)
## 
## Call:
## lm(formula = Crime ~ UrbanPop + Income + HighSchoolGrad, data = FloridaRenamed)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -35.407 -15.080  -6.588  16.178  50.125 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     59.7147    28.5895   2.089   0.0408 *  
## UrbanPop         0.6972     0.1291   5.399 1.08e-06 ***
## Income          -0.3831     0.9405  -0.407   0.6852    
## HighSchoolGrad  -0.4673     0.5544  -0.843   0.4025    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.95 on 63 degrees of freedom
## Multiple R-squared:  0.4728, Adjusted R-squared:  0.4477 
## F-statistic: 18.83 on 3 and 63 DF,  p-value: 7.823e-09
AIC(simplecrimemodel,Twowaycrimemodel,Fullcrimemodel)
##                  df      AIC
## simplecrimemodel  3 601.4300
## Twowaycrimemodel  4 602.4276
## Fullcrimemodel    5 603.6764

The simple crime model and two way crime model are effectively the same when it comes to AIC. So, the simple crime model is likely the best (being that it involves the fewest different variables). The simple model explains about 46% of the variance in crime (Adjusted R² ≈ 0.45), which is only slightly lower than the other models. Because it explains a similar amount of variance while using the fewest predictors, the simple crime model is the most parsimonious. In addition, the other variables are not significant when urban population is included in the model (p > .05 for both high school graduation and income). It is, therefore, relatively clear that urban population is the strongest predictor of crime. This makes intuitive sense: The more people in a given area, the more people there are who are capable of committing crimes.

Communicate Your Findings

The best model for predicting crime is the “simple crime model.” It explains the same amount of variance as the other models, has the lowest AIC, and is the most parsimonious (being that it only includes one variable). As a result, the Florida PD should invest more resources in more populated areas.

A limitation of this analysis is that factors which result from large population (such as crowded living conditions or food scarcity) may be at the heart of crime issues. It may be more effective to address these issues directly than to simply put more resources into more populated areas. If this is the case, the simple crime model is not wrong (per se) — it is merely too broad. A future analysis should explore which variables associated with large population may or may not be at the root of crime.