Crime rate data for 67 Florida counties, including measures of crime prevalence, education levels, high school completion rates, and urbanization. This dataset is a central example in the course for demonstrating multiple regression with two continuous predictors, confounding/omitted variable bias, partial correlations, and interaction effects between continuous variables.
Format
A tibble with 67 rows and 5 columns:
- county
County name. Type: character. 67 unique Florida counties (e.g., ALACHUA, BAKER, BAY, BRADFORD, BREVARD, BROWARD).
- c
Crime rate: number of crimes per year per 1,000 population. Type: numeric. Range: (0, 128). Mean = 52.4. This is the primary outcome variable.
- i
Median household income in thousands of dollars. Type: numeric. Range: (15.4, 35.6). Mean = 24.5.
- hs
Education: percentage of adults with at least a high school education. Type: numeric. Range: (54.5, 84.9). Mean = 69.5.
- u
Urbanization: percentage of the population living in an urban environment. Type: numeric. Range: (0.0, 99.6). Mean = 49.6.
Details
This dataset is used in Chapter 4 (Continuous Predictors) and Chapter 5 (Interactions) to illustrate several key regression concepts. Key analyses include:
Confounding: Education has a positive bivariate association with crime rate (slope = 1.5), but after controlling for urbanization, the effect reverses to negative (slope = -0.6). This demonstrates omitted variable bias: urbanization is correlated with both education and crime.
Partial correlations: The partial correlation between crime rate and education controlling for urbanization is -0.15, compared to the Pearson correlation of 0.47.
Interaction: The interaction model \(y = \alpha + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_1 x_2\) shows that the effect of education on crime depends on the level of urbanization.
Examples
data(crime)
head(crime)
#> # A tibble: 6 × 5
#> county c i hs u
#> <chr> <int> <dbl> <dbl> <dbl>
#> 1 ALACHUA 104 22.1 82.7 73.2
#> 2 BAKER 20 25.8 64.1 21.5
#> 3 BAY 64 24.7 74.7 85
#> 4 BRADFORD 50 24.6 65 23.2
#> 5 BREVARD 64 30.5 82.3 91.9
#> 6 BROWARD 94 30.6 76.8 98.9
# Simple regression: education appears to increase crime
lm(c ~ hs, data = crime)
#>
#> Call:
#> lm(formula = c ~ hs, data = crime)
#>
#> Coefficients:
#> (Intercept) hs
#> -50.857 1.486
#>
# Multiple regression: controlling for urbanization reverses the effect
lm(c ~ hs + u, data = crime)
#>
#> Call:
#> lm(formula = c ~ hs + u, data = crime)
#>
#> Coefficients:
#> (Intercept) hs u
#> 59.1181 -0.5834 0.6825
#>
# Interaction between education and urbanization
lm(c ~ hs * u, data = crime)
#>
#> Call:
#> lm(formula = c ~ hs * u, data = crime)
#>
#> Coefficients:
#> (Intercept) hs u hs:u
#> 19.31754 0.03396 1.51431 -0.01205
#>