What Data Set are we going to explore? (Objective)

• For this Project we are going to explore the “USArrests” data set that is provided by Rstudio.
• Given this Data Set, we will answer the question provided:
• Are there regional trends in violent crime rates across the United States?
• In the following slides we will break down this data and answer this question

Step 1 - Import the Data

• The First Step of this project is to import the Data Provided By R Studio
• It is also very crucial to know and understand your data
• We do both of these by executing the following commands

data("USArrests") 
summary(USArrests)

##      Murder          Assault         UrbanPop          Rape      
##  Min.   : 0.800   Min.   : 45.0   Min.   :32.00   Min.   : 7.30  
##  1st Qu.: 4.075   1st Qu.:109.0   1st Qu.:54.50   1st Qu.:15.07  
##  Median : 7.250   Median :159.0   Median :66.00   Median :20.10  
##  Mean   : 7.788   Mean   :170.8   Mean   :65.54   Mean   :21.23  
##  3rd Qu.:11.250   3rd Qu.:249.0   3rd Qu.:77.75   3rd Qu.:26.18  
##  Max.   :17.400   Max.   :337.0   Max.   :91.00   Max.   :46.00

Steps neccesary to complete goal

1. Assign Regions to Each State
2. Calculate Average Crime Rates By Region
3. Visualize Crime Rates By Region
4. Conduct Tests for Significance
5. Interpret Results

Step 1 - Assign Regions to Each State

• Here we are adding a new column named State with State Names
• We are going to define U.S regions (Northeast, Midwest, South, West)
• We are then going to eassign each state to its respective region
• Code is viewable on the next slide

Step 1A - Code for Step 1

data("USArrests")
USArrests$State <- rownames(USArrests)

northeast <- c("Connecticut", "Maine", "Massachusetts", "New Hampshire", "New Jersey", 
               "New York", "Pennsylvania", "Rhode Island", "Vermont")
midwest <- c("Illinois", "Indiana", "Iowa", "Kansas", "Michigan", "Minnesota", 
             "Missouri", "Nebraska", "North Dakota", "Ohio", "South Dakota", "Wisconsin")
south <- c("Alabama", "Arkansas", "Delaware", "Florida", "Georgia", "Kentucky", 
           "Louisiana", "Maryland", "Mississippi", "North Carolina", "Oklahoma", 
           "South Carolina", "Tennessee", "Texas", "Virginia", "West Virginia")
west <- c("Alaska", "Arizona", "California", "Colorado", "Hawaii", "Idaho", 
          "Montana", "Nevada", "New Mexico", "Oregon", "Utah", "Washington", "Wyoming")

USArrests$Region <- ifelse(USArrests$State %in% northeast, "Northeast",
                    ifelse(USArrests$State %in% midwest, "Midwest",
                    ifelse(USArrests$State %in% south, "South", "West")))

Step 2

• Calculate the Average Crime Rates by Region
• Group the data by Region and calculate the mean values for each crime type
• Murder, Assault, Rape

library(dplyr)

regional_summary <- USArrests %>%
  group_by(Region) %>%
  summarise(
    Mean_Murder = mean(Murder),
    Mean_Assault = mean(Assault),
    Mean_Rape = mean(Rape)
  )

Step 2A - Regional Summary using knitr and kable

library(knitr)

kable(regional_summary, format = "markdown", caption = "Regional Crime Summary")

Step 3 - Visualize Crime Rates By Region

• Use box plots to visualize the distribution of crime rates across regions +This will Show whether certain regions have higher or lower crime rates than others
• This approach provides a comprehensive view of regional crime +Helps identify potential areas of focus
• Sets up further analysis or targeted interventions

Step 3A - Code for Step 3

+ Here we can see a clear breakdown of the data by region

Step 4 - Conduct Statistical Tests for Significance

• We are now going to conduct ANOVA tests to determine if the differences in crime rates between regions are statistically significant for each crime type
• ANOVA tests compare the means of groups to determine if there are significant differences between them
• Below is the code for these ANOVA tests

# Perform ANOVA tests
anova_murder <- summary(aov(Murder ~ Region, data = USArrests))
anova_assault <- summary(aov(Assault ~ Region, data = USArrests))
anova_rape <- summary(aov(Rape ~ Region, data = USArrests))

# Extract results from each ANOVA summary and convert them to data frames
murder_df <- as.data.frame(anova_murder[[1]])
murder_df$Crime <- "Murder"

assault_df <- as.data.frame(anova_assault[[1]])
assault_df$Crime <- "Assault"

rape_df <- as.data.frame(anova_rape[[1]])
rape_df$Crime <- "Rape"

Step 4A - Formatted Table of ANOVA Statistical Tests

Step 5 - Anova Interpretation

• Murder: P-Value: 0.0000128 - This is well below the 0.05 threshold indicating a very strong statistical difference in murder rates across the 4 different regions
• Rape P-Value: 0.0004119
• Assault P-Value: 0.0024782
• Regional differences in crime rates ARE statistically significant
• Each Region Contributing meaningfully to the observed variation in crime rates
• Targeted Crime Prevention, Enhanced Law Enforcement Training, Data-Driven Policing and Real-Time Crime Mapping