R Notebook

####Check the current working directory to confirm the location of the dataset files.

getwd()

[1] "C:/Users/p1044411/Downloads"

####Load the incidents dataset and inspect its structure to understand variable types and dimensions.

regression1<-read.csv("incidents.csv",header=T,sep = ",")
str(regression1)

'data.frame':   16 obs. of  4 variables:
 $ area      : chr  "Boulder" "California-lexington" "Huntsville" "Seattle" ...
 $ zone      : chr  "west" "east" "east" "west" ...
 $ population: chr  "107,353" "326,534" "444,752" "750,000" ...
 $ incidents : int  605 103 161 1703 1003 527 721 704 105 403 ...

####Generate summary statistics to explore distributions and identify potential data issues.

####Ensure that all required packages are installed for analysis and visualization.

####Convert the population variable from a comma-formatted string to a numeric variable for modeling.

####Remove the first column (likely an identifier) to create a cleaner dataset for regression analysis.

####Fit a simple linear regression model to examine the relationship between incidents and population.

reg.fit1<-lm(regression2$incidents~regression2$population)
summary(reg.fit1)

####Fit a multiple linear regression including both zone and population to control for regional differences.

reg.fit2<-lm(incidents~zone+population,data=regression2)
summary(reg.fit2)

####Recode the zone variable as a binary indicator and create an interaction term to test whether the effect of population differs by zone.

regression2$zone<-ifelse(regression2$zone=="west",1,0)

interaction<-regression2$zone*regression2$population

reg.fit3<-lm(regression2$incidents~interaction+regression2$population+regression2$zone)
summary(reg.fit3)

####Fit a linear model including main effects and the interaction term to evaluate moderation effects.

reg.fit4<-lm(regression2$incidents~interaction)
summary(reg.fit4)

####Fit a simplified linear model using only the interaction term for comparison purposes.

# Running the Poisson GLM
model_glm <- glm(incidents ~ zone + offset(log(population)), 
                 data = regression2, 
                 family = poisson(link = "log"))

# Check the results
summary(model_glm)

####Run a Poisson Generalized Linear Model (GLM) for count data, using an offset to model incident rates per population.

model_simple_glm <- glm(incidents ~ zone, data = regression2, family = poisson)
summary(model_simple_glm)

####Fit a simpler Poisson model without the offset to compare results with the rate-based model.

model_int_glm <- glm(incidents ~ zone * population + offset(log(population)), 
                     data = regression2, 
                     family = poisson)
summary(model_int_glm)

####Fit a Poisson model including an interaction term to evaluate whether population effects differ by zone.

# Calculate McFadden's Pseudo-R2
pseudo_r2 <- 1 - (model_int_glm$deviance / model_int_glm$null.deviance)
print(pseudo_r2)

####Calculate McFadden’s pseudo R² to assess model improvement relative to the null model.