Florida Crime Analytics
Crystal Adote
2025-11-06
Loading and Preparing the Data
library(readxl)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 4.0.0 ✔ tibble 3.3.0
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.1.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(dplyr)
library## function (package, help, pos = 2, lib.loc = NULL, character.only = FALSE,
## logical.return = FALSE, warn.conflicts, quietly = FALSE,
## verbose = getOption("verbose"), mask.ok, exclude, include.only,
## attach.required = missing(include.only))
## {
## conf.ctrl <- getOption("conflicts.policy")
## if (is.character(conf.ctrl))
## conf.ctrl <- switch(conf.ctrl, strict = list(error = TRUE,
## warn = FALSE), depends.ok = list(error = TRUE, generics.ok = TRUE,
## can.mask = c("base", "methods", "utils", "grDevices",
## "graphics", "stats"), depends.ok = TRUE), warning(gettextf("unknown conflict policy: %s",
## sQuote(conf.ctrl)), call. = FALSE, domain = NA))
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## if (!missing(include.only) && !missing(exclude))
## stop("only one of 'include.only' and 'exclude' can be used",
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## if (is.null(built <- pkgInfo$Built))
## stop(gettextf("package %s has not been installed properly\n",
## sQuote(pkgname)), call. = FALSE, domain = NA)
## R_version_built_under <- as.numeric_version(built$R)
## if (R_version_built_under < "3.0.0")
## stop(gettextf("package %s was built before R 3.0.0: please re-install it",
## sQuote(pkgname)), call. = FALSE, domain = NA)
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## for (dep in Rdeps) if (length(dep) > 1L) {
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## res <- do.call(dep$op, if (is.character(target))
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## "", target)))
## else list(current, as.numeric_version(target)))
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## from <- gsub(".__T__(.*):([^:]+)", "\\2", these)
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## "CheckExEnv"), sp, 0L))]
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## function(.) !identical(TRAFO(get(., i)), TRAFO(get(.,
## lib.pos)), ...), NA)
## if (length(same))
## same <- same[not.Ident(same)]
## if (length(same) && identical(sp[i], "package:base"))
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## if (length(same)) {
## conflicts[[sp[i]]] <- same
## cpos[sp[i]] <- i
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## if (length(conflicts)) {
## if (stopOnConflict) {
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## pkg <- names(conflicts)
## notOK <- vector("list", 0)
## for (i in seq_along(conflicts)) {
## pkgname <- sub("^package:", "", pkg[i])
## if (pkgname %in% canMaskEnv$canMask)
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## same <- conflicts[[i]]
## if (is.list(mask.ok))
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## if (isTRUE(myMaskOK))
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## else if (is.character(myMaskOK))
## same <- setdiff(same, myMaskOK)
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## msg <- .maskedMsg(sort(same), pkg = sQuote(pkg[i]),
## by = cpos[i] < lib.pos)
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## }
## }
## if (length(notOK)) {
## msg <- gettextf("Conflicts attaching package %s:\n%s",
## sQuote(package), emsg)
## stop(errorCondition(msg, package = package,
## conflicts = conflicts, class = "packageConflictError"))
## }
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## if (warn.conflicts) {
## packageStartupMessage(gettextf("\nAttaching package: %s\n",
## sQuote(package)), domain = NA)
## pkg <- names(conflicts)
## for (i in seq_along(conflicts)) {
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## by = cpos[i] < lib.pos)
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## domain = NA)
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## sys.call()))
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## else gettext("no library trees found in 'lib.loc'")
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## which.lib.loc <- normalizePath(dirname(pkgpath),
## "/", TRUE)
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## lib.loc = which.lib.loc)
## if (!nzchar(pfile))
## stop(gettextf("%s is not a valid installed package",
## sQuote(package)), domain = NA)
## pkgInfo <- readRDS(pfile)
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## if (is.character(pos)) {
## npos <- match(pos, search())
## if (is.na(npos)) {
## warning(gettextf("%s not found on search path, using pos = 2",
## sQuote(pos)), domain = NA)
## pos <- 2
## }
## else pos <- npos
## }
## deps <- unique(names(pkgInfo$Depends))
## depsOK <- isTRUE(conf.ctrl$depends.ok)
## if (depsOK) {
## canMaskEnv <- dynGet("__library_can_mask__",
## NULL)
## if (is.null(canMaskEnv)) {
## canMaskEnv <- new.env()
## canMaskEnv$canMask <- union("base", conf.ctrl$can.mask)
## "__library_can_mask__" <- canMaskEnv
## }
## canMaskEnv$canMask <- unique(c(package, deps,
## canMaskEnv$canMask))
## }
## else canMaskEnv <- NULL
## if (attach.required)
## .getRequiredPackages2(pkgInfo, quietly = quietly,
## lib.loc = c(lib.loc, .libPaths()))
## cr <- conflictRules(package)
## if (missing(mask.ok))
## mask.ok <- cr$mask.ok
## if (missing(exclude))
## exclude <- cr$exclude
## if (isNamespaceLoaded(package)) {
## newversion <- as.numeric_version(pkgInfo$DESCRIPTION["Version"])
## oldversion <- as.numeric_version(getNamespaceVersion(package))
## if (newversion != oldversion) {
## tryCatch(unloadNamespace(package), error = function(e) {
## P <- if (!is.null(cc <- conditionCall(e)))
## paste("Error in", deparse(cc)[1L], ": ")
## else "Error : "
## stop(gettextf("Package %s version %s cannot be unloaded:\n %s",
## sQuote(package), oldversion, paste0(P,
## conditionMessage(e), "\n")), domain = NA)
## })
## }
## }
## tt <- tryCatch({
## attr(package, "LibPath") <- which.lib.loc
## ns <- loadNamespace(package, lib.loc)
## env <- attachNamespace(ns, pos = pos, deps, exclude,
## include.only)
## }, error = function(e) {
## P <- if (!is.null(cc <- conditionCall(e)))
## paste(" in", deparse(cc)[1L])
## else ""
## msg <- gettextf("package or namespace load failed for %s%s:\n %s",
## sQuote(package), P, conditionMessage(e))
## if (logical.return && !quietly)
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## else stop(msg, call. = FALSE, domain = NA)
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## {
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## package)
## if (isFALSE(conf.ctrl$generics.ok) || (stopOnConflict &&
## !isTRUE(conf.ctrl$generics.ok)))
## nogenerics <- TRUE
## if (stopOnConflict || (warn.conflicts && !exists(".conflicts.OK",
## envir = env, inherits = FALSE)))
## checkConflicts(package, pkgname, pkgpath, nogenerics,
## ns)
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## else return(invisible(.packages()))
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## sQuote(package)), domain = NA)
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## else if (!missing(help)) {
## if (!character.only)
## help <- as.character(substitute(help))
## pkgName <- help[1L]
## pkgPath <- find.package(pkgName, lib.loc, verbose = verbose)
## docFiles <- c(file.path(pkgPath, "Meta", "package.rds"),
## file.path(pkgPath, "INDEX"))
## if (file.exists(vignetteIndexRDS <- file.path(pkgPath,
## "Meta", "vignette.rds")))
## docFiles <- c(docFiles, vignetteIndexRDS)
## pkgInfo <- vector("list", 3L)
## readDocFile <- function(f) {
## if (basename(f) %in% "package.rds") {
## txt <- readRDS(f)$DESCRIPTION
## if ("Encoding" %in% names(txt)) {
## to <- if (Sys.getlocale("LC_CTYPE") == "C")
## "ASCII//TRANSLIT"
## else ""
## tmp <- try(iconv(txt, from = txt["Encoding"],
## to = to))
## if (!inherits(tmp, "try-error"))
## txt <- tmp
## else warning("'DESCRIPTION' has an 'Encoding' field and re-encoding is not possible",
## call. = FALSE)
## }
## nm <- paste0(names(txt), ":")
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## 3L)
## }
## else if (basename(f) %in% "vignette.rds") {
## txt <- readRDS(f)
## if (is.data.frame(txt) && nrow(txt))
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## txt$File)), paste(txt$Title, paste0(rep.int("(source",
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## ""), ")")))
## else NULL
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## }
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## class(y) <- "packageInfo"
## return(y)
## }
## else {
## if (is.null(lib.loc))
## lib.loc <- .libPaths()
## db <- matrix(character(), nrow = 0L, ncol = 3L)
## nopkgs <- character()
## for (lib in lib.loc) {
## a <- .packages(all.available = TRUE, lib.loc = lib)
## for (i in sort(a)) {
## file <- system.file("Meta", "package.rds", package = i,
## lib.loc = lib)
## title <- if (nzchar(file)) {
## txt <- readRDS(file)
## if (is.list(txt))
## txt <- txt$DESCRIPTION
## if ("Encoding" %in% names(txt)) {
## to <- if (Sys.getlocale("LC_CTYPE") == "C")
## "ASCII//TRANSLIT"
## else ""
## tmp <- try(iconv(txt, txt["Encoding"], to,
## "?"))
## if (!inherits(tmp, "try-error"))
## txt <- tmp
## else warning("'DESCRIPTION' has an 'Encoding' field and re-encoding is not possible",
## call. = FALSE)
## }
## txt["Title"]
## }
## else NA
## if (is.na(title))
## title <- " ** No title available ** "
## db <- rbind(db, cbind(i, lib, title))
## }
## if (length(a) == 0L)
## nopkgs <- c(nopkgs, lib)
## }
## dimnames(db) <- list(NULL, c("Package", "LibPath", "Title"))
## if (length(nopkgs) && !missing(lib.loc)) {
## pkglist <- paste(sQuote(nopkgs), collapse = ", ")
## msg <- sprintf(ngettext(length(nopkgs), "library %s contains no packages",
## "libraries %s contain no packages"), pkglist)
## warning(msg, domain = NA)
## }
## y <- list(header = NULL, results = db, footer = NULL)
## class(y) <- "libraryIQR"
## return(y)
## }
## if (logical.return)
## TRUE
## else invisible(.packages())
## }
## <bytecode: 0x12439f000>
## <environment: namespace:base>florida_crime<- read_xlsx("Florida County Crime Rates data.xlsx")
View(florida_crime)
florida_crime<- florida_crime %>% rename(Crime = C, Income= I, HighSchoolGrad = HS, UrbanPop = U)
florida_crime$County<- str_to_title(florida_crime$County)
str(florida_crime)## tibble [67 × 5] (S3: tbl_df/tbl/data.frame)
## $ County : chr [1:67] "Alachua" "Baker" "Bay" "Bradford" ...
## $ Crime : num [1:67] 104 20 64 50 64 94 8 35 27 41 ...
## $ Income : num [1:67] 22.1 25.8 24.7 24.6 30.5 30.6 18.6 25.7 21.3 34.9 ...
## $ HighSchoolGrad: num [1:67] 82.7 64.1 74.7 65 82.3 76.8 55.9 75.7 68.6 81.2 ...
## $ UrbanPop : num [1:67] 73.2 21.5 85 23.2 91.9 98.9 0 80.2 31 65.8 ...Exploratory Data Analysis
library(mosaic)## Registered S3 method overwritten by 'mosaic':
## method from
## fortify.SpatialPolygonsDataFrame ggplot2##
## The 'mosaic' package masks several functions from core packages in order to add
## additional features. The original behavior of these functions should not be affected by this.##
## Attaching package: 'mosaic'## The following object is masked from 'package:Matrix':
##
## mean## The following objects are masked from 'package:dplyr':
##
## count, do, tally## The following object is masked from 'package:purrr':
##
## cross## The following object is masked from 'package:ggplot2':
##
## stat## The following objects are masked from 'package:stats':
##
## binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
## quantile, sd, t.test, var## The following objects are masked from 'package:base':
##
## max, mean, min, prod, range, sample, sumlibrary(ggplot2)
summary(florida_crime)## 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. :99.60scatter_florida<- ggplot(florida_crime, aes(x=Income, y=Crime)) +
geom_point()+
labs(
title = "Income and Crime",
x = "Income",
y="Crime"
)
theme.mosaic()## $background
## $background$col
## [1] "transparent"
##
##
## $plot.polygon
## $plot.polygon$col
## [1] "#7171B8"
##
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## [1] "#38389C" "lightskyblue3" "darkgreen" "tan"
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## [1] "#1C1C8E"
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## [1] 16
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## [1] 16
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## $regions$col
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## [15] "#FF3000" "#FF3400" "#FF3700" "#FF3B00" "#FF3E00" "#FF4100" "#FF4500"
## [22] "#FF4800" "#FF4C00" "#FF4F00" "#FF5300" "#FF5600" "#FF5A00" "#FF5D00"
## [29] "#FF6000" "#FF6400" "#FF6700" "#FF6B00" "#FF6E00" "#FF7200" "#FF7500"
## [36] "#FF7900" "#FF7C00" "#FF8000" "#FF8300" "#FF8600" "#FF8A00" "#FF8D00"
## [43] "#FF9100" "#FF9400" "#FF9800" "#FF9B00" "#FF9F00" "#FFA200" "#FFA500"
## [50] "#FFA900" "#FFAC00" "#FFB000" "#FFB300" "#FFB700" "#FFBA00" "#FFBE00"
## [57] "#FFC100" "#FFC400" "#FFC800" "#FFCB00" "#FFCF00" "#FFD200" "#FFD600"
## [64] "#FFD900" "#FFDD00" "#FFE000" "#FFE300" "#FFE700" "#FFEA00" "#FFEE00"
## [71] "#FFF100" "#FFF500" "#FFF800" "#FFFC00" "#FFFF00" "#FFFF05" "#FFFF0F"
## [78] "#FFFF19" "#FFFF24" "#FFFF2E" "#FFFF38" "#FFFF42" "#FFFF4D" "#FFFF57"
## [85] "#FFFF61" "#FFFF6B" "#FFFF75" "#FFFF80" "#FFFF8A" "#FFFF94" "#FFFF9E"
## [92] "#FFFFA8" "#FFFFB3" "#FFFFBD" "#FFFFC7" "#FFFFD1" "#FFFFDB" "#FFFFE6"
## [99] "#FFFFF0" "#FFFFFA"
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## [1] "#e8e8e8"
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## [1] "gray20"
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## [1] 2
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## $superpose.line$lty
## [1] 1
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## [1] "#1C1C8E" "lightskyblue3" "darkgreen" "tan"
## [5] "orange" "purple" "pink" "lightgreen"
##
##
## $superpose.symbol
## $superpose.symbol$pch
## [1] 16 15 18 1 3 6 0 5
##
## $superpose.symbol$cex
## [1] 0.7 0.7 0.7 0.7 0.7 0.7 0.7
##
## $superpose.symbol$col
## [1] "#1C1C8E" "lightskyblue3" "darkgreen" "tan"
## [5] "orange" "purple" "pink" "lightgreen"
##
##
## $strip.background
## $strip.background$alpha
## [1] 1
##
## $strip.background$col
## [1] "#ffe5cc" "#DDE8F1" "#ccffff" "#cce6ff" "#ffccff" "#ffcccc" "#ffffcc"
##
##
## $strip.shingle
## $strip.shingle$alpha
## [1] 1
##
## $strip.shingle$col
## [1] "#ff7f00" "#1C1C8E" "#00ffff" "#0080ff" "#ff00ff" "#ff0000" "#ffff00"
##
##
## $par.strip.text
## $par.strip.text$cex
## [1] 0.5scatter_florida
This scatterplot conveys that as the Income increases, the crime rate
slowly increases as well.
hist_florida<- ggplot(florida_crime, aes(x=Income)) +
geom_histogram()+
labs(
title = "Florida Income",
x = "Income",
y = "Count"
)
theme_minimal()## <theme> List of 144
## $ line : <ggplot2::element_line>
## ..@ colour : chr "black"
## ..@ linewidth : num 0.5
## ..@ linetype : num 1
## ..@ lineend : chr "butt"
## ..@ linejoin : chr "round"
## ..@ arrow : logi FALSE
## ..@ arrow.fill : chr "black"
## ..@ inherit.blank: logi TRUE
## $ rect : <ggplot2::element_rect>
## ..@ fill : chr "white"
## ..@ colour : chr "black"
## ..@ linewidth : num 0.5
## ..@ linetype : num 1
## ..@ linejoin : chr "round"
## ..@ inherit.blank: logi TRUE
## $ text : <ggplot2::element_text>
## ..@ family : chr ""
## ..@ face : chr "plain"
## ..@ italic : chr NA
## ..@ fontweight : num NA
## ..@ fontwidth : num NA
## ..@ colour : chr "black"
## ..@ size : num 11
## ..@ hjust : num 0.5
## ..@ vjust : num 0.5
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## [list output truncated]
## @ complete: logi TRUE
## @ validate: logi TRUEhist_florida## `stat_bin()` using `bins = 30`. Pick better value `binwidth`.
This histogram shows us that many individuals income is between $21,000
- $30,000 in across the state of Florida.
Correlation Analysis
library(ggcorrplot)
florida_matrix<- florida_crime %>% dplyr::select(Crime, Income, HighSchoolGrad, UrbanPop)
florida_crime_matrix<- cor(florida_matrix, use="pairwise.complete.obs")
florida_crime_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 1.0000000ggcorrplot(florida_crime_matrix, lab=TRUE, type="lower")+
labs(title="Correlation Matrix: Florida Crime")## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation idioms with `aes()`.
## ℹ See also `vignette("ggplot2-in-packages")` for more information.
## ℹ The deprecated feature was likely used in the ggcorrplot package.
## Please report the issue at <https://github.com/kassambara/ggcorrplot/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
The variable that shows the strongest relationship with Crime is UrbanPop (0.68). All variables have positive relationships, however, some are stronger than others.
The relationship between HighSchoolGrad and UrbanPop is 0.79 which is one of the strongest, positive correlations among all the variables. The relationship between HighSchoolGrad and Income is also 0.79, which makes it another strong, positive correlation.
The relationship between Income and UrbanPop is 0.73, making it another strong, positive correlation. The relationship between Crime and HighSchoolGrad is 0.47, making it a moderate, positive correlation. The relationship between Crime and Income is 0.43, making it another moderate, positive correlation.
Building Regression Models
library(broom)
flordia_lm<- lm(Crime ~ UrbanPop, data = florida_crime)
flordia_lm##
## Call:
## lm(formula = Crime ~ UrbanPop, data = florida_crime)
##
## Coefficients:
## (Intercept) UrbanPop
## 24.5412 0.5622summary(flordia_lm)##
## Call:
## lm(formula = Crime ~ UrbanPop, data = florida_crime)
##
## 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-10tidy(flordia_lm)## # A tibble: 2 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 24.5 4.54 5.41 9.85e- 7
## 2 UrbanPop 0.562 0.0757 7.42 3.08e-10florida_lm2<- lm(Crime ~ HighSchoolGrad, data=florida_crime)
florida_lm2##
## Call:
## lm(formula = Crime ~ HighSchoolGrad, data = florida_crime)
##
## Coefficients:
## (Intercept) HighSchoolGrad
## -50.857 1.486summary(florida_lm2)##
## Call:
## lm(formula = Crime ~ HighSchoolGrad, data = florida_crime)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.74 -21.36 -4.82 17.42 82.27
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -50.8569 24.4507 -2.080 0.0415 *
## HighSchoolGrad 1.4860 0.3491 4.257 6.81e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.12 on 65 degrees of freedom
## Multiple R-squared: 0.218, Adjusted R-squared: 0.206
## F-statistic: 18.12 on 1 and 65 DF, p-value: 6.806e-05tidy(florida_lm2)## # A tibble: 2 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -50.9 24.5 -2.08 0.0415
## 2 HighSchoolGrad 1.49 0.349 4.26 0.0000681florida_lm3<- lm(Crime ~ Income, data=florida_crime)
florida_lm3##
## Call:
## lm(formula = Crime ~ Income, data = florida_crime)
##
## Coefficients:
## (Intercept) Income
## -11.606 2.611summary(florida_lm3)##
## Call:
## lm(formula = Crime ~ Income, data = florida_crime)
##
## Residuals:
## Min 1Q Median 3Q Max
## -42.452 -21.347 -3.102 17.580 69.357
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11.6059 16.7863 -0.691 0.491782
## Income 2.6115 0.6729 3.881 0.000246 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.6 on 65 degrees of freedom
## Multiple R-squared: 0.1881, Adjusted R-squared: 0.1756
## F-statistic: 15.06 on 1 and 65 DF, p-value: 0.0002456tidy(florida_lm3)## # A tibble: 2 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -11.6 16.8 -0.691 0.492
## 2 Income 2.61 0.673 3.88 0.000246florida_m1<- lm(Crime ~ Income+HighSchoolGrad, data = florida_crime)
florida_m1##
## Call:
## lm(formula = Crime ~ Income + HighSchoolGrad, data = florida_crime)
##
## Coefficients:
## (Intercept) Income HighSchoolGrad
## -46.109 1.031 1.054glance(florida_m1)## # A tibble: 1 × 12
## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.229 0.205 25.1 9.50 0.000244 2 -310. 627. 636.
## # ℹ 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>tidy(florida_m1)## # A tibble: 3 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -46.1 25.0 -1.85 0.0695
## 2 Income 1.03 1.08 0.951 0.345
## 3 HighSchoolGrad 1.05 0.573 1.84 0.0705florida_m2<- lm(Crime ~ Income+UrbanPop, data=florida_crime)
florida_m2##
## Call:
## lm(formula = Crime ~ Income + UrbanPop, data = florida_crime)
##
## Coefficients:
## (Intercept) Income UrbanPop
## 39.9723 -0.7906 0.6418glance(florida_m2)## # A tibble: 1 × 12
## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.467 0.450 20.9 28.0 0.00000000181 2 -297. 602. 611.
## # ℹ 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>tidy(florida_m2)## # A tibble: 3 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 40.0 16.4 2.44 0.0173
## 2 Income -0.791 0.805 -0.982 0.330
## 3 UrbanPop 0.642 0.111 5.78 0.000000236florida_m3<- lm(Crime ~ HighSchoolGrad+Income + UrbanPop, data = florida_crime)
florida_m3##
## Call:
## lm(formula = Crime ~ HighSchoolGrad + Income + UrbanPop, data = florida_crime)
##
## Coefficients:
## (Intercept) HighSchoolGrad Income UrbanPop
## 59.7147 -0.4673 -0.3831 0.6972glance(florida_m3)## # A tibble: 1 × 12
## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.473 0.448 21.0 18.8 0.00000000782 3 -297. 604. 615.
## # ℹ 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>tidy(florida_m3)## # A tibble: 4 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 59.7 28.6 2.09 0.0408
## 2 HighSchoolGrad -0.467 0.554 -0.843 0.403
## 3 Income -0.383 0.941 -0.407 0.685
## 4 UrbanPop 0.697 0.129 5.40 0.00000108florida_m4<- lm(Crime ~ UrbanPop + HighSchoolGrad, data=florida_crime)
florida_m4##
## Call:
## lm(formula = Crime ~ UrbanPop + HighSchoolGrad, data = florida_crime)
##
## Coefficients:
## (Intercept) UrbanPop HighSchoolGrad
## 59.1181 0.6825 -0.5834summary(florida_m4)##
## Call:
## lm(formula = Crime ~ UrbanPop + HighSchoolGrad, data = florida_crime)
##
## Residuals:
## Min 1Q Median 3Q Max
## -34.693 -15.742 -6.226 15.812 50.678
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 59.1181 28.3653 2.084 0.0411 *
## UrbanPop 0.6825 0.1232 5.539 6.11e-07 ***
## HighSchoolGrad -0.5834 0.4725 -1.235 0.2214
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.82 on 64 degrees of freedom
## Multiple R-squared: 0.4714, Adjusted R-squared: 0.4549
## F-statistic: 28.54 on 2 and 64 DF, p-value: 1.379e-09tidy(florida_m4)## # A tibble: 3 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 59.1 28.4 2.08 0.0411
## 2 UrbanPop 0.683 0.123 5.54 0.000000611
## 3 HighSchoolGrad -0.583 0.472 -1.23 0.221glance(florida_m4)## # A tibble: 1 × 12
## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.471 0.455 20.8 28.5 0.00000000138 2 -297. 602. 611.
## # ℹ 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>library(AICcmodavg)
AIC(florida_m1, florida_m2, florida_m3, florida_m4)## df AIC
## florida_m1 4 627.1524
## florida_m2 4 602.4276
## florida_m3 5 603.6764
## florida_m4 4 601.8526library(modelsummary)##
## Attaching package: 'modelsummary'## The following object is masked from 'package:mosaic':
##
## msummarymodelsummary(list(florida_m1, florida_m2, florida_m3, florida_m4))| (1) | (2) | (3) | (4) | |
|---|---|---|---|---|
| (Intercept) | -46.109 | 39.972 | 59.715 | 59.118 |
| (24.972) | (16.354) | (28.590) | (28.365) | |
| Income | 1.031 | -0.791 | -0.383 | |
| (1.084) | (0.805) | (0.941) | ||
| HighSchoolGrad | 1.054 | -0.467 | -0.583 | |
| (0.573) | (0.554) | (0.472) | ||
| UrbanPop | 0.642 | 0.697 | 0.683 | |
| (0.111) | (0.129) | (0.123) | ||
| Num.Obs. | 67 | 67 | 67 | 67 |
| R2 | 0.229 | 0.467 | 0.473 | 0.471 |
| R2 Adj. | 0.205 | 0.450 | 0.448 | 0.455 |
| AIC | 627.2 | 602.4 | 603.7 | 601.9 |
| BIC | 636.0 | 611.2 | 614.7 | 610.7 |
| Log.Lik. | -309.576 | -297.214 | -296.838 | -296.926 |
| F | 9.500 | 28.022 | 18.834 | 28.539 |
| RMSE | 24.57 | 20.43 | 20.32 | 20.34 |
When running the simple regression, we can see that UrbanPop is the most influential predictor. The reason is because it has the most shared variance with Crime (45.88%) compared to the other variables. HighSchoolGrad could also be a somewhat influential predictor, with a shared variance of 21.8% with Crime.
When running a multiple regression, one model that seems to balance accuracy and simplicity would be the one with both UrbanPop and HighSchoolGrad as predictors for Crime. The AIC is the lowest out of the 4 multiple regression models (601.8526).
Communicate Your Findings
I would say that the best model for predicting crime rates would be the simple regression model with UrbanPop as the most influential predictor. This model explains 45.88% of the shared variance with the variable Crime. One recommendation for where the PD should focus its resources would be in Urban communities and possibly High Schools, to help steer/keep individuals on the right path. One limitation in my analysis would be how correlation doesn’t equal causation. This means that just because Crime and UrbanPop have a strong correlation when looking at which factors are correlated with Crime, doesn’t mean that UrbanPop causes Crime.