Linear Regression

BEFORE TRANSFORMATION

## Extract crime rate variables and violence rates
crimeClean <- read.csv(file = "crimeClean.csv", header = TRUE, row.names = 1)
# colnames(crimeClean)
subs <- c(106, 108, 110, 112, 121, 114, 116, 118, 120, 122)
crimeRates <- crimeClean[, subs]
colnames(crimeRates) <- c("Murder", "Rape", "Robbery", "Assault", "All Violent", 
    "Burglary", "Larceny", "AutoTheft", "Arson", "Non Violent")
violenceRates <- crimeRates[, 1:5]

## Look at Violent Crime Variables
source("classDensity.r")
source("classEda.r")
library(car)

# Make better labels
lab1 <- colnames(violenceRates)
lab1[5] <- "All Violent Crimes"

# loop through the variables
for (i in 1:5) {
    classEda(violenceRates[, i], lab1 = lab1[i], units = "Rate per 100,000")
}

AFTER TRANSFORMATION

for (i in 1:5) {

    classEda(violenceRates[, i]^0.02, lab1 = lab1[i], lab2 = "Raised to the .02 Power", 
        units = "Rate per 100,000 **.02")
}

CORRELATION PLOT

round(cor(violenceRates), 2)

##             Murder Rape Robbery Assault All Violent
## Murder        1.00 0.43    0.67    0.56        0.68
## Rape          0.43 1.00    0.45    0.51        0.58
## Robbery       0.67 0.45    1.00    0.62        0.84
## Assault       0.56 0.51    0.62    1.00        0.95
## All Violent   0.68 0.58    0.84    0.95        1.00

corMat <- cor(crimeRates)
distMat <- 1 - abs(corMat)
xloc <- cmdscale(distMat, k = 1)
ord <- order(xloc)
xloc[ord, 1]

##     Larceny        Rape Non Violent    Burglary     Assault       Arson 
##    -0.35584    -0.20322    -0.17547    -0.08668     0.03242     0.05243 
## All Violent     Robbery      Murder   AutoTheft 
##     0.08622     0.20170     0.21523     0.23321

corMatOrd <- corMat[ord, ord]

source("panelCorrgram.r")
library(lattice)
library(grid)
library(ellipse)

## 
## Attaching package: 'ellipse'
## 
## The following object is masked from 'package:car':
## 
##     ellipse

levelplot(corMatOrd, at = do.breaks(c(-1.01, 1.01), 20), xlab = NULL, ylab = NULL, 
    colorkey = list(space = "top"), scales = list(x = list(rot = 90)), panel = panel.corrgram, 
    label = TRUE)

levelplot(corMatOrd, xlab = NULL, ylab = NULL, at = do.breaks(c(-1.01, 1.01), 
    100), panel = panel.corrgram.2, scales = list(x = list(rot = 90)), colorkey = list(space = "top"), 
    col.regions = colorRampPalette(c("red", "white", "blue")))

Scatterplot matrices and hexagon binning

## Run
pairs(violenceRates, main = "Scatterplot Matrix", gap = 0, las = 1, row1attop = FALSE)

library(lattice)
library(hexbin)

splom(violenceRates, cex.labels = 0.2, pscale = 0, trans = function(x) x^0.5, 
    panel = panel.hexbinplot)

Scatterplot matrix with smoothes

splom(violenceRates, main = "Rates per 100000", lwd = 2, col.line = "red", pscale = 0, 
    type = c("p", "g", "smooth"))

Regression diagnostics after transformation

lm2 <- lm(ViolentCrimesPerPop^0.02 ~ ., data = crimeRegLog)
plot(lm2)

Stepwise regression variable removal

plot(lm3)

Looking at their univariate distributions

tmp <- lm3$terms
termLab <- attr(tmp, which = "term.labels")
for (i in 1:length(termLab)) {
    par(ask = TRUE)
    classEda(crimeRegLog[, termLab[i]], lab1 = termLab[i])
}