es3307 wk4 tutorial

Load Libraries

library(tidyverse)

Group 4 (USArrests) Load the ‘USArrests’ data set using this code:

{data(USArrests)}

Describe and summarize your assigned data set. Which states have the highest murder and assault rates? Is there a relationship between urban population percentage and crime rates? Graph your data.

Load data

data(USArrests)

Describe and summarise

head(USArrests)

##            Murder Assault UrbanPop Rape
## Alabama      13.2     236       58 21.2
## Alaska       10.0     263       48 44.5
## Arizona       8.1     294       80 31.0
## Arkansas      8.8     190       50 19.5
## California    9.0     276       91 40.6
## Colorado      7.9     204       78 38.7

str(USArrests)

## 'data.frame':    50 obs. of  4 variables:
##  $ Murder  : num  13.2 10 8.1 8.8 9 7.9 3.3 5.9 15.4 17.4 ...
##  $ Assault : int  236 263 294 190 276 204 110 238 335 211 ...
##  $ UrbanPop: int  58 48 80 50 91 78 77 72 80 60 ...
##  $ Rape    : num  21.2 44.5 31 19.5 40.6 38.7 11.1 15.8 31.9 25.8 ...

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

hist(USArrests$Murder)

hist(USArrests$Assault)

hist(USArrests$UrbanPop)

hist(USArrests$Rape)

USArrests$State  <- rownames(USArrests)

As we can see from the histograms

• only Urban Population seems to be normally distributed

• Rape seems to be right skewed

• Murder and Assault is not normally distributed

Tried logging the data but it does not make it normal

Which states have the highest murder and assault rates?

Top 10 states for murder

# Murder
USArrests %>%
  select(State, Murder) %>%
  arrange(desc(Murder)) %>%
  head(10)

##                         State Murder
## Georgia               Georgia   17.4
## Mississippi       Mississippi   16.1
## Florida               Florida   15.4
## Louisiana           Louisiana   15.4
## South Carolina South Carolina   14.4
## Alabama               Alabama   13.2
## Tennessee           Tennessee   13.2
## North Carolina North Carolina   13.0
## Texas                   Texas   12.7
## Nevada                 Nevada   12.2

Top 10 states for assault

# Assault
USArrests %>%
  select(State, Assault) %>%
  arrange(desc(Assault)) %>%
  head(10)

##                         State Assault
## North Carolina North Carolina     337
## Florida               Florida     335
## Maryland             Maryland     300
## Arizona               Arizona     294
## New Mexico         New Mexico     285
## South Carolina South Carolina     279
## California         California     276
## Alaska                 Alaska     263
## Mississippi       Mississippi     259
## Michigan             Michigan     255

Is there a relationship between urban population percentage and crime rates? Graph your data.

Urban Population affects murder/rape/assault, but murder/assault/rape does not affect urban population. There is a clear y (crime rate) and x (urban population rate). Thus, we run linear regression and not correlation test to determine if there is a relationship.

# Murder
fit <- lm(Murder ~ UrbanPop, data = USArrests)

r2_val <- summary(fit)$r.squared
p_val  <- summary(fit)$coefficients[2, 4]
df_res <- df.residual(fit)

label_text <- paste0("R² = ", round(r2_val, 3), 
                     ", p = ", round(p_val, 3))

ggplot(USArrests, aes(x = UrbanPop, y = Murder)) +
  geom_point(alpha = 0.6, size = 1.5) +
  geom_smooth(method = "lm", color = "black", se = FALSE) +
  labs(x = "Urban population percentage (%)", y = "Murder (per 100000)", subtitle = label_text) +
  theme_classic()

## `geom_smooth()` using formula = 'y ~ x'

# Assault
fit <- lm(Assault ~ UrbanPop, data = USArrests)

r2_val <- summary(fit)$r.squared
p_val  <- summary(fit)$coefficients[2, 4]

label_text <- paste0("R² = ", round(r2_val, 3), 
                     ", p = ", round(p_val, 3))

ggplot(USArrests, aes(x = UrbanPop, y = Assault)) +
  geom_point(alpha = 0.6, size = 1.5) +
  geom_smooth(method = "lm", color = "black", se = FALSE) +
  labs(x = "Urban population percentage (%)", y = "Assault (per 100000)", subtitle = label_text) +
  theme_classic()

## `geom_smooth()` using formula = 'y ~ x'

# Rape
fit <- lm(Rape ~ UrbanPop, data = USArrests)

r2_val <- summary(fit)$r.squared
p_val  <- summary(fit)$coefficients[2, 4]

label_text <- paste0("R² = ", round(r2_val, 3), 
                     ", p = ", round(p_val, 3))

ggplot(USArrests, aes(x = UrbanPop, y = Rape)) +
  geom_point(alpha = 0.6, size = 1.5) + 
  geom_smooth(method = "lm", color = "black", se = FALSE) +
  labs(x = "Urban population percentage (%)", y = "Rape (per 100000)", subtitle = label_text) +
  theme_classic()

## `geom_smooth()` using formula = 'y ~ x'

R-squared values for all three are low (<0.5). Best fit line does not explain the data well. Relationship is not statistically significant for murder and assault (p>0.05), but is statistically significant for rape (p<0.05).