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## Author: Joshua M. Tebbs
## Date: 27 July 2016
## Update: 21 March 2024
## STAT 110 course notes: R Code Chapter 14
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# Example 14.1
# Page 138
# Manatee data
manatee = read.table("C:\\Users\\tebbs\\OneDrive - University of South Carolina\\Documents\\texfiles\\Classes\\USC\\stat110\\s24\\data\\manatees.txt",header=TRUE)
# Create variables
boats = manatee[,2]
manatees = manatee[,3]

# Histograms (Figure 14.1)
hist(boats,xlab="Number of boat registrations (in thousands)",ylab="Count",main="",col="lightblue")
hist(manatees,xlab="Number of manatees killed",ylab="Count",main="",col="lightblue")

# Line graphs (Figure 14.1)
boats.ts = ts(data=boats,start=1977,end=2018,frequency=1)
plot(boats.ts,ylab="Number of boat registrations (in thousands)",xlab="Year",type="o",pch=19,cex=0.75)
manatees.ts = ts(data=manatees,start=1977,end=2018,frequency=1)
plot(manatees.ts,ylab="Number of manatees killed",xlab="Year",type="o",pch=19,cex=0.75)

# Scatterplot (Figure 14.2)
plot(boats,manatees,xlab="Number of boat registrations (in thousands)",ylab="Number of manatees killed",pch=16)


# Example 14.2
# Page 141
# Florida FCAT data
FCAT.reading = c(165,157,164,162,162,164,162,165,163,161,169,172,172,174,174,170,181,180,178,175,181,183)
poverty = c(91.7,90.2,86.0,83.9,80.4,76.5,66.0,65.8,75.6,75.0,74.7,63.2,52.9,48.5,39.1,38.4,34.3,30.3,30.3,29.6,26.5,13.8)
# Scatterplot (Figure 14.3)
plot(poverty,FCAT.reading,xlab="Students below poverty level (%)",ylab="Average FCAT reading score",pch=16)


# Figure 14.4
# Page 144
# Each subfigure is created separately
# Upper left
x = rnorm(100,50,10)
y.strong = x + rnorm(100,0,1)
plot(x,y.strong,xlab="x",ylab="y",pch=16,cex.lab=1.5)
# Upper right
y.moderate = x + rnorm(100,0,10)
plot(x,y.moderate,xlab="x",ylab="y",pch=16,cex.lab=1.5)
# Lower left
y.weak = x + rnorm(100,0,25)
plot(x,y.weak,xlab="x",ylab="y",pch=16,cex.lab=1.5)
# Lower right
y.none = rnorm(100,0,1)
plot(x,y.none,xlab="x",ylab="y",pch=16,cex.lab=1.5)


# Figure 14.5
# Page 145
# STAT 110 exam data
scores = read.table("C:\\Users\\tebbs\\OneDrive - University of South Carolina\\Documents\\texfiles\\Classes\\USC\\stat110\\s24\\data\\examscores.txt",header=TRUE)
# Create variables
exam.1 = scores[,1]
exam.2 = scores[,2]
exam.3 = scores[,3]
final = scores[,4]
# Create average midterm score
midterm = (exam.1+exam.2+exam.3)/3
# Scatterplot 
plot(midterm,final,xlab="Average of three midterm scores",ylab="Final exam score",pch=16)


# Scatterplots with different correlations
# Page 147
# Each subfigure is created separately using the code below
rho = -0.5 # correlation
library(MASS) # must type this first
Sigma = matrix(c(1,rho,rho,1),2,2)
Sigma
data = mvrnorm(n = 200, rep(0,2), Sigma)
cor(data)
plot(data[,1],data[,2],xlab="x",ylab="y",pch=16,cex.lab=1.5,title(main="Correlation = -0.5",cex.main=1.5))


# Figure 14.6
# Page 149
# These are the same scatterplots in Figures 14.2 and 14.3.


# Figure 14.7
# Page 150
# Manatee data in Example 14.1
plot(boats,manatees,xlab="Number of boat registrations (in thousands)",ylab="Number of manatees killed",pch=16)
# Switch the roles of x and y
plot(manatees,boats,ylab="Number of boat registrations (in thousands)",xlab="Number of manatees killed",pch=16)
# Calculate correlations
cor(boats,manatees)
cor(manatees,boats)


# Figure 14.8
# Page 151
# Satisfaction and happiness data
hours = c(6,9,12,14,20,30,35,40,47,51,55,60,65)
satisfaction = c(14,28,50,70,80,89,94,90,75,59,44,27,18)
plot(hours,satisfaction,xlab="Number of hours worked per week",ylab="Satisfaction score",pch=16)

# Superimpose quadratic regression
hours.sq = hours^2
fit = lm(satisfaction~hours+hours.sq)
plot(hours,satisfaction,xlab="Number of hours worked per week",ylab="Satisfaction score",pch=16)
# Add red curve
curve(expr = fit$coefficients[1] + fit$coefficients[2]*x + fit$coefficients[3]*x^2,col="red",lty="solid",lwd=1.5,add=TRUE)

# Calculate correlation
cor(hours,satisfaction)


# Figure 14.9
# Page 152
# Effect of outliers
FCAT.reading = c(165,157,164,162,162,164,162,165,163,161,169,172,172,174,174,170,181,180,178,175,181,183)
# The "9.2" (second observation) was changed from "90.2" in the original data set (poverty)
poverty = c(91.7,9.2,86.0,83.9,80.4,76.5,66.0,65.8,75.6,75.0,74.7,63.2,52.9,48.5,39.1,38.4,34.3,30.3,30.3,29.6,26.5,13.8)
# Construct scatterplot (with and without outlier)
# Left; same as Figure 14.3
# Right
plot(poverty,FCAT.reading,xlab="Students below poverty level (%)",ylab="Average FCAT reading score",pch=16)