##############################
#
# Script: assignment03a.R
#   Answers to the third 
#   homework assignment
#
##############################


# Preamble

library(RFS)
gd <- read.csv("http://courses.kvasaheim.com/pols6123/data/gdpcap.csv")
names(gd)
attach(gd)



#####
# Problem 1

summary(gd)
sd(gd)


#####
# Problem 2

cor(gd)  # Missing values

# Which ones are missing?
del <- which(is.na(democracy))

#let's remove them from consideration
cor(gd[-del,])

# Correlation tests
cor.test(gdpcap,hig)
cor.test(democracy[-del],hig[-del])
cor.test(democracy[-del],gdpcap[-del])


# Alternatively
summary(lm(hig~democracy))
0.1986^0.5
summary(lm(gdpcap~democracy))
0.02294^0.5



#####
# Problem 3

png("boxplot3.png", height=4,width=6,units="in",res=600)
boxplot(gdpcap[region=="Africa"], horizontal=TRUE)
dev.off()

shapiro.test(gdpcap[region=="Africa"])

t.test(gdpcap[region=="Africa"], mu=5000)        # Wrong!   (why?)
wilcox.test(gdpcap[region=="Africa"], mu=5000)   # Correct! (why?)



#####
# Problem 4 (and 5) =)

png("boxplot4.png", height=5,width=6,units="in",res=600)
boxplot(gdpcap[region=="Africa"], gdpcap[region=="Latin America"])      # Ugly!
dev.off()

shapiro.test(gdpcap[region=="Africa"])

t.test(gdpcap[region=="Africa"], gdpcap[region=="Latin America"])       # Wrong!
wilcox.test(gdpcap[region=="Africa"], gdpcap[region=="Latin America"])  # Correct!



#####
# Problem 6

model1 <- lm(gdpcap ~ hig + region)
summary.aov(model1)
summary(model1)