# Associations between variables
# Dennis E. Slice (c) 2012

# Clean house
rm(list = ls())

# Pause between plots
par(ask=T)

# Load data
X = read.table("16_criminal_cambridge.RData")
head(X)
dim(X)

# Extract the criminals
X.criminal = subset(X, source == "criminal")
head(X.criminal)
dim(X.criminal)

# Extract height and middle finger length
Y = X.criminal[, 2:3]
head(Y)

# Put into separate variables for easier manipulation
h = Y[, 1]
l = Y[, 2]

# Plot l v. h
plot(h, l)

# Compute r
print(cor(l, h))
print(cor(h, l))

# Test r
print(cor.test(l, h))

#Generates benign error msg.
stop()

# Note, ?cov()
cov(l, h)
# Recall formula for cov, cor
cov(l, h)/sqrt(var(l) * var(h))
cor(l,h)

# Standardize h, l
# Subtract mean
h.dev = h - mean(h)
l.dev = l - mean(l)
# Divide by standard deviation
h.prime = h.dev/sd(h)
l.prime = l.dev/sd(l)

# Plot
plot(h.prime,l.prime)

# Compute cor from standardized variables
# Sum of products
scp = sum(h.prime*l.prime)
# divide by n-1
r.direct = scp/length(h.prime-1)
print(r.direct)
# Compare
cor.test(h,l)
cor.test(h.prime,l.prime)