# Playing with correlation
# Dennis E. Slice (c) 2012

# Clear the room
rm(list = ls())

# For instance,...
n=100

# Ask between plots
par(ask=T)

#  ====  CREATE A FUNCTION ====
cor_play <- function(r,n, mu1=0, sd1 = 1, mu2=0, sd2=1) {
   print("--------------")
   y1 = rnorm(n)
   yy = rnorm(n)
   y2 = y1*r + yy*sqrt(1-r*r)
   y1 = (y1*sd1) + mu1
   y2 = (y2*sd2) + mu2
   print("r, n, mu1, ds1, mu2, sd2")
   print(paste(r,n,mu1,sd1,mu2,sd2))
   print(cor.test(y1,y2))
   plot(y1,y2)
}
#  ================================
# Generate and plot  and compute r, ...
# y1,y2 ~ N(0,1); r=1.0, -1.0, 0, 0.3, -0.7
r_vals = c(1,-1,0,0.3,-0.7)
for (r in r_vals) cor_play(r,n)

# y1,y2 ~ N(0,0.2),N(0,2.3); r=1.0, 0, -0.7
r_vals = c(1,0,-0.7)
sd_vals = c(0.2,2.3)
for (r in r_vals) cor_play(r,n,sd1=sd_vals[1],sd2=sd_vals[2])


# y1,y2 ~ N(1,0.7),N(100,12.5); r=0.3
r_vals = c(1,0,-0.7)
mu_vals = c(1,100)
sd_vals = c(0.7,12.5)
for (r in r_vals) 
	cor_play( r,
			  n,
			  mu1=mu_vals[1], 
			  sd1=sd_vals[1],
			  mu2=mu_vals[2],
			  sd2=sd_vals[2])

# y1', y2' – subtract off means and divide by sd