Quiz 3 (10 minutes, 3 points):

Write code to

a) Take 100 points from a unif dist between -1 and 1, and call it x.

b) Make a y variable such that it is purely quadratic in x 
(i.e. y = x squared, without any noise).

c) Compute the correlation between x and y, and explain why it is near zero.

# a)
x = runif(100,-1,1)
# b)
y = x^2
# c)
cor(x,y)
# Because r measures linear association.

# Note that the correlation is nearly zero, even though 
plot(x,y)
# shows that x and y are highly correlated. The resolution to
# this "paradox" is, of course, that r measures linear correlation,
# i.e., the amount of scatter about a straight line (not a parabola)