:

 x y

 0 0
 1 1
 -1 1
 2 4
 -2 4

Notice that the y-value of each point is the square of its x-
value. Thus the y-value of a point is completely determined by
its x-value.  If correlation measured association in general, the
correlation coefficient of this scatter diagram would have to
reflect this perfect association. It would have to have a value
of -1 or 1.  Instead, the value of the correlation coefficient is
equal to

 a.  -0.5

 b.    0

 c.   0.5

 d.  -0.75
 
 e.   0.75