The relationship between the distance an object has fallen, d, and the length of time it has been falling, t, is d = 1/2 a x t2, where a is the acceleration due to gravity and is constant at the surface of the Earth. Clink the link below to see the plot of distance fallen vs. time.
Clearly the results are correlated -- they both increase together. But a straight line is not a good model of these data -- it will yield a positive correlation coefficient and, for short enough times, a significant one, but eventually the points will depart more and more from the line, and the correlation coefficient will cease to be significant. This does not mean the points are uncorrelated, just that they are not linearly related. A parabola, describing a relationship with d proportional to t2 is, as shown, a perfect fit.
|Squared Correlation Graph|