Rich Ulrich <[EMAIL PROTECTED]> wrote in news:[EMAIL PROTECTED]:
> How do *you* describe the correlation of (say) > height with weight of a set of objects, where > every object is exactly the same height? > > - well, there is no "co"- variation, so you might > settle for zero. But I think that depends on how > limited your needs are. It's rather odd that "intuitively" to me, it depends on whether or not you treat one variable as "independent" and another as "dependent." If I look at a scatterplot where all the points are arrayed along a horizontal line, my first thought is "zero correlation" whereas if I see one where all the points fall on a vertical line, my first thought is "not enough information to tell whether there is a correlation." But mathematically, that's nonsensical; zero correlation implies a roughly circular pattern of points (I like Stephen Jay Gould's heuristic that correlation measures the "skinniness" of a scatterplot), and it's rather obvious that if you simply interchange axes, there's no difference between the two situations. I think this is a case where we're encountering what Sir Francis Bacon called an "idol," a prejudice of thought that distorts our view of reality. We want to believe that correlation is defined for any pair of random variables, but in fact it's meaningless if one of those RVs has all its density concentrated at a single point. We somehow expect that because we call it a random "variable" it has to *vary*, but the definition of a random variable is merely "a function whose domain is a probability space" and constants meet that definition. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
