Wednesday, November 28, 2012
Correlation coefficients as angles
Harry Altman has an interesting piece over at Less Wrong suggesting that it makes more sense to think of correlation coefficients as angles. To many people a correlation coefficient is nothing more than a number between -1 and 1 which shows in some easy to quantify but hard to intuit way of how related two variables are. Harry's suggestion gives a useful way of thinking about them and is worth a read.
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Maybe it's just my research area, but I'm more comfortable thinking about the dot product of (unit) vectors than the angle between them. 0 is orthogonal, > 0 they point in the same direction, < 0 in the opposite direction. 0 makes more sense to me as the pivot than \pi/2.
Sure, if you're used to thinking about dot products of vectors that way. My point was just to note that this is an inner product (well, almost) in the first place and thus that you can think about it geometrically. If you don't need to take the inverse cosine to see it, then great. But regardless of which way you do it, I feel like the geometric viewpoint is underemphasized.
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