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Aug 2, 2015 at 21:04 comment added meh imho, Paul Teetor gives a superb explanation of what is going on in, for example quanttrader.info/public/betterHedgeRatios.pdf . He is interested in 'spread trades' but the explanation he gives is universal and excellent. As others have said, the point is that ols minimizes 'x distance' which can be very different from 'y distance' particularly if the slope of the regression line is very close to zero.
Dec 9, 2010 at 15:38 vote accept dsimcha
Mar 24, 2010 at 14:05 comment added dsimcha Right. I was aware in the back of my mind that vertical distance is what's used in regression and that the reason for this is that you the interpretation of a regression is that it gives you the best possible predictor of Y given X (minimum vertical distance) assuming the relevant assumptions are met. However, for some reason I kept visualizing the problem as using perpendicular distance.
Mar 24, 2010 at 2:50 history answered JBL CC BY-SA 2.5