I have two variables: ordering & length. The former measures the ordering of a sequence (i.e. all permutations of A-B-C), and the former is the length of the sequence (i.e. A-B-C has a length of 3). These are highly correlated, and I want to normalize the ordering measure by length. I was expecting this normalization to completely eradicate the correlation - but it doesn't. How can this be the case?
id order length order/length X1 4 3 1.333333333 X33 2 1 2 X566 44 6 7.333333333 X681 4 2 2 X682 46 6 7.666666667 X80 2 1 2 correlation before normalization: 0.958 correlation AFTER normalization: 0.610
The correlation has been reduced, but the variables are still highly correlated. My ambition was to partial out the component of "order" that is separate from "length", but it doesn't seem like I'm achieving that here. How can I do this? Where has my thinking gone wrong?