- #1
headphones543
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Hi,
I have a problem that is giving me a headache. I have measured two angles that I believe to be related to one another, and they are (this is a data set where I have measured the angle from a datum to two features on a bone. There are 14 bones in the data set):
Angles to feature 1 (F1):
15.225
14.2318
9.4301
12.2947
14.8846
7.6533
9.0948
11.9725
4.2773
14.1819
8.841
17.1037
20.2373
13.4599
Angles to feature 2 (F2):
3.1227
9.4799
7.9047
13.4962
8.5454
24.2871
11.443
12.6693
21.5271
4.0733
5.0085
4.0101
5.4445
16.424
When I plot F1 vs F2 and do a linear correlation I get an r^2 = 0.47. Related, but not very strongly.
The thing is, I'm doing this because I have a bunch partial bone specimens and cannot define the datum, so in general I'm going to have the angle between feature 1 and feature 2, and am hoping to be able to get the position of the datum from this angle. So if I plot (F1-F2) vs F1 I get a much better correlation (r^2 = 0.74) and (F1-F2) vs F2 gets even better (r^2 = 0.9)!
What I don't understand is, how can a linear combination of the two be better than either one alone? I have added no information and the equations are not linearly independent. What am looking at in the plots with the difference?
I have attached plots of F1 vs F2, Diff vs F1 and Diff vs F2 with the regressions plotted.
Thanks for your help.
I have a problem that is giving me a headache. I have measured two angles that I believe to be related to one another, and they are (this is a data set where I have measured the angle from a datum to two features on a bone. There are 14 bones in the data set):
Angles to feature 1 (F1):
15.225
14.2318
9.4301
12.2947
14.8846
7.6533
9.0948
11.9725
4.2773
14.1819
8.841
17.1037
20.2373
13.4599
Angles to feature 2 (F2):
3.1227
9.4799
7.9047
13.4962
8.5454
24.2871
11.443
12.6693
21.5271
4.0733
5.0085
4.0101
5.4445
16.424
When I plot F1 vs F2 and do a linear correlation I get an r^2 = 0.47. Related, but not very strongly.
The thing is, I'm doing this because I have a bunch partial bone specimens and cannot define the datum, so in general I'm going to have the angle between feature 1 and feature 2, and am hoping to be able to get the position of the datum from this angle. So if I plot (F1-F2) vs F1 I get a much better correlation (r^2 = 0.74) and (F1-F2) vs F2 gets even better (r^2 = 0.9)!
What I don't understand is, how can a linear combination of the two be better than either one alone? I have added no information and the equations are not linearly independent. What am looking at in the plots with the difference?
I have attached plots of F1 vs F2, Diff vs F1 and Diff vs F2 with the regressions plotted.
Thanks for your help.