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I am trying to calculate a regression curve for a dataset, where my independent variable ranges from 0 to 1, but 0 is equivalent to 1. In other words, my independent variable loops around. Therefore, I would expect the regression curve at 0.1 to be heavily influenced by the data at 0.9, unlike a normal regression curve. Ideally I'd like to use a LOESS type of method, but I'm open to anything at the moment that can deal with this problem. I'm at a complete loss as to how to achieve this. Can anyone point me in the direction of a technique that I need? I understand that there is a whole sub-field of statistics called 'circular statistics', although I'm not sure if my problem falls into the 'circular' category.

Any advice or pointers would be appreciated. I can work with MATLAB (ideally), or R.

CaptainProg
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  • Some other relevant threads:L https://stats.stackexchange.com/questions/148380/use-of-circular-predictors-in-linear-regression https://stats.stackexchange.com/questions/203103/test-of-association-for-a-normally-distributed-dv-by-directional-independent-var Your predictor $x \in [0,1]$ can be expressed as $\sin(2 \pi x), \cos(2 \pi x), \sin(4 \pi x), \cos(4 \pi x), \dots$. Ironically, or otherwise, this technique is often **not** covered in texts on circular statistics. A further tutorial is accessible at https://www.stata-journal.com/sjpdf.html?articlenum=st0116 – Nick Cox Nov 28 '18 at 07:41

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