Angular speed of rotation of received IQ samples

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I would like to find the speed of rotation of received IQ samples caused by a carrier frequency offset. The plot below shows 50 samples at a time. I have tried linear regression on the points but the model becomes undefined for angles close to 90 (should have realized this before trying). After that I tried converting the data to polar coordinates but am not sure how to perform regression on polar data. I would appreciate being pointed in the right direction to solve this problem!

IQ samples over time