This Demonstration considers an application of circular regression. Starting with a scatter plot of experimental data, we try to determine the center and radius of the circle that best fit the observations.[more]
The first application of least squares minimizes the objective function with center at and radius :
Since this represents the averaged distance of the observed points from the optimal circumference, it is referred to as a geometric fit.
The second objective function is referred to as an algebraic fit:
In the latter case, an expedient redefinition of the parameters reduces the problem to a linear regression.[less]
 N. Chernov, Circular and Linear Regression: Fitting Circles and Lines by Least Squares, Boca Raton: Taylor & Francis, 2010.