y = A * sin ( (2π/31) x + c) + μ,

where μ is the mean of all 31 values (I don't know how to make an x-bar symbol), and A = x

_{max}- x

_{min}. (c, which determines the phase shift (-31c/2π), is my variable which I am adjusting to find the best fit.)

My problem is trying to objectively compare how well the model fit different groups of data. I need a correlation coefficient, but R

^{2}is only meaningful for linear regression.

I tried taking the arcsine of both my data and my model, in order to get a linear model, but I haven't gotten this to work, or at least to provide me with an R

^{2}value that makes sense.

Can someone help, please?