I am developing a physiological test using R that requires some parameters optimised. In comparing the new method against the existing method, the values of individual readings correlate in a linear way but are very heteroscedastic - the variance approximately proportional to the mean.
I would like to compare the effects of various parameter changes by examining the goodness-of-fit of the linear models compared with each other. Confidence intervals around the linear model parameters are not needed. Comparing R squareds does not seem appropriate given the heteroscedasticity. Would distance correlation or R squared after HCCM correction be appropriate ways to test if one method is superior to another ?
