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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 ?

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    $\begingroup$ So to confirm, you are asking about how to compare model fit when the models compared have heteroscedastic errors? $\endgroup$ – Jeromy Anglim Jul 31 '12 at 5:54
  • $\begingroup$ yes - were it not for the heteroscedasticity I would be comparing r squareds or correlation coefficients $\endgroup$ – Marc Sarossy Jul 31 '12 at 8:01

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