Overfitting and correlations in model fitting with separation ratios

Abstract

The $r_{01}$ and $r_{10}$ separation ratios are not independent so combing them into a single series $r_{010}$ is overfitting the data, this can lead to almost singular covariance matrices with very large condition numbers, and hence to spurious results when comparing models and observations. Since the $r_{02}$ ratios are strongly correlated with $r_{10}$ and $r_{01}$ ratios, they should be combined into a single series $r_{102}$ (or $r_{012}$), which are not overfitted, and models and observation compared using the covariance matrix $cov_{102}$ (or $cov_{012}$) of the combined set. I illustrate these points by comparing the revised Legacy Project data with my results on the 10 Kepler stars in common.