How, if at all, can one compare the "fit" of a simple linear vs. non-linear regression model to observed data?
I apologize if I didn't search long/hard enough for the answer, but I cannot find anything concrete.
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Perform cross-validation on each model on a development set to find the best hyper-parameters / accuracy estimate for each. Then check that the accuracy estimates are still valid on some held out data that you did not use during the model selection / parameter tuning phase.