Only if you don't have a complexity penalty in your fit. This is a model selection problem and you should have a prior on the structure of the model that leads

Only if you don't have a complexity penalty in your fit. This is a model selection problem and you should have a prior on the structure of the model that leads to something like the BIC. Curve fitting is hard. The elimination of epicycles was due to Tyco Brahe collecting more data and a lower complexity model being proposed to explain the data.