If we don’t have a model that tells us what degree it should be, or what the model should look like, we can use the coefficient of determination, r-squared. It doesn’t depend on the size of the data. If we can get R2 to zero, it means we can fit the data perfectly. If it’s closest to one, it means we cannot properly account to any of the variability in the data.

In a case like this, it would be easier to just pick the best choice, but there are multiple reasons to choose a model: one of them is to explain phenomena. It is possible that a 16-degree phenomena is not a good explanation for such phenomena.