Which data set, when given more data, results in more stable predictive models?

The training data set is essential for developing predictive models because it provides the foundational information that the model uses to learn patterns and relationships within the data. As more data is added to the training set, the model benefits from increased exposure to various scenarios and examples, which typically leads to better generalization.

When a training set is expanded, the model can better capture the underlying relationships in the data rather than memorizing specific instances. This enhancement results in more stable predictive models because they are less likely to be affected by noise or outliers in the data and can yield more robust predictions on unseen instances.

In contrast, while the test and validation sets are critical for evaluating model performance, they do not directly contribute to the model's ability to learn. Instead, they are used to assess how well the model generalizes to new data. Therefore, increasing the amount of data in the test or validation sets would not lead to the same improvements in the stability of predictive models.