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Overfitting on the training dataset is a common challenge in predictive modeling because it occurs when a model learns not only the underlying patterns in the training data but also the noise or random fluctuations associated with it. This leads to a model that performs exceptionally well on the training dataset but fails to generalize to unseen data, resulting in poor predictive performance.

When a model is overfitted, it essentially memorizes the training data instead of relying on the general trends that are likely to occur in new data. This can happen when there are too many parameters relative to the amount of training data, or when the model is overly complex. Consequently, the model's accuracy diminishes significantly when applied to test data, indicating that it cannot effectively make predictions beyond the dataset it was trained on.

Common strategies to prevent overfitting include using simpler models, employing regularization techniques, and implementing cross-validation to ensure robust model performance across different datasets. These methods help to enhance the model's ability to generalize and improve its predictive power on new data.