You've learned that splitting your data into a training set and a test set is fundamental for evaluating how well your model generalizes to new, unseen data. We train the model on the training set and then use the test set to get an unbiased estimate of its performance.

However, relying on just one single train-test split has its own potential problems. Think about the random shuffling step we discussed. When you randomly divide your data, the specific data points that end up in the training set versus the test set can vary significantly just by chance.

Imagine you have a dataset, and you perform an 80/20 split.

Scenario 1: The "Lucky" Split: By pure chance, the 20% of data points allocated to the test set might be particularly "easy" examples for your model to predict. Maybe they are very similar to the majority of the training data, or they lack the tricky edge cases. If this happens, your evaluation metrics (like accuracy, MAE, or R-squared) calculated on this test set will look fantastic. You might conclude your model is performing exceptionally well.
Scenario 2: The "Unlucky" Split: Conversely, the random split might place a disproportionate number of the most difficult or unusual data points into the test set. These might be outliers or examples representing rare patterns that weren't well-represented in the 80% training data. In this case, your model will likely perform poorly on this specific test set, even if it learned the general patterns quite well. Your evaluation metrics will look disappointing, potentially leading you to discard a reasonably good model.

The core issue is variance. The performance estimate you get from a single train-test split can be highly dependent on which specific data points landed in the test set purely due to the randomness of the split. Your evaluation result might be overly optimistic or pessimistic, not because of the model's inherent quality, but because of the specific random sample chosen for testing.

Different random splits of the same dataset can lead to test sets with varying characteristics, potentially resulting in different performance evaluations for the same model.

So, while a single train-test split is far better than evaluating on the training data, it doesn't give you the most stable or reliable picture of your model's true generalization ability. The performance score you get might not be representative of how the model would perform on another random sample of unseen data.

This limitation leads us to more robust evaluation techniques. If one split can be lucky or unlucky, maybe we can average the results over multiple different splits? This is the core idea behind cross-validation, a technique we will introduce conceptually in the next section. It aims to provide a more stable and reliable estimate of model performance by repeating the splitting and evaluation process multiple times.