1Cademy - How do extra predictors and regularization affect bias and variance?

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When Increasing Capacity Helps One Error and Hurts the Other

Essay

How do extra predictors and regularization affect bias and variance?

Question: A team is building a model to estimate used-car prices. They can either add more input variables, such as mileage, year, and engine size, or apply stronger L2 regularization. Explain how each choice usually changes bias and variance.

Sample answer: Adding more useful predictors usually makes the model more flexible, so it can fit the training data more closely and often lowers bias. However, that extra flexibility can make the model more sensitive to the particular sample it was trained on, which can increase variance. Stronger regularization works in the opposite direction: it constrains the model, which usually lowers variance but may raise bias because the model becomes less able to fit the training data perfectly.

Key points:

Adding predictors often reduces bias and can increase variance.
Increasing regularization often reduces variance and can increase bias.
The tradeoff is that reducing one kind of error often makes the other kind worse.

Rubric: The response should explain that adding features tends to reduce bias while increasing variance, and that stronger regularization tends to reduce variance while increasing bias. It should clearly describe the tradeoff between the two error sources.

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Updated 2026-08-12

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