Which statements are true regarding variance and bias in statistical learning methods?

The correct answer is based on understanding how bias and variance behave in relation to model flexibility in statistical learning methods.

When we consider the relationship between variance and bias, we often discuss the bias-variance tradeoff. Variance refers to the model's sensitivity to fluctuations in the training data, while bias indicates the error introduced by approximating a real-world problem, which may be inherently complex, by a simplified model. The first statement highlights a misconception about their relationship. A more nuanced view is that variance and bias do not have a straightforward inversely proportional relationship; increasing model flexibility usually decreases bias but increases variance.

The second statement accurately describes a fundamental aspect of statistical modeling. As we make a model less flexible, we often impose stronger assumptions on the data (e.g., linear models compared to more flexible ones like polynomials). This greater rigidity leads to a less accurate approximation of the underlying data structure, resulting in an increase in squared bias.

While the first statement does not hold true, the second one does, indicating that, although both statements cannot be true at the same time, the answer indicating that both statements are true is not correct. Thus, the correct conclusion is that the second statement stands valid while the first does not, emphasizing the model complexity