IBM Data Science Practice Test

Which statistical method requires the fitted line to be non-decreasing?

1. Linear regression

2. Isotonic regression

3. Logistic regression

4. Multiple regression

The correct answer is: Isotonic regression

The method that requires the fitted line to be non-decreasing is isotonic regression. This type of regression is particularly useful in situations where the relationship between the independent and dependent variables is expected to be monotonic but not necessarily linear. In isotonic regression, the fitted values must be arranged such that they do not decrease as the input values increase, which aligns with the requirement for a non-decreasing relationship. In contrast, linear regression allows for both increases and decreases in the fitted line, depending on the underlying data; it tries to fit the best linear model without monotonic constraints. Logistic regression focuses on modeling binary outcomes and does not concern itself with the nature of the continuous input-output relationship in terms of monotonicity. Multiple regression, similar to linear regression, can model various types of relationships without the specific requirement of being non-decreasing. Therefore, isotonic regression stands out because it explicitly imposes the monotonicity condition, making it the correct choice for this question.