What distinguishes isotonic regression from linear regression?

Isotonic regression is characterized by its requirement for the fitted line to be non-decreasing. This means that it can only create a model where the value of the dependent variable does not decrease as the value of the independent variable increases, allowing it to fit data that has a monotonic relationship. This distinctly contrasts with traditional linear regression, which does not impose any such restriction and can fit both increasing and decreasing trends.

The aspect of isotonic regression being non-decreasing is particularly useful in situations where the expected relationship between variables should be ordered, such as in cumulative probability scenarios or when modeling situations where a logical order exists among values. Therefore, this unique feature of isotonic regression is what clearly distinguishes it from linear regression.