An example of isotonic regression (solid red line) compared to linear regression on the same data, both fit to minimize the mean squared error. The free-form property of isotonic regression means the line can be steeper where the data are steeper; the isotonicity constraint means the line does not decrease.
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In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing (or non-increasing) everywhere, and lies as close to the observations as possible.
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