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  "body": "\n## Summary\n\nIsotonic regression fits a non-decreasing sequence to data by [[least squares|0BYTQ4X1HC]].\nIt is used when a response is known to increase with a covariate, as for dose and response.\nNo formula for the trend is assumed.\nThe fit is the projection of the data onto a closed convex cone, so it exists and is unique.\nIt can be computed quickly by the pool adjacent violators algorithm.\n\n## Explanations\n\n### L1 human\n\nSuppose a measurement should grow with the dose, but noise makes some values go down.\nIsotonic regression finds the staircase that never goes down and stays as close as possible to the data.\nWhenever a value is higher than the next one, the two merge into a block that takes their average.\nBlocks keep merging in this way until no drop remains.\nFor the data $1, 3, 2$, the drop from $3$ to $2$ is replaced by $2.5, 2.5$, giving $1, 2.5, 2.5$.\n",
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