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  "body": "\n## Summary\n\nQuantile regression models a conditional [[quantile|0X60VE98HN]] of a response, such as the conditional median, as a function of covariates.\nWhere ordinary [[linear regression|41FVC4P5JB]] fits the conditional mean by least squares, quantile regression minimises an asymmetric absolute loss, the check function.\nFitting several quantile levels shows how the whole conditional distribution changes with the covariates, not only its centre.\nKoenker and Bassett introduced it in 1978, and the median case is robust to outliers in the response.\n\n## Explanations\n\n### L1 human\n\nThe usual regression line tells you the average weight of children at each age.\nQuantile regression can tell you instead the weight below which $90\\%$ of children of each age fall.\nIt does this by penalising points above the line nine times as much as points below it, so the line settles where $90\\%$ of the points lie below.\nWith equal penalties on both sides, it gives the median line, which a few extreme points cannot drag far.\n",
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