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  "body": "\n## Summary\n\nLocal regression estimates a regression function $m(x) = E[Y \\mid X = x]$ by fitting a low-degree polynomial near each point $x$.\nThe fit at $x$ is a [[weighted least squares|H5CGZHBR58]] fit.\nData points close to $x$ get large weights, and distant points get small or zero weights.\nIt needs no global formula for $m$, so it is a basic tool of [[nonparametric statistics|VFAJ1EG3X5]].\nThe methods LOESS and LOWESS are popular versions of it.\n\n## Explanations\n\n### L1 human\n\nImagine a cloud of points that follows a curved trend.\nA single straight line cannot follow the curve, but over a short window the curve looks almost straight.\nSo at each point $x$ one draws a line through the nearby data only, and keeps the height of that line at $x$.\nSliding the window along the axis traces a smooth curve through the cloud.\nFor example, with a window of width $1$ around $x = 3$, only data with $X$ between $2$ and $4$ matter for the estimate at $3$.\n",
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