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  "body": "\n## Summary\n\nThe partial correlation of two random variables given some control variables is a [[correlation|0DNN9B6Q2F]].\nIt is the correlation that remains after the linear effect of the controls is removed from both variables.\nIt separates a direct linear association from one that only passes through the controls.\nFor jointly normal variables it is zero exactly when the two variables are [[conditionally independent|0THJ7416DX]] given the controls.\nThis makes it the basic tool of Gaussian [[graphical models|Q3FQAD1BXG]].\n\n## Explanations\n\n### L1 human\n\nIce cream sales and sunburn cases rise and fall together, but both follow the temperature.\nTo see whether they are linked beyond the temperature, predict each one from the temperature by a straight line and keep only the leftover parts.\nThe partial correlation is the correlation of these two leftovers.\nIf $X = Z + U$ and $Y = Z + V$ with $Z, U, V$ uncorrelated, then $X$ and $Y$ are correlated, but their partial correlation given $Z$ is $0$.\n",
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