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  "body": "\n## Summary\n\nThe coefficient of determination, written $R^2$, measures how much of the variation of a response is explained by a fitted regression model.\nIt compares the residual sum of squares with the total sum of squares around the mean.\nFor [[ordinary least squares|YM708KHV2W]] with an intercept, it lies between $0$ and $1$ and equals the squared correlation between the observed and the fitted values.\nIt is the most common summary of goodness of fit in [[linear regression|41FVC4P5JB]].\n\n## Explanations\n\n### L1 human\n\nImagine predicting each data point by the overall average; the squared errors add up to the total variation.\nA regression line usually does better, and $R^2$ is the share of that total variation that the line removes.\nAn $R^2$ of $0.9$ means the fitted model leaves only a tenth of the original variation unexplained.\nFor the points $(0,0)$, $(1,1)$, $(2,3)$, the least squares line gives $R^2 = 27/28$.\nA high $R^2$ does not prove that the model is correct or that one variable causes the other.\n",
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