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  "body": "\n## Summary\n\nAn errors-in-variables model is a regression model in which the regressors are measured with error, not only the response.\nIn that case [[ordinary least squares|YM708KHV2W]] on the observed regressors is biased and not [[consistent|0AS800VAYX]].\nIn the simple linear case the slope is pulled towards zero, an effect called attenuation or regression dilution.\nConsistent estimation needs extra information, such as the ratio of the error variances, repeated measurements, or [[instrumental variables|6ETK64HYK6]].\nDeming regression and total least squares are methods for such models.\n\n## Explanations\n\n### L1 human\n\nSuppose the true effect of a quantity $\\xi$ on $y$ has slope $2$, but $\\xi$ can only be measured with noise.\nThe noisy readings spread out more than the true values, and the extra spread is unrelated to $y$.\nThe fitted line therefore looks flatter than the true one.\nIf the measurement noise has the same variance as the true values, the least squares slope tends to $1$ instead of $2$.\n",
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