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I am wondering if I can use Chauvenet's criterion for a dataset of 240 measurements of one y variables in order to detect outliers. I assume that the ys have a nonlinear relationship in parameters with about 12 x-variables.

In general I did not quite understand on which y data the criterion is performed. Would you perform it on your complete set of y-variables, even if you assume a simple linear model with a small number of x-variables. I assumed that expected value and variance vary with the value of x, so I thought you would only perform it on a set of y variables which do not differ in x. Am I right?

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  • $\begingroup$ Short answer is Never. There is no infallible, single, simple rule of thumb that determines which data points should be rejected. Bad data points that are impossible require substantive knowledge to identify. More usually possible outliers can just be accommodated by working on a transformed scale or using a more suitable model. There is much more detailed advice on outliers in the many threads on this topic. $\endgroup$
    – Nick Cox
    Commented Feb 12, 2018 at 17:27

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Recall that Chauvenet's criterion is used in univariate statistics, so it wouldn't be applied in a regression example. The criterion was introduced in A Manual of Spherical and Practical Astronomy, printed 1863.

This begs the question, how are outliers detected in a regression model? The answer is through the diagnostics plots. If you are using R, I would suggest checking out RBloggers for examples.

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