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What are some options for dealing with outliers?

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As outliers are observed data points, the very first step that should be taken is to understand what resulted in the outlier. If it is an issue with the data generation process, or something like measurement error, that is something that needs to be addressed before modeling on the data. If there is a sufficiently large sample size, and there is nothing systematic about the existence of the outliers, it might be possible to remove them from the dataset; however, this should be done with caution. If the sample size is not so large, another option is to trim the values of the outliers to more reasonable values so that they do not reside so far away from the concentration of data that they have an undue effect on the regression line. Finally, using quantile regression, which models a quantile such as the median rather than the mean of the data, is more robust to outliers than linear regression and might be of interest depending on the application. 

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