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I used step() in R to select a model. I found an data point with a high cook's distance and decided to remove it. After removing the outlier, should I used the current model or start again from the beginning and use step() again?

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I would be very wary of removing data points as outliers. You need to ask yourself why this data point is an outlier (data entry error or is it just very different from what the modeller expects). If it is the latter then removing it would seem dubious. You should try methods that are more robust to outliers instead.

If it is the former I would remove the data point and refit the model to the data without the outlier.

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    $\begingroup$ Excellent advice in my view, but you could add cross-references to many other threads here with other attitudes and approaches, e.g. work on transformed scale. $\endgroup$ – Nick Cox Sep 10 '17 at 7:28

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