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I've performed an non linear regression with 3 variables and 5 parameters, using Wolfram Mathematica. Now I want to detect the outliers that are far from 2*(standard deviation) of my function. I've done a little software that investigate the outliers. But now I'm wondering if this technique has got a statistical basis. Can you help me to find this basis or some bibliography or if I can perform a non linear regression with mathematica bearing in mind the outliers? If you want I can post an example of my funcion. Thanks in advance.

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    $\begingroup$ Yes, it has a statistical basis: and that basis shows your technique is not a valid way to identify outliers! If you use Mathematica's NonlinearModelFit procedure, it will give you influence measures, prediction confidence intervals, prediction standard errors, and standardized and studentized residuals: all of these are useful for identifying outliers (of various types). $\endgroup$ – whuber Mar 26 '13 at 14:36
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you should fit your linear regression first, then use several measures to detect the outliers. if you fit with classic methods such as least square, will face with masking and swamping effect.

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    $\begingroup$ Would you please clarify the distinction you are making between "linear regression" and "least square"? (To most people, the default method of linear regression is that of ordinary least squares.) And, if you would like this answer to have any real informative content, please elaborate on what your "several measures" are and explain what you mean by "masking" and "swamping." $\endgroup$ – whuber Mar 26 '13 at 14:32

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