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I am working with a data set and trying to fit a model to it. I transformed, the data and satisfied the assumptions of multiple linear regression. After doing this using regsubsets() in r and backward and forward regression I found the best model, finally I tested for interactions after all this and found that there were interactions that should be included in the model, after including these however there is now a violation of normality, should I transform the data from this day forth or reapply a model selection process using backward selection or forward selection and regsubsets. Lastly is there a specific order of operations that should be used when fitted a regression model?

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Sorry, but I think there are some more fundamental issues:

  1. You should not use forward, backward or similar methods to select variables. The output is wrong. (p values are too low, parameter estimates are biased away from 0, standard errors are too small). In addition, these methods prevent you from thinking and can often yield nonsensical models. This has been discussed a lot both here and elsewhere.

  2. Rather than transform your data to fit a model, I think you should use a model that fits your data. Two suggestions are quantile regression and robust regression. These make no assumptions about the distribution of the residuals.

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    $\begingroup$ Hi Peter I agree with you whole heartedly, (I have read some of your statements and work on the subject outside of StackExchange) however I am not able to apply other methods, I am working on a project for a linear regression course that requires the use of these methods. Assuming that I am forced to use erroneous methods, is there anyway to make the best of the situation? $\endgroup$ Jun 10, 2020 at 0:11
  • $\begingroup$ I have seen some evidence that backwards is less bad than forward or stepwise. $\endgroup$
    – Peter Flom
    Jun 11, 2020 at 12:03

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