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If you have a number of variables you're interested in and want to perform linear regression, is there a clear preference between:

Method A.

  1. Perform variable selection techniques (e.g. using stepwise AIC/BIC)
  2. Remedy multicollinearity

Method B.

  1. Remedy multicollinearity
  2. Perform variable selection techniques
  3. (Potentially remedy multicollinearity again if necessary)

Note: The technique I'm familiar with for 'remedying' multicollinearity is removing one variable at a time (if necessary) by looking at variance inflation factors.

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In linear regression, multi-collinearity problem leads to unreliable coefficients and corresponding p-values. Therefore if p-values are used to do step-wise variable selection/elimination, then you have to remedy multi-collinearity first before taking the decision to select or eliminate a variable.

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