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I have a typical linear regression model:
Y = B0 + B1*X1 + B2*X2

where B0, B1 and B2 are the regression coefficients which I solve for.

Before I do any regression modeling, I standardize the predictor variables X1 and X2. I also standardize the dependent(outcome) variable Y.

X1_standardized = (X1 - X1_mean) / X1_std
X2_standardized = (X2 - X2_mean) / X2_std
Y_standardized = (y - y_mean) / y_std

I would like to use the standardized values for my regression, however, to improve interpretation, I would like to revert (or de-standardize) the beta coefficients after solving for them.

How can I do this?

user121
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  • For a simple linear regression like this, there really isn't any advantage to pre-standardizing this way. Just don't pre-standardize and you will get coefficients with easily interpretable values. – EdM Nov 06 '17 at 16:39
  • @EdM I have found that the prediction on unseen ('hold out sample') data varies when I standardize and do not standardize. Any reason for this? – user121 Nov 06 '17 at 16:43
  • Standardization will differ from sample to sample as both the observed mean and standard deviation will differ from sample to sample. That is yet another reason NOT to standardize in simple linear regression like this. – EdM Nov 06 '17 at 17:04

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