I recently performed a multiple linear regression using a standardized set of data, and I was wondering if it possible to convert the standardized coefficients from the regression into usable unstandardized coefficients. I found and attempted to implement the method found here: https://www3.nd.edu/~rwilliam/stats1/x92.pdf

but I got significantly different (and very wrong) results compared to what I got using the standardized coefficients and standardized data. All I did was convert each coefficient by multiplying by the ratio of the standard deviations of y and the corresponding x. To calculate the results, I then multiplied each new unstandardized coefficient by each corresponding unstandardized entry in the data set, summed them, and added the intercept (which I believe does not change through the unstandardization process). Is there something I'm doing wrong. Any help would be greatly appreciated!

  • $\begingroup$ Did you handle interaction variables properly? $\endgroup$
    – Aksakal
    Dec 18, 2014 at 18:50
  • $\begingroup$ I think so. Here is my data and calculations, sorry if it's a bit ugly: docs.google.com/spreadsheets/d/… $\endgroup$
    – dwm8
    Dec 18, 2014 at 19:11
  • $\begingroup$ Where did your "Intercept" term come from? The spreadsheet suggests it is the constant term in a regression involving the standardized variables--but in that case it should have been zero rather than $-2.45$. To make progress on this question we really need to see the calculations you made to standardize the data and to perform the regression. $\endgroup$
    – whuber
    Jun 16, 2015 at 21:23

1 Answer 1


Let's say a model is: $y=1+x+xz+z^3$, and $\sigma_y,\sigma_x,\sigma_z$ - standard deviations of variables. You would transform the equation like follows: $Y=\sigma_y+\frac{\sigma_y}{\sigma_x}X+\frac{\sigma_y}{\sigma_x\sigma_z}XZ+\frac{\sigma_y}{\sigma_z^3}Z^3$

  • $\begingroup$ I believe that's what I did. My calculations are in the comment link above. $\endgroup$
    – dwm8
    Dec 18, 2014 at 20:04

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