# Multiple Regression - Converting Standardized Coefficients to Unstandardized

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!

• Did you handle interaction variables properly? – Aksakal Dec 18 '14 at 18:50
• I think so. Here is my data and calculations, sorry if it's a bit ugly: docs.google.com/spreadsheets/d/… – dwm8 Dec 18 '14 at 19:11
• 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. – whuber Jun 16 '15 at 21:23

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: $Y=\sigma_y+\frac{\sigma_y}{\sigma_x}X+\frac{\sigma_y}{\sigma_x\sigma_z}XZ+\frac{\sigma_y}{\sigma_z^3}Z^3$