Scale back linear regression coefficients in R from scaled and centered data

Question

I\'m fitting a linear model using OLS and have scaled my regressors with the function scale in R because of the different units of measure between variables. Then, I fit the

Answer 1

To de-scale or back-transform regression coefficients from a regression done with scaled predictor variable(s) and non-scaled response variable the intercept and slope should be calculated as:

A = As - Bs*Xmean/sdx
B = Bs/sdx

thus the regression is,

Y = As - Bs*Xmean/sdx + Bs/sdx * X

where

As = intercept from the scaled regression
Bs = slope from the scaled regression
Xmean = the mean of the scaled predictor variable
sdx = the standard deviation of the predictor variable

This can be adjusted if Y was also scaled but it appears you decided not to do that ultimately with your dataset.