If we write the regression equation like so: $y = B x + C$ But if both sides are standardized, then we have: $\dfrac{y - \bar y}{\sigma_y} = B \dfrac{x - \bar x}{\sigma_x} + C$ Now solving for $y$ by multiplying by $\sigma_y$ then adding $\bar y$: $y = B \dfrac{x - \bar x}{\sigma_x} \sigma_y + C \sigma_y + \bar y$ $y = B \dfrac{\sigma_y}{\sigma_x} x - B \dfrac{\sigma_y}{\sigma_x} \bar x + C \sigma_y + \bar y$ Therefore the metric coefficients are: $B' = B \dfrac{\sigma_y}{\sigma_x}$ $C' = B \dfrac{\sigma_y}{\sigma_x} \bar x + C \sigma_y + \bar y$ In the above notation, the multiplication operator is implied. R test code: coef(m)[1]*sd(d0$y)+mean(d0$y)- (coef(m)['x1']*sd(d0$y)*mean(d0[['x1']])/sd(d0[['x1']]) + coef(m)['x2']*sd(d0$y)*mean(d0[['x2']])/sd(d0[['x2']])) Gives 1 as desired.