# Regression: centered vs. uncentered predictors [duplicate]

I'm trying to understand how/why centering predictors in a 2 predictor regression model would change the coefficients

Lets say I have 2 centered predictors and an interaction term, predicting a continuous Y variable that is not centered, and I have gone through the process of calculating all the regression coefficients (b0-3).

Now, the question is, if I were to uncenter the 2 predictors, how would the coefficients change (if at all)?

From my understanding, the distribution of data points would not change, nor would the regression plane. However, by centering/uncentering we change the (X1, X2, Y) value of each datapoint. I don't believe this would change the b3 interaction coefficient because the relationship between the simple slopes would not be affected. The coefficients for the intercept and the 2 predictors, however, should change because we've essentially changed the scale for each of the predictors.

Can anyone shed some light on why/how this happens? and how do you determine the magnitude/direction of these changes?

• When there is no interaction term centering just change the intercept not the other coefficients. When there is an interaction term then the coefficient will change after you centering. I think this can be proved mathematically, intuitively, you can think when you centering (add or decrease some value) the effect of one variable on the other variable is not linear then the coefficient before the centering and after centering will change. – Deep North Oct 8 '15 at 1:29
• – Scortchi - Reinstate Monica Oct 8 '15 at 15:50