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Subject:

Re: Centring predictors in regression and interpretation

From:

Raja, Dr. Edwin Amalraj

Date:

Mon, 2 Jul 2018 11:20:04 +0000

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 ```Kim, You can meaningfully interpret the alpha in eqn(2). That is the advantage. I am not sure centering is good when x1 & x2 are correlated( multicollinear). The interpretation of b1 or b2 is same as the interpretation from multivariate linear regression. ( ie., Suppose if you have two individual with same x2 unit but differ a unit in x1 between them there will be a difference of b1 in Yhat between them.) Regards Amalraj Raja Aberdeen -----Original Message----- From: A UK-based worldwide e-mail broadcast system mailing list [mailto:[log in to unmask]] On Behalf Of Kim Pearce Sent: 02 July 2018 11:35 To: [log in to unmask] Subject: Centring predictors in regression and interpretation Hello everyone, I wonder if someone has any views on the following. Say we have a multiple linear regression model talking the usual form: Yhat = alpha + B1*X1 * B2*X2(1) We centre X1 and X2 (i.e. subtract the mean of the X1 values from each individual value of X1 and subtract the mean of the X2 values from each individual value of X2) We arrive at the following: Yhat = alpha1+B1*(X1-X1bar) + B2*(X2-X2bar)(2) The predicted values and residuals are the same for (1) and (2) and both models (1) and (2) fit the data equally well. It is also obvious that, with a little rearrangement: alpha = alpha1 - B1*X1bar - B2*X2bar Now my question is about interpretation...in (1) we have the standard interpretation, that alpha = the average value of Y when X1 and X2 are equal to 0 and B1 = the average change in Y associated with a unit change in X1 when X2 is held constant and B2= the average change in Y associated with a unit change in X2 when X1 is held constant. I would like to ask how (2) is interpreted. It seems clear that: alpha1 = the average value of Y when X1 is at its mean value and X2 is at its mean value. But how do we interpret B1 and B2 in model (2) ? Is B1, for example, interpreted as the average change in Y associated with a unit change in X1 when X2 is at its mean value? Many thanks for your advice on this. Kind Regards, Kim Dr Kim Pearce PhD, CStat, Fellow HEA Senior Statistician FMS Graduate School Room 3.14 3rd Floor Ridley Building 1 Newcastle University Queen Victoria Road Newcastle Upon Tyne NE1 7RU Tel: (0044) (0)191 208 8142 You may leave the list at any time by sending the command SIGNOFF allstat to [log in to unmask], leaving the subject line blank. The University of Aberdeen is a charity registered in Scotland, No SC013683. Tha Oilthigh Obar Dheathain na charthannas clàraichte ann an Alba, Àir. SC013683. You may leave the list at any time by sending the command SIGNOFF allstat to [log in to unmask], leaving the subject line blank. ```