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.
Dr Kim Pearce PhD, CStat, Fellow HEA
FMS Graduate School
Ridley Building 1
Queen Victoria Road
Newcastle Upon Tyne
Tel: (0044) (0)191 208 8142
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