Consider the simple linear regression model (a) Let Xci = Xi − denote the centered input variable. Show that is a reparameterization of the preceding model. (b) Express α0 and α1 in terms of β0 and...

Consider the simple linear regression model

(a) Let X_ci
= X_i
−
denote the centered input variable. Show that

is a reparameterization of the preceding model.

(b) Express α₀
and α₁
in terms of β₀
and β₁
and vice versa.

(c) Are there any advantages in using the centered model?