I now think that the betas would have to be within [-1,+1]. Suppose you do a
standarized regression with response Y, and have p variables (X matrix) already in.
Call the estimates for the current X matrix is beta_hat. Then by induction thru the
standard two-step least-squares betas should be [-1,+1]:
In the case p=1, beta_hat is [-1,+1]. If it's true for a certain p, then if you add
in another variable Z, beta_hat for this new varible (gamma_hat)=inv(Z'RZ)Z'RY. This
must also be [-1,+1]. When Z is added in, beta_hat for X becomes
inv(X'X)X'(Y-Z*gamma_hat), which are again [-1,+1]. Then it's clear that beta-hats
will be [-1,+1].
> > Hi, thanks for the reply. But is beta really just b/SD_b? In the standardized
> > case, the X and Y variables are centered and scaled. If Rxx is the corr matrix
> [ ... ]
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