TITLE: Transformation of variables in linear regression Theorem question
QUESTION [1 upvotes]: Theorem 3.8 in Greene's Econometric Analysis 7th edition on page 47 says:
In the linear regressions of $\textbf{y}$ on $\textbf{Z = XP}$ where $\textbf{P}$ is a nonsingular matrix that transforms the columns of $\textbf{X}$, the coefficients will equal $P^{-1}\textbf{b}$ where $\textbf{b}$ is the vector of coefficients in the linear regression of $\textbf{y}$ on $\textbf{X}$, and $R^2$ will be identical.
Proof:
$\textbf{d}$ = $\textbf{(Z'Z)}^{-1}\textbf{Z'y} = \textbf{(P'X'XP)}^{-1}\textbf{P'X'y}$ = $\textbf{P}^{-1}(\textbf{X'X})^{-1}\textbf{(P')}^{-1}\textbf{P'y}$ = $\textbf{P}^{-1}\textbf{b}$
I think this should be:
$\textbf{d}$ = $\textbf{(Z'Z)}^{-1}\textbf{Z'y} = \textbf{(P'X'XP)}^{-1}\textbf{P'X'y}$ = $\textbf{P}^{-1}(\textbf{X'X})^{-1}\textbf{(P')}^{-1}\textbf{P'X'y}$ = $\textbf{P}^{-1}\textbf{b}$.
Otherwise I dont know where the $\textbf{X'}$ went and the first version implies that $\textbf{b} = \textbf{X'X}^{-1}\textbf{y} $, which is false since it should be that $\textbf{b} = \textbf{(X'X)}^{-1}\textbf{X'}\textbf{y} $ for the OLS estimator of beta. 
Can anyone confirm that this is a typo (the missing X' matrix)? Or have I missed something in interpreting the original proof?

REPLY [1 votes]: It's a typo; your version is right.
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