# Linear project when X includes a constant

In Hamilton's text I ran across the following statement: if $$X$$ includes a constant then the linear projection of $$aY+b$$ is $$aP(Y\mid X)+b$$ where $$P(Y\mid X)$$ is the linear projection of $$y$$ on $$x$$. I’m having trouble proving this. Specifically this implies that if $$X$$ has a constant then $$E(X’)E(XX’)X=I$$ which I don’t see.

• In Hamilton text? – StatsStudent Jan 10 at 16:23
• James Hamilton Times series analysis – Alex Jan 10 at 16:24
• Do you have a page number? – StatsStudent Jan 10 at 17:17
• It’s the first section of chapter 4 discussing linear projection right before he talks about OLS estimate – Alex Jan 10 at 17:37
• It’s page 75 of Hamilton – Alex Jan 10 at 18:11