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Past question paper problem.[1]

I am stuck at this question. For example I have B=(X'X)^-1X'Y but I cannot go further and make He a part of the model. Any suggestions on how to proceed?

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  • $\begingroup$ Note that $H\epsilon$ is not a part of the model in the sense that you imply. You are trying to decompose the structure of $\hat{\mathbf{Y}}$, which is not exactly the same thing. $\endgroup$
    – Gumeo
    Commented Oct 12, 2015 at 9:26

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Note that you have $$ \hat{\mathbf{Y}}=\mathbf{H}\mathbf{Y} $$ Now you can replace $\mathbf{Y}$ in the equation above with $\mathbf{Y}=\mathbf{X}\beta + \epsilon$. Then you get $$ \hat{\mathbf{Y}}=\mathbf{H}(\mathbf{X}\beta + \epsilon) = \mathbf{H}\mathbf{X}\beta + \mathbf{H}\epsilon $$ Now you need to find the expression for $\mathbf{H}$, (i.e. the hat matrix) plug it in the first term and see what happens.

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You are on the right way. You have just to do some multiplications. Please check over here. enter image description here

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