1
$\begingroup$

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?

$\endgroup$
1
  • $\begingroup$ 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
    Oct 12, 2015 at 9:26

2 Answers 2

2
$\begingroup$

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.

$\endgroup$
1
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.