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Sweater Monkey · #5 10-06-2013, 11:00 PM

I'm not sure if I'm going about part (e) correctly.

I'm under the impression that $E_{\text{test}}(\mathbf{w}_{\text{lin}})=\frac{1}{N}||X{\mathbf{w}}_{lin}-\mathbf{y'}||^2$

where $\hat{\mathbf{y}}=X{\mathbf{w}}_{lin}=X\mathbf{w}^*+H\mathbf{\epsilon}$ as derived earlier
and $\mathbf{y'}=\mathbf{w}^{*T}\mathbf{x}+\mathbf{\epsilon'}=X\mathbf{w}^*+\mathbf{\epsilon'}$

This lead me to $\frac{1}{N}||H\mathbf{\epsilon}-\mathbf{\epsilon'}||^2$

I carried out the expansion of this expression and then simplified into the relevant terms but my final answer is $\sigma^2(1+(d+1))$ because the N term cancels out.

Am I starting out correctly up until this expansion or is my thought process off from the start? And if I am heading in the right direction is there any obvious reason that I may be expanding the expression incorrectly? Any help would be greatly appreciated.