Exercise 3.4

Re: Exercise 3.4
You can consider doublechecking your answer of 3.4(b). Hope this helps.

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I am not sure how to approach part (a). Are we supposed to explain why that insample estimate intuitively makes sense, or (algebraically) manipulate expressions given earlier into it?

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1. I got $y^{\prime}=y\epsilon+\epsilon^{\prime}$.
and $\hat{y}y^{\prime}=H\epsilon +\epsilon^{\prime}$. 
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You got it mostly right. Your error is assuming both term, the H term and the one without the H give an N to cancel the N in the denominator. One term gives an N and the other gives a (d+1).
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I think my problem is how I'm looking at the trace of the matrix. I'm under the impression that produces an NxN matrix with a diagonal of all values and 0 elsewhere. I come to this conclusion because the are all independent so when multiplied together the covariance of any two should be zero while the covariance of any should be the variance of . So then the trace of this matrix should have a sum along the diagonal of , shouldn't it? :clueless: 
Re: Exercise 3.4
I'm having a bit of difficulty with 3.4b. I take \hat(y)  y and multiply by (XX^T)^{1}XX^T, which ends up reducing the expression to just H\epsilon. However, then I can't use 3.3c in simplifying 3.3c, which makes me think I did something wrong. Can somebody give me a pointer?
Also, it'd be great if there was instructions somewhere about how to post in math mode. Perhaps I just missed them? 
Re: Exercise 3.4
Yes, that is right. You have to be more careful but use similar reasoning with
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is not , but that is close. Recall
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For part (c), would the result of (yhat  y) (from part b) be Ein(wlin) in terms of epsilon, since (yhat  y) is the insample error?

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y and yhat are vectors. The normsquared of (yhat  y) divided by N is the insample error.
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