#1




Exercise 3.4
I asked the question at math stack exchange,
http://math.stackexchange.com/questi...toadatasetd Can anyone explain me how it works ? 
#2




Re: Exercise 3.4
In my textbook, there is a statement mentioned on the topic of linear regression/machine learning, and a question, which is simply quoted as,
Consider a noisy target, , for generating the data, where is a noise term with zero mean and variance, independently generated for every example . The expected error of the best possible linear fit to this target is thus . For the data , denote the noise in as , and let ; assume that is invertible. By following the steps below, ***show that the expected insample error of linear regression with respect to is given by***, Below is my methodology, Book says that, Insample error vector, , can be expressed as , which is simply, hat matrix, , times, error vector, . So, I calculated insample error, , as, Since it is given by the book that, , and also is symetric, I got the following simplified expression, Here, I see that, And, also, the sum formed by , gives the following sum, I undestand that, However, I don't understand why, should be equal to zero in order to satisfy the equation, ***Can any one mind to explain me why leads to a zero result ?*** 
#3




Re: Exercise 3.4

#4




Re: Exercise 3.4
Thank you for the question and the answer.
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#5




Re: Exercise 3.4
Why the last statement is 0? I don't quite understand. Does the mean being zero imply E(e_i) and E(e_j) = 0? I find it weird if that is the case. Because that will mean E(e_i) = 0 but E(e_i^2) = \sigma^2. I understand E(e_i^2) = \sigma^2 from statistics but not the first part.
If it is not the case, then what is the reason for the last statement to be 0? 
#6




Re: Exercise 3.4
In the problem statement, I think "zero mean of the noise" is a given condition?
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#7




Re: Exercise 3.4

#8




Re: Exercise 3.4
Never mind. It's just a typo in the original post. The answer is still correct.

#9




Re: Exercise 3.4
I still don't understand why "eq1" leads to zero. I know that e_i and e_j are zero mean independent variables. However, H_ij is dependent on both e_i and e_j,, so I don't know how to prove that the sum of H_ij*e_i*e_j has an expected value of zero.
Quote:

#10




Re: Exercise 3.4
Is it because the noise is generated independently for each datapoint?

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