# Elements of Statistical Learning training set [closed]

I am trying to read the Elements of Statistical Learning Tibshirani, Hastie and Friedman, however I have a problem with understanding the expected (squared) prediction error ($$EPE$$) formula that they provide on page $$26$$:

The start they assume that the relationship between $$X$$ and $$Y$$ is linear so:

$$Y = X^TB+\epsilon$$, where $$\epsilon$$~$$N(0,\sigma^2)$$, the task is to feed the model to the training data. Now

$$EPE(x_0) = E_{x_0|y_0}[E_T(y_0-\hat y_0)^2]$$

What is the $$E_T$$? What is the reason to compute the $$EPE$$ of $$x_0$$ insted of $$\hat y_0$$?

On page $$23$$ there is written that $$T$$ is the training set, so my understanding is that it consists of some $$X$$'s. Is it right?

• I'm voting to close this question as off-topic because it is cross-posted on Mathematics here: Understanding the expectation over training set. Oct 18 '18 at 17:20
• Please do not cross post. Decide which site you want your question on & delete the other version. Oct 18 '18 at 17:21

$$E_T$$ is the expectation taken over the training set. $$\hat y_0$$ is a deterministic function of $$x_0,$$ i.e., $$\hat y_0 = \hat \beta^Tx_0.$$ The training set consists of rows of covariate values, that is correct.
• So, the training set consists of pairs (x,y)'s, input and output pairs. It was defined in the beginning of the book. Can you explain to me why only $\hat y$ is dependent on $E_T$ and not also y ? Oct 18 '18 at 14:03