Reference for ESLII Chapter 3

Here is the reference for chapter which includes explanations, and definitions for chapter 3 of The Elements of Statistical Learning.

E(Y|X) is linear in the inputs:

Linear in the inputs mean that there is a direct linear correlation between X and Y. A transformation of your input data, X can be used directly as components of Y.

What this means is that, the combinations of your parameters $\beta$ end up becoming linear. Remember that your parameters are numerical representations of the relationship between your X and Y.