Quote:
Originally Posted by prithagupta.nsit
How to generalize noise and during the calculation of bias and variance, how can we ignore the error e in the target function?
How to determine the predictions and prediction errors for different values of x?

The formula for decomposing the outofsample error into bias+variance+noise is discussed in Lecture 11 of the Learning From Data online course, in the part corresponding to slides 1820.
If you look at this derivation, what you refer to as the error in the target function (which I assume is the noisy part) is not ignored. Also, the formula is given for each value of
.
Of course, evaluating these terms explicitly requires knowledge of
, which is the case in biasvariance analysis in general. You can calculate them in your example since you spelled out the target. The benefit is to illustrate how these quantities change as you vary the number of data points, the level of noise, etc.