 Suppose we predict that the value of Y is h. How should we evaluate whether this prediction is any good? Intuitively, the best we can do is to pick an h that is as close to Y as we can make it, one that would minimize the difference \(Y - h\). If we are indifferent to the direction of our errors, viewing positive errors of a particular magnitude to be no worse than negative errors of the same magnitude, and vice versa, then a common practice is to measure the performance of h by its squared difference from Y, \((Y - h)^2\). (We are not always indifferent; consider the plight of William Tell aiming at that apple.) Finally, since the values of Y vary, we might be interested in the average value of \((Y - h)^2\) by computing its expectation, \(\mathbb{E} \left[ (Y - h)^2 \right]\). This quantity is the mean squared error of h, 