 At the other extreme, suppose you aim to make your bias error zero. This occurs just when the predicted value of Y and the actual value of Y are identical, that is, \(h(x_i) = y_i\), for every \((x_i, y_i)\). Since you are presumed to not know the true function \(r(X)\) but instead only see a sample of data from the true model, \(\mathcal{D}\), it is from this sample that you will aspire to construct an estimator that generalizes to accurately predict examples outside your training data \(\mathcal{D}\). Yet if you were to fit \(h_{\mathcal{D}}(X)\) perfectly to \(\mathcal{D}\), then the variance of your estimator will be very high, since a different data set \(\mathcal{D}'\) from the true model is not, by definition, identical to \(\mathcal{D}\). How different is \(\mathcal{D}'\) to \(\mathcal{D}\)? The variation from one data set to another among all the possible data sets is the variance or irreducible noise of the data generated by the true model, which may be considerable. Therefore, in this zero-bias case your model will massively overfit your data.