figure statistical learning algorithms often require the data to be divided into training and test data if the latter is used for model selectiona third set is needed for testing the performance of the selected model we next consider concrete example that illustrates the concepts introduced so far ( which is depicted by the dashed curve in figure data points true (upolynomial regression model example (polynomial regressionin what followsit will appear that we have arbitrarily replaced the symbols xgg with uhhrespectively the reason for this switch of notation will become clear at the end of the example the data (depicted as dotsin figure are points (ui yi ) drawn from iid random points (ui yi ) nwhere the {ui are uniformly distributed on the interval ( andgiven ui ui the random variable yi has normal distribution with expectation ui and variance ` this is an example of polynomial regression model using squared-error lossthe optimal prediction function (ue[ uis thus figure training data and the optimal polynomial prediction function