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okay so we've seen a variety of of different models from linear models which are rather simple and easy to work with and interpret to more complex models like nearest neighbor averaging and thin plate splines and we need to know how to decide amongst these models and so we need a way of assessing model accuracy and when is a model adequate and when may we improve it okay so suppose we have a model f hat of x that's been fit to some training data and we'll denote the training data by tr and that consists of n data pairs x i y i and remember x i r the notation now x i means the i observation and x may be a vector so it may have a bunch of components y i is is typically a single y a scalar and we want to see how well this model performs well we could compute the average squared prediction error over the training data so that means we take our y the observed y we subtract from it f hat of x we square the difference to get rid of the sign and we just average those ov

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