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In page 51, of ESL, it says "The mean prediction error on the test data is 0.521. In contrast, prediction using the mean training value of lpsa has a test error of 1.057 , which is called the "base error rate".

I am wondering what we mean by base error rate here and what is prediction using the mean training value?

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Consider two methods of prediction:

  1. Using the mean training value of lpsa, i.e., use the average lpsa value from the training set as your predicted value (you are not using predictor values here), and
  2. Using the linear model fitted to the training set, i.e., $E(Y|X)$ is linear in betas.

If $\bar Y$ is the mean training value of lpsa, then base error rate is $\sum(Y^*_i - Y_i)^2$. If the mean prediction error does not improve the base error rate, then it is not an adequate model.

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