EXAMPLE 10.7 Predicting Log Income from Years of Education

CASE 10.1 Alexander Miller is an entrepreneur with years of education. We don’t know his log income, but we can use the data on other entrepreneurs to predict his log income.

Statistical software usually allows prediction of the response for each -value in the data and also for new values of . Here is the output from the prediction option in the Minitab regression command for when we ask for 95% intervals:

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The “Fit” entry gives the predicted log income, 10.0560. This agrees with our hand calculation within rounding error. Minitab gives both 95% intervals. You must choose which one you want. We are predicting a single response, so the prediction interval “95% PI” is the right choice. We are 95% confident that Alexander’s log income lies between 7.81924 and 12.2929. This is a wide range because the data are widely scattered about the least-squares line. The 95% confidence interval for the mean log income of all entrepreneurs with , given as “95% CI,” is much narrower.