10.45 Compare the estimates.
Case 18 in Table 10.3 (Purdue) has a 2000 tuition of $3872 and a 2008 tuition of $7750. A predicted 2013 tuition amount based on 2008 tuition was computed in Exercise 10.43, while one based on the 2000 tuition was computed in Exercise 10.44. Compare these two estimates and explain why they differ. Use the idea of a prediction interval to interpret these results.
10.45
Using the 2008 tuition the prediction interval is (5900, 12384), using the 2000 tuition the prediction interval is (5173, 12980). The intervals are different because they are based on two different models using different predictors. That said, the intervals don’t differ that much, with the 1st interval entirely in the 2nd interval. It could be that the 2008 data better predict the 2013 tuition because such data are closer in time to 2013 and thus give a better estimate than the 2000 data.