Question 10.47

10.47 Predicting income from age.

Figures 10.11 and 10.12 (pages 506 and 507) analyze data on the age and income of 5712 men between the ages of 25 and 65. Here is Minitab output predicting the income for ages 30, 40, 50, and 60 years:

Predicted Values

Fit SE Fit 95% CI 95% PI
51638 948 (49780, 53496) (−41735, 145010)
60559 637 (59311, 61807) (−32803, 153921)
69480 822 (67870, 71091) (−23888, 162848)
78401 1307 (75840, 80963) (−14988, 171790)
  1. Use the regression line from Figure 10.11 (page 506) to verify the “Fit” for age 30 years.
  2. Give a 95% confidence interval for the income of all 30-year-old men.
  3. Joseph is 30 years old. You don’t know his income, so give a 95% prediction interval based on his age alone. How useful do you think this interval is?

10.47

(a) . (b) (49780, 53496). (c) (−41735, 145010). The interval isn’t very useful; we could have guessed he was in a similar range without any statistics.