Chapter 13.4, Problem 37E

A subset of data read from a graph that appeared in the paper “Decreased Brain Volume in Adults with Childhood Lead Exposure” (Public Library of Science Medicine [May 27, 2008]: e112) was used to produce the following Minitab output, where x = Mean childhood blood lead level (μg/dL) and y = Brain volume change (percentage). (See Exercise 13.21 for a more complete description of the study described in this paper.)

1. a. What is the equation of the estimated regression line?
2. b. For this data set, $n=100$, $\bar{x}=11.5$, $s_e=0.032$, and $S_{xx}=1764$. Estimate the mean brain volume change for people with a childhood blood lead level of 20 μg/dL, using a 90% confidence interval.
3. c. Construct a 90% prediction interval for brain volume change for a person with a childhood blood lead level of 20 μg/dL.
4. d. Explain the difference in interpretation of the intervals computed in Parts (b) and (c).