Does exercise improve the human immune system? An experiment was conducted by a physiologist at the University of Florida to determine whether such a relationship exists. Thirty subjects volunteered to participate in the study. The amount of immunoglobulin known as IgG (an indicator of long-term immunity) and the maximal oxygen uptake (a measure of aerobic fitness level) were recorded for each subject. The resulting data are given in the accompanying table.

a. Construct a scattergram for the IgG–maximal oxygen uptake data.

b. Hypothesize a probabilistic model relating IgG to maximal oxygen uptake.

c. Fit the model to the data and give the least-squares prediction equation.

d. Assess the adequacy of the model.

IMMUNE Maximal Maximal Oxygen Uptake x subject Oxygen Uptake x subject igG y IgG y 1 881 34.6 16 1,660 52.5 1,290 45.0 17 2,121 69.9 3 2,147 62.3 18 1,382 38.8 4 1,909 58.9 19 1,714 50.6 5 1,282 42.5 20 1,959 69.4 1,530 44.3 21 1,158 37.4 2,067 67.9 22 965 35.1 8 1,982 58.5 23 1,456 43.0 9 1,019 35.6 24 1,273 44.1 10 1,651 49.6 25 1,418 49.8 11 752 33.0 26 1,743 54.4 12 1,687 52.0 27 1,997 68.5 13 1,782 61.4 28 2,177 69.5 14 1,529 50.2 29 1,965 63.0 15 969 34.1 30 1,264 43.2 7,