A physiologist wants to investigate the impact of exercise on the human immune system. The physiologist theorizes that the amount of immunoglobulin y in blood (called IgG, an indicator of long-term immunity) is related to the maximal oxygen uptake x (a measure of aerobic tness level) of a person by the model y=n+1x+2x2+s To t the model, values of y and x were measured for each of 30 human subjects. The data are shown in Table 4.2. (a) Construct a scatterplot for the data. Is there evidence to support the use of a quadratic model? (b) Use the method of least squares to estimate the unknown parameters g, ,6], and ,3; in the quadratic model. AEROBIC Table 4.2 Data on immunity and fitness level of 30 subjects IgG Maximal Oxygen Uptake IgG Maximal Oxygen Uptake Subject y, milligrams x, milliliters per kilogram Subject y, milligrams x, milliliters per kilogram 881 34.6 16 1,660 52.5 N 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 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 (c) Graph the prediction equation and assess how well the model fits the data, both visually and numerically. (d) Interpret the B estimates. (e) Is the overall model useful (at a = .01) for predicting IgG