Consider the regression model fit to the arsenic data in Exercise 12-16. Use arsenic in nails as the response and age, drink use, and cook use as the regressors.

(a) Calculate 99% confidence intervals on each regression coefficient.

(b) Calculate a 99% confidence interval on mean arsenic concentration in nails when age = 30, drink use = 4, and cook use = 4.

(c) Calculate a prediction interval on arsenic concentration in nails for the same values of the regressors used in part (b).

Exercise 12-16

An article in Cancer Epidemiology, Biomarkers and Prevention (1996, Vol. 5, pp. 849–852) reported on a pilot study to assess the use of toenail arsenic concentrations as an indicator of ingestion of arsenic-containing water. Twenty-one participants were interviewed regarding use of their private (unregulated) wells for drinking and cooking, and each provided a sample of water and toenail clippings. Table E12-8 showed the data of age (years), sex of person (1 = male, 2 = female), proportion of times household well used for drinking (1≤ 1 / 4, 2 = 1 / 4, 3 = 1 / 2, 4 = 3 / 4, 5 ≥ 3 / 4), proportion of times household well used for cooking (1≤ 1/4,

2 = 1/4, 3 = 1/2, 4 = 3/4, 5 ≥ 3/4), arsenic in water (ppm), and arsenic in toenails (ppm) respectively.