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.

(a) Fit a multiple linear regression model using arsenic concentration in nails as the response and age, drink use, cook use, and arsenic in the water as the regressors.

(b) Estimate σ² and the standard errors of the regression coefficients.

(c) Use the model to predict the arsenic in nails when the age is 30, the drink use is category 5, the cook use is category 5, and arsenic in the water is 0.135 ppm.

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Arsenic Water Cook Drink Use Arsenic Nails Sex Age Use 0.00087 0.119 44 5 5 0.00021 45 4 0.118 0.099 44 1 5 66 2 3 5 0.00115 0.118 37 5 0.277 45 2 5 0.358 47 1 5 5 0.00013 0.08 0.00069 38 2 4. 5 0.158 41 3 0.00039 0.31 49 4 5 0.105 72 5 5 0.073 45 2 5 0.046 0.832 53 0.0194 0.517 86 2 5 5 0.137 2.252 2 5 5 0.0214 0.851 0.269 32 5 0.0175 0.0764 44 1 5 0.433 63 2 5 5 0.141 42 0.0165 0.275 0.00012 62 1 5 0.135 36 1 5 5 0.0041 0.175