Consider the arsenic data in Exercise 12-16. Use arsenic in nails as the response and age, drink use, and cook use as the regressors. Build regression models for the data using the following techniques:

(a) All possible regressions.

(b) Stepwise regression.

(c) Forward selection.

(d) Backward elimination.

(e) Comment on the models obtained. Which model would you prefer? Why?

(f) Now construct an indicator variable and add the person€™s sex to the list of regressors. Repeat the model building in the previous parts. Does your conclusion in part (e) change?

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.

Arsenic Drink Cook Arsenic Use Nails Age Sex Use Water 44 0.119 2 5 5 0.00087 45 2 4 0.00021 0.118 44 1 5 5 0.099 66 2 3 5 0.00115 0.118 37 1 2 5 0.277 45 2 5 5 0.358 47 1 5 5 0.00013 0.08 38 0.00069 0.158 41 3 0.00039 0.31 49 2 4 5 0.105 72 5 5 0.073 45 2 5 0.046 0.832 53 0.0194 0.517 86 2 0.137 2.252 8. 0.0214 0.851 32 2 5 0.0175 0.269 44 0.0764 0.433 63 0.141 42 1 5 0.0165 0.275 62 0.00012 5 5 0.135 36 5 0.0041 0.175 4555 uuu u n nnn nnnn n