The basic process of making paper has not changed in more than 2,000 years. It involves two stages: the breaking up of raw material in water to form a suspension of individual fibers and the formation of felted sheets by spreading this suspension on a suitable porous surface, through which excess water can drain. Most paper is made from wood pulp that has been bleached with chlorine. This bleaching takes place for two reasons: to remove the last traces of a material called lignin from the raw pulp in order to make the paper stronger and to create a brilliant white writing surface. Chlorine is an ideal chemical for these tasks, but unfortunately its use in paper mills also results in a wide variety of toxic substances being released into the environment. Studies have been conducted to determine which factors in the paper process are most highly correlated with the brightness of finished paper. The article €œAdvantages of CE- HDP Bleaching for High Brightness Kraft Pulp production€ [Tappi (1964) 47: 170A€“ 175A] contains the following data on these variables: y = brightness of finished paper, x1 = hydrogen peroxide (% by weight), x2 = sodium hydroxide (% by weight), x3 = silicate (% by weight), and x4 = process temperature (in ° F). There were 31 runs in the study.

a. Use scatterplots and VIF to determine if there is evidence of collinearity in the ­explanatory variables.
b. This was a designed experiment with nonrandom explanatory variables. Was it really necessary to investigate collinearity in this type of study?
c. Use a variable selection procedure with minimum BIC as the criterion to formulate a model.
d. Use a variable selection procedure with maximum R2adj as the criterion to formulate a model.
e. Compare the results of parts (c) and (d).

Run x 1 .2 .2 L5 145 83.9 2 4 15 45 84.9 3 245 145 83.419 31 2.5 160 852 4 4 35 145 84.2 5 2 35 145 83.8 23 3 25 160 84.7 6 4 35 45 84.7 7 235 145 84.0 8 415 175 848 2433 2.5 160 84.0 9 2 2 15 17s 84.5 10 4 215 175 86.0 11 2 415 175 826 12 4 435 175 85.1 13 2 3S 5 84.529 3 3 25 160 84.9 14 4 35 175 86.0 15 2 35 175 84.0 16 3.5 175 854 17 32.5 160 829 18 5 32.5 0 855 20 3 .5 2.5 160 845 22 3 3 2.5 160 85.0 23 3 2.5 160 849 25 3 3 25 160 845 26 3 2.5 160 84.7 27 3 32.5 160 84.6 28 3 3 2.5 6 84.9 30 3 3 2.5 160 84.5 31 3 3 2.5 160 84.6