12.55 Rayon whiteness is an important factor for scientists dealing in fabric quality. Whiteness is affected by pulp quality and other processing variables. Some of the variables include acid bath temperature, ◦C (x1 );

cascade acid concentration, % (x2 ); water temperature,

◦C (x3 ); sulfide concentration, % (x4 ); amount of chlorine bleach, lb/min (x5 ); and blanket finish temperature,

◦C (x6 ). A set of data from rayon specimens is given here. The response, y, is the measure of whiteness.

y x1 x2 x3 x4 x5 x6 88.7 43 0.211 85 0.243 0.606 48 89.3 42 0.604 89 0.237 0.600 55 75.5 47 0.450 87 0.198 0.527 61 92.1 46 0.641 90 0.194 0.500 65 83.4 52 0.370 93 0.198 0.485 54 44.8 50 0.526 85 0.221 0.533 60 50.9 43 0.486 83 0.203 0.510 57 78.0 49 0.504 93 0.279 0.489 49 86.8 51 0.609 90 0.220 0.462 64 47.3 51 0.702 86 0.198 0.478 63 53.7 48 0.397 92 0.231 0.411 61 92.0 46 0.488 88 0.211 0.387 88 87.9 43 0.525 85 0.199 0.437 63 90.3 45 0.486 84 0.189 0.499 58 94.2 53 0.527 87 0.245 0.530 65 89.5 47 0.601 95 0.208 0.500 67

(a) Use the criteria MSE, Cp , and PRESS to find the

“best” model from among all subset models.

(b) Plot standardized residuals against Y and do a normal probability plot of residuals for the “best”

model. Comment.