dealing in fabric quality

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, C_p, 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.

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