Myers, Montgomery and Anderson-Cook (Response Surface Methodology 4th edition, Wiley, New York, 2016) discuss an experiment to determine the influence of five factors:$x_{1}$ - acid bath temperature

$x_{2}$ - cascade acid concentration

$x_{3}$-water temperature

$x_{4}$-sulfide concentration

$x_{5}$-amount of chlorine bleach

on an appropriate measure of the whiteness of rayon $(y)$. The engineers conducting this experiment wish to minimize this measure. The experimental results follow.

a. Perform a thorough analysis of the results including residual plots.

b. Perform the appropriate test for lack of fit.