R$.$ D Snee $("$Experiment with a large number of variables", in Experiments in industry: Design,

analysis and interpretation of results, by R$.$ D$.$ Snee, L$.$ B Hare, and J$.$ B$.$ Trout, Editors, ASQC,

$1985)$ describes an experiment in which a $2^{5-1}$ design with $I=$ABCDE was used to investigate the

effects of five factors on the color of chemical product. The factors are A: solvent$/$reactant$,$ B:

catalyst$/$reactant$,$ C: temperature, D: reactant purity, E: reactant $pH.$ The responses obtained were

follows:

$e=-0,06,d=6,85$

$a=2,55$ ade $=5,50$

$b=-2,68$ bde $=3,48$

abe $=1,60$ abd $=5,75$

$c=2,06$ cde $=5,25$

ace $=1,22$ acd $=4,40$

bce $=-2,09bcd=4,32$

$abc=1,93$ abcde $=4,00$

a$.$ Prepare a normal probability plot of the effects. Which effect seem active?

b$.$ Calculate the residuals. Construct a normal probability plot of the residual and plot the residual

versus the fitted values. Comment on the plots.

c$.$ If any factors are negligible, collapse the $2^{5-1}$ design into a full factorial in the active factors.

Comment on the resulting design, and interpret the results.

answerd with minitab $!!$