Conclusions from the DOE Interaction Effects Plot

We make the following conclusions from the DOE interaction
effects plot.
 Important Factors: Looking for the plots that have the steepest
lines (that is, the largest effects), and noting that the legends
on each subplot give the estimated effect, we have that
 The diagonal plots are the main effects. The important
factors are: X2, X7, X1, and
X3. These four factors have effect > 60. The
remaining three factors have effect < 10.
 The offdiagonal plots are the 2factor interaction
effects. Of the 21 2factor interactions, 9 are nominally
important, but they fall into three groups of three:
 X1*X3, X4*X6,
X2*X7 (effect = 70)
 X2*X3, X4*X5,
X1*X7 (effect approximately 63.5)
 X1*X2, X5*X6,
X3*X7 (effect = 59.6)
All remaining 2factor interactions are small having an
effect < 20. A virtue of the interaction effects
matrix plot is that the confounding structure of
this Resolution IV design can be read off the plot. In
this case, the fact that X1*X3,
X4*X6, and X2*X7 all
have effect estimates identical to 70 is not a
mathematical coincidence. It is a reflection of the
fact that for this design, the three 2factor interactions
are confounded. This is also true for the other two
sets of three (X2*X3, X4*X5,
X1*X7, and X1*X2,
X5*X6, X3*X7).
 Best Settings: Reading down the diagonal plots, we select,
as before, the best settings "on the average":
(X1,X2,X3,X4,X5,X6,X7)
= (+,,+,+,+,,)
For the more important factors (X1, X2, X3,
X7), we note that the best settings (+, , +, ) are
consistent with the best settings for the 2factor interactions
(crossproducts):
X1: +, X2:  with X1*X2: 
X1: +, X3: + with X1*X3: +
X1: +, X7:  with X1*X7: 
X2: , X3: + with X2*X3: 
X2: , X7:  with X2*X7: +
X3: +, X7:  with X3*X7: 
