15.31 Consider an example in which there are two control variables x1 and x2 and a single noise variable z. The goal is to determine the levels of x1 and x2 that are robust to changes in z, i.e., levels of x1 and x2 that minimize the variance produced in the response y as z moves between −1 and +1. The variables x1 and x2 are at two levels, −1 and +1, in the experiment. The data produce the plots in Figure 15.22 above. Note that x1 and x2 interact with the noise variable z. What settings on x1 and x2 (−1 or +1 for each) result in minimum variance in y? Explain.