Consider Exercise 15.11. Suppose there was some experimental difficulty in making the runs. In fact, the total experiment had to be halted after only 4 runs. As a result, the abbreviated experiment is given by With only these runs, we have the signs for contrasts given by Comment. In your comments, determine whether or not the contrasts are orthogonal. Which are and which are not? Are main effects orthogonal to each other? In this abbreviated experiment (called a fractional factorial), can we study interactions independent of main effects? Is it a useful experiment if we are convinced that interactions are negligible? Explain.