A company that manufactures large electric motors has to pay attention to the noise levels produced by the motors. Measurements of noise levels were obtained for three different motor speeds. These measurements were made at two positions, in front of the machine and at the side of the machine, and also for four different types of cooling, which involve different internal fans and ventilation covers. The data obtained are given in DS 14.3.7. Show that there is a three-way interaction effect between the factors speed, cooler, and position. Considering just the data obtained at position 1, make an interaction plot of the effects of speed and cooler at that position. Make a similar interaction plot for the data obtained at position 2. Compare the two interaction plots to investigate the three-way interaction.