2. A manufacturer of cases for sound equipment requires drilling holes for metal screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also for lost production. Engineers varied the rotation speed of the drill and measured the lifetime y (thousands of holes drilled) of four bits at each of five speeds x. The data were: X: 60 60 60 60 80 80 80 80 100 100 4.6 3.8 4.9 4.5 4.7 5.8 5.5 5.4 5.0 4.5 X: 100 100 120 120 120 120 140 140 140 140 y: 3.2 4.8 4.1 4.5 4.0 13.8 3.6 3.0 13.5 3.4 Create a scatterplot of the data. Does there appear to be a relation? Does it appear to be linear? b. Is there any evident outlier? If so, does it have high influence? a Test the paired data for lack of fit at 5% level of significance. d. Fit the best regression model on Y based on X. Provide justifications. e. Optimize lifetime y by identifying the best value for speed x