The lathe1 data set from the alr4 package contains the results of an experiment on characterizing the life of a drill bit in cutting steel on a lathe. Two factors were varied in the experiment, Speed and Feed rate. The response is Life, the total time until the drill bit fails, in minutes. The values of Speed and Feed in the data have been coded by computing Speed = (Actual speed in feet per minute − 900)/300 Feed = (Actual feed rate in thousandths of an inch per revolution − 13)/6 .(a) Starting with the full second-order model E(Life|Speed, Feed) = β0+β1Speed+β2Feed+β11Speed2+β22Feed 2+β12Speed∗Feed, use the Box–Cox method to show that an appropriate scale for the response is the logarithmic scale.(b) Find the two cases that are most influential in the fit of the quadratic mean function for log(Life), and explain why they are influential. Delete these points from the data, refit the quadratic mean function, and compare with the fit with all the data.