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
(a) Starting with the full second-order model E(Life | Speed, Feed) = ?0 + ?1 Speed + ?2 Feed + ?11 Speed2 + ?22 Feed2 + ?12 Speed Ã- Feed use the Box-Cox method to show that an appropriate scale for the response is the logarithmic scale.
(b) State the null and alternative hypotheses for the overall F-test for this model using log(Life) as the response. Perform the test and summarize results.
(c) Explain the practical meaning of the hypothesis H0 : ?1 = ?11 = ?12 = 0 in the context of the above model.
(d) Perform a test for the hypothesis in part (c) and summarize your results.
(e) 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