Consider the attached data set smooth.txt . It is from an experiment that was carried out to examine the effects of five different lubricants and of three different lathes on the surface smoothness of a finished article. The three lathes will be used regularly and are of particular interest. The five lubricants were selected from a large number of possible choices and aren’t of particular interest. Two observations were made on the surface roughness (determined optically) for each of the fifteen possible combinations of lathe and lubricant. The 30 material samples were randomly assigned to the combinations and the combinations were run in a random order The smoother the surface, the lower the reading.

1) Write the model equation corresponding to this problem.

2) Explain why each of factorial, balanced, with replications, and fixed effects seem to hold or not for this example. Justify your answer.

3) From the ANOVA table, state the hypothesis tested by the Lathe, Lube, and Lathe*Lube p-values, and give your conclusion in terms of the problem at the a=0.05 level.

4) Make an interaction plot for thie data. What about the ANOVA table doesn’t seem to match what you would expect based on your answer to (3).

5) From the output of the summary function, which treatment combination is R using as the baseline? I will send you the data after