Johnson and Leone (Statistics and Experimental Design in Engineering and the Physical Sciences, Wiley, 1977) describe an experiment to investigate warping of copper plates. The two factors studied were the temperature and the copper content of the plates. The response variable was a measure of the amount of warping. The data are as follows:

Copper Content (%)

Temperature (∘C) 40 60 80 100 50 17, 20 16, 21 24, 22 28, 27 75 12, 9 18, 13 17, 12 27, 31 100 16, 12 18, 21 25, 23 30, 23 125 21, 17 23, 21 23, 22 29, 31

(a) Is there any indication that either factor affects the amount of warping? Is there any interaction between the factors? Use ???? = 0.05.

(b) Analyze the residuals from this experiment.

(c) Plot the average warping at each level of copper content and compare them to an appropriately scaled t distribution. Describe the differences in the effects of the different levels of copper content on warping. If low warping is desirable, what level of copper content would you specify?

(d) Suppose that temperature cannot be easily controlled in the environment in which the copper plates are to be used. Does this change your answer for part (c)?