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

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

(b) Analyze the residuals from this experiment.

(c) Plot the average warping at each level of copper content and compare the levels using Fisher€™s LSD method. 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)?

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