Life tests of cutting tools. To improve the quality of the output of any production process, it is necessary first to understand the capabilities of the process. (For example, see Gitlow, H., Quality Management Systems: A Practical Guide, 2000.) In a particular manufacturing process, the useful life of a cutting tool is linearly related to the speed at which the tool is operated. The data in the accompanying table were derived from life tests for the two different brands of cutting tools currently used in the production process. For which brand would you feel more confident using the least squares line to predict useful life for a given cutting speed? Explain.

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Useful Life (hours) Cutting Speed (meters per minute) Brand A Brand B 30 4.5 6.0 30 3.5 6.5 30 5.2 5.0 40 5.2 6.0 40 4.0 4.5 40 2.5 5.0 50 4.4 4.5 50 2.8 4.0 50 1.0 3.7 60 4.0 3.8 60 2.0 3.0 60 1.1 70 1.1 70 .5 70 3.0 2729 2.4 1.5 2.0 1.0