To improve the quality of the output of any production process, it is necessary first to understand the capabilities of the process (Gitlow, et al., Quality Management: Tools and Methods for Improvement, 1995). In a particular manufacturing process, the useful life of a cutting tool is related to the speed at which the tool is operated. The data in the table on page 494 were derived from life tests for the two different brands of cutting tools currently used in the production process.

a. Construct a scattergram for each brand of cutting tool.

b. For each brand, the method of least squares was used to model the relationship between useful life and cutting speed. Find the least squares line for each brand on the EXCEL printouts shown on p. 495.

c. Locate SSE, s2, and s for each least squares line on the printouts.

d. For a cutting speed of 70 meters per minute, find jj f 2s for each least squares line.

e. For which brand would you feel more confident In using the least squares line to predict useful life for a given cutting speed? Explain.