An industrial engineer working for a manufacturing company has noticed a deviation in the accuracy of a machine after it runs for long periods without a cool-down cycle. This is especially concerning because the company wants to increase production (longer machine operating times without a cool-down) because of a large contract the company will start in 3- 4 months. The industrial engineer decides to monitor the machining process to determine the point (hours of operation) when the machine is producing parts that could be out of tolerance. Over the course of several months, the industrial engineer monitored the machining process to determine a relationship between hours of machine use and millimetres off-target the machine was. The data collected is shown in tabular form as shown in the table 2 below. Table 2: Off-target measured as a function of machine use. Hours of Machine 32 33 34 35 36 37 38 39 40 41 42 43 used Millimetres 1.00 1.21 | 1.25| 1.23 | 1.24 | 1.28 | 1.30 || 1.30 | 1.38 | 1.35 | 1.38 | 1.38 off-target Based on the above data, the industrial engineer would like to determine the number of hours of machine use that would produce a 2 millimetres off-target because many parts would fail quality check at that point. a) State the hypothesis b) Calculate the correlation coefficient between the hours of machine used and off-target. Describe the strength of the association between the two variables. b) Calculate the "best-fit" regression line using the least square method. c) Plot the "best-fit" regression line on a graph paper showing the point of interception and the slope of the line. d) Determine the number of hours of operation that produces 2 millimetres off-target based on a least-squares method.

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