Employees at Precision Engine Parts Company produce parts according to exact design specifications. The employees are paid according to a piece-rate system, wherein the faster they work and the more parts they produce, the greater their chances for monthly bonuses. Management suspects that this method of pay may contribute to an increased number of defective parts. A specific part requires a normal, standard time of 23 minutes to produce. The quality control manager has checked the actual average times to produce this part for 10 different employees during 20 days selected at random during the past month and determined the corresponding percentage of defective parts, as follows:

Develop a linear regression model relating average production time to percentage defects to determine whether a relationship exists and the percentage of defective items that would be expected with a normal production time of 23minutes.

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Average Time (min.) 21.6 22.5 23.1 24.6 22.8 23.7 20.9 19.7 24.5 26.7 Defective (%) Average Time (min.) 20.8 18.9 21.4 23.7 23.8 24.9 19.8 19.7 21.2 20.8 Defective (%) 2.7 4.5 2.8 4.6 2.7 3.5 3.2 3.7 1.2 2.3 0.8 1.2 3.6 4.2