Problem 2 (20) In a manufacturing process, the assembly line speed (feet per minute) was thought to affect the number of defective parts found during the inspection process. To test this theory, management devised a situation where the same batch of parts was inspected visually at a variety of line speeds. The following data were collected: Line Speed (fpm) Number of defective parts found 20 21 22 19 40 15 30 18 60 12 40 17 50 15 50 14 a. Develop a model that relates line speed to the number of defective parts found. Show your output below for your selected model. Explain why and how you chose that model. (5 points) b. Using the model you developed in part (a), forecast the number of defective parts found for line speeds of 30 and 40 feet per minute. Show how you arrived at your forecast. (5 points) c. Based on the forecasting model you developed in part (a), explain the relationship between line speed and number of defectives found. Your explanation should include discussion of the nature of the relationship (e.g. direct or inverse, the strength of association between the variables, and how well (or poorly) the line speed impacts the variation in number of defective parts produced by the assembly process. Support your explanation with appropriate numeric measures. Opinions, suppositions, and unfounded explanations are to be avoided. (10 points)