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 divided 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   20 19   40 15   30 16   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.                                                                                        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.         For x = 30, y = -0.1807(30) + 23.1261 = 17.71 (Say 18)    For x = 40, y = -0.1807(40) + 23.1261 = 15.10 (Say 16)       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.