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Problem 1: (30 Points) Linear Regression and Interpretation A small company that has been converting manual production to automatic equipment and robotic methods over the past seven years is interested in evaluating its effort, and is considering establishing a group incentive plan for its employees to maintain the continuous improvement momentum. The following data shows the annual contract shipments in dollars, and the number of employees during the respective year. Year 1 2 3 4 6 7 Number of employees 157 156 154 153 154 152 152 Contact shipments 573 606 648 720 765 798 848 $ x1014 5 a. Use a Linear Regression model to determine the annual rate of increase in contract shipments due to improvement in Production Methods b. if the company is considering providing 10% of the annual increase in contract shipments as the base for the incentive plan, estimate the dollar amount than an employee would have received over each of the past seven years. (Use the Regression Model gradient for this purpose)