In a manufacturing process that involves a single machine, decisions must be made on whether to deliver the product to the customer immediately upon completion of the job or to hold the finished product in a batch with other jobs to be delivered at a later time. A computerized mathematical model for solving the batch scheduling problem was proposed in the Asian Journal of Industrial Engineering (Vol. 4, 2012). The performance of the model was graded using a variable called Value of Object Function (VOF). Simulation yielded the following data on VOF and run time (in seconds) for six software runs, each run with a different number of held batches.

a. Use simple linear regression to estimate the equation, y = β_{o} + β_{1}x + ∈, where y = VOF and x = number of batches.

b. Find an estimate of σ^{2} = V(∈), and σ = √V(∈).

c. Which of the two estimates, part b, can be practically interpreted? Give the interpretation.