The inventory manager at a warehouse distributor wants to predict inventory cost based on order quantity. She thinks it may be a nonlinear relationship since its two primary components move in opposite directions: (1) order processing cost (costs of procurement personnel, shipping, transportation), which decreases as order quantity increases (due to fewer orders needed), and (2) holding cost (costs of capital, facility, warehouse personnel, equipment), which increases as order quantity increases (due to more inventory held). She has collected monthly inventory costs and order quantities for the past 36 months. A portion of the data is shown in the accompanying table.

Inventory Cost Order Quantity

($1,000s)..................................(units)

844...........................................54.4

503...........................................52.1

⋮...................................................⋮

870...........................................55.5

a. Create a scatterplot of inventory cost as a function of quantity. Superimpose a linear trendline and quadratic trendline.

b. Estimate the linear regression model to predict inventory cost as a function of order quantity.

Then estimate the quadratic regression model to predict inventory cost as a function of order quantity and order quantity squared.

c. Evaluate the two models in terms of significance tests (α = 0.05) and adjusted R2.