FILE Inventory$\_$Cost. The inventory manager at a warehouse distributor wants to predict inventory cost $($Cost in $$)$ based on order quantity $($Quantity in units$).$ She thinks it may be a nonlinear relationship because 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$).$ The accompanying data file includes monthly inventory costs and order quantities for the past $36$ months.

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