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.

Click here for the Excel Data File

a$.$ 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.

Note: Negative values should be indicated by a minus sign. Round your answers to $2$ decimal places.

b$-1.$ Evaluate the linear model in terms of variable significance $(a=0\mathrm{.}05)$ and adjusted $R^2.$

significant.

b$-2.$ Evaluate the quadratic model in terms of variable significance $(=0\mathrm{.}05)$ and adjusted $R^2.$

Note: Round your answer to $2$ decimal places.

The adjusted $R^2$ is

$\%$ and the explanatory variables

significant.

c$.$ Use the best$-$fitting model to predict monthly inventory cost for an order quantity of $800$ units.

Note: Do not round the estimates or intermediate calculations. Round your final answer to $2$ decimal places.

The

cost$.$