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). 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.
ONLY ANSWER B3!!!
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). 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.
| Cost | Quantity |
| 54.4 | 844 |
| 52.1 | 503 |
| 60.2 | 300 |
| 53.8 | 869 |
| 51.7 | 525 |
| 57.1 | 1030 |
| 61.1 | 288 |
| 49.8 | 577 |
| 53.9 | 490 |
| 48.2 | 588 |
| 47.5 | 606 |
| 57.4 | 325 |
| 59.6 | 1160 |
| 58.2 | 1072 |
| 58.7 | 308 |
| 58.1 | 1140 |
| 48.4 | 627 |
| 63.4 | 214 |
| 62.5 | 207 |
| 62.5 | 1174 |
| 62.7 | 1190 |
| 61.2 | 1166 |
| 55.9 | 1067 |
| 51.3 | 655 |
| 57.1 | 384 |
| 58.2 | 367 |
| 55.8 | 927 |
| 54.9 | 890 |
| 54.7 | 495 |
| 50.2 | 780 |
| 60.8 | 1168 |
| 54.8 | 403 |
| 51.3 | 741 |
| 51.9 | 712 |
| 49.8 | 612 |
| 55.5 | 870 |
a. Estimate the linear regression model to predict inventory cost as a
Cost = 54.43 + 0.01 Quantity
Cost = 74.64 + -0.07 Quantity + 0.00 Quanity (squared)
b-1. Evaluate the linear model in terms of variable significance (α = 0.05) and adjusted R2.
The adjusted R squared is negative and the explanatory variable is not significant
b-2. Evaluate the quadratic model in terms of variable significance (α = 0.05) and adjusted R2. (Round your answer to 2 decimal places.)
The adjusted R squared is 0.86 % and the explanatory variables are significant
b3. Use the best-fitting model to predict monthly inventory cost for an order quantity of 800 units. (Do not round the estimates or intermediate calculations. Round your final answer to 2 decimal places.)
The linear or quadratic model is best providing a predicted value of ___?___ cost.
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