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 function of order quantity. Then estimate the quadratic regression model to predict inventory cost as a function of order quantity and order quantity squared. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Cost = ? + ? Quantity Cost = ? + ? Quantity + ? Quanity (squared) b-1. Evaluate the linear model in terms of variable significance (α = 0.05) and adjusted R2. The adjusted R squared is ____?_____ and the explanatory variable ___is or 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 ____?_____% and the explanatory variables ___are or are not __significant
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 = ? + ? Quantity
Cost = ? + ? Quantity + ? Quanity (squared)
b-1. Evaluate the linear model in terms of variable significance (α = 0.05) and adjusted R2.
The adjusted R squared is ____?_____ and the explanatory variable ___is or 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 ____?_____% and the explanatory variables ___are or are not __significant
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