8. (18 points)
Holding goods in inventory is costly because inventoried goods are susceptible to breakage and other forms of physical damage. Typically, the amount of damage (in dollars) increases with the level of inventory (expressed in dollars), but some of the damage is unrelated to the amount of inventory. The following data show a company’s inventory damage experience.
Period Inventory Level (Millions of Dollars) Damage (Thousands of Dollars) Average Age of Inventory (Days)
1 $11 $80 31
2 $15 $90 45
3 $13 $70 98
4 $10 $60 15
5 $7 $50 25
6 $9 $70 31
7 $13 $80 82
You are interested in developing a forecast for the Damage for period 9.
a) You believe that there is a cause-and-effect relationship between damage and the inventory level. You believe that the damage is a function of the inventory level. Develop and provide the linear regression equation for the damage given the inventory level using the appropriate independent and dependent variables.
b) How good is the relationship you found in a)? Based on the considerations used during class related to the strength of the relationship, would you recommend using this relationship? Explain your reasoning.
c) If the forecasted inventory level for period 9 is $15,000,000, what is the forecasted damage for Period 9?
d) Your boss believes that there might be a cause-and-effect relationship between damage and the average age of the inventory. He wonders if the damage level might be influenced by the average age of the inventory. Based on the information provided, what would you tell him? Explain your answer. If you do agree with your boss, what would you forecast the damage level for inventory with an average age of 60 days?
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