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Regression, Basic Statistics

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Read the article “Apple turns over entire inventory every five days.”1
It is not surprising that, the
success of managing inventory can lead to the success of a firm’s operational performance.
Although we have not talked about the inventory management models, we will first look at real
inventory data to identify some of the important factors that affect a firm’s inventory
performance.
The Excel file of Assignment 5 contains the quarterly information (Q1 to Q4) for more than 250
firms (mostly in the retailer and wholesaler industries, where inventory management is crucial to
firms’ performance) in the fiscal year of 20102
. Most of the variables are fairly straightforward,
except the following ones whose definitions are shown below:
Account Payable = can be approximated to be the trade credit owed to the
firm’s suppliers.
Inventory turnover = how fast a firm turns their inventory into sales
= (cost of goods sold)/(this period and last period’s
inventory average)
Gross Margin = (sales – cost of goods sold)/sales
Capital Intensity = (Gross fixed assets)/( Gross fixed assets + inventory)
Trade Credit Ratio = Account Payable/sales
You may use Excel and turn in the printout as well as the Excel file (by email). You still need to
answer all questions asked in the problem by writing on your printout. For the significance level,
you can test for ?=1%, 5%, and 10%, respectively.
Two inventory performance measures can be used here: the inventory level (Column H) or the
inventory turnover (Column L). First, we investigate the variables that are correlated with the
inventory level.
Hypothesis 1: The inventory level is positively correlated with the assets.
Hypothesis 2: The inventory level is positively correlated with the market value.
Hypothesis 3: The inventory level exhibits a seasonality pattern.
Hypothesis 4: The inventory level is generally higher in Q3 than Q1, Q2, and Q4, after
controlling for the firm size measured by assets.
Hypothesis 5: The inventory level is positively correlated with the natural logarithm of
(Account payable+1) after controlling for the firm size.
Hypothesis 6: The inventory level is positively correlated with Account payable after
controlling for the firm size.
1
https://appleinsider.com/articles/12/05/31/apple_turns_over_entire_inventory_every_five_days
2
See COMPUSTAT for data source.1. Build a regression model to test Hypothesis 1. Does the data support Hypothesis 1? Explain
why.
2. Build a regression model to test Hypothesis 2. Does the data support Hypothesis 2? Explain
why.
3. Build a regression model to jointly test Hypotheses 1 and 2. Does the data support both in
this test? Explain why. Do you observe any issues?
4. Build a regression model to test Hypothesis 3. Does the data support Hypothesis 3? Explain
why.
5. Build a regression model to test Hypothesis 4. Does the data support Hypothesis 4? Explain
why. (Hint: you can “control” an independent variable simply by adding this variable into the
regression model.)
6. Build models to test Hypotheses 5 and 6. Which model is better? Why?
Next, we investigate the variables that are correlated with the inventory turnover.
Hypothesis 7: The inventory turnover is negatively correlated with the gross margin.
Hypothesis 8: The inventory turnover is positively correlated with the capital intensity.
Hypothesis 9: The inventory turnover is negatively correlated with the trade credit to
sales ratio.
7. Build a model to jointly test Hypotheses 7-9, with and without controlling for the firm size
measured by log(asset). Comment on the results and the insights you learn from the
regression model.
also an excel data file

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